Crexielle GRE
37. Which of the following has the least value? A. 0.27 B. 1/4 C. 3/8 D. 2/11 E. 11%
37. E
Mike and Norm walked a total of 38 miles last week. If Norm had walked 2 fewer miles than he did, then he would have walked one-third of the distance that Mike walked. How many miles did Norm walk last week? A. 10 B. 11 C. 12 D. 13 E. 14
38 = M + N or M = 38 - N or N = 38 - M N - 2 = .333M 38 - M - 2 = .333M 36 - M = .333M 36/1.333 = 1.333M/1.333 27 = M N = 38 - M N = 38 - 27 N = 11 B. 11 Yea! I got this one right.
What is the difference in odds between the Exacta and Trifecta in a 20 horse race?
380:1 versus 6,840:1
An integer is divisible by 9 if its digits add up to a multiple of:
9
10. If n > 0 Column A: 24/25 of n Column B: 95% of n
Answer Key 10. A
10. Which of the following fractions is the equivalent of 0.5% A. 1/20 B. 1/200 C. 1/2000 D. 1/5 E. 1/500
Answer Key 10. B
11. Which of these numbers is a factor of 21 A. 2 B. 5 C. 7 D. 42 E. 44
Answer Key 11. C
13. 1.75 x 10^5= A. 175,000 B. 17,500 C. 1,750 D. 0.00175 E. 0.000175
Answer Key 13. A
14. You have orders to give a patient 20 mg of a certain medication. The medication is stored 4 mg per 5-mL dose. How many milliliters will need to be given? A. 15 mL B. 20 mL C. 25 mL D. 30 mL E. 35 mL
Answer Key 14. C
16. One slice of bread is 80 calorie. Approximately how many calories are in 2 1⁄2 slices of bread? A. 140 calories B. 200 calories C. 220 calories D. 240 calories E. 260 calories
Answer Key 16. B
17. 25% of 400 = A. 100 B. 200 C. 800 D. 10,000 E. 12,000
Answer Key 17. A
17. John pays $650 in property tax. What is the assessed value of his property if property taxes are 1.2% of assessed value? A. $28,800.27 B. $41,328.90 C. $43,768.99 D. $54,166.67 E. $64,333.39
Answer Key 17. D
18. If the value of x and y in the fraction XZ/Y are both tripled, how does the value of the fraction change? A. increases by half B. decreases by half C. triples D. doubles E. remains the same
Answer Key 18. E
19. Which of the following percentages is equal to 0.45? A. 0.045% B. 0.45% C. 4.5% D. 45% E. 0.0045%
Answer Key 19. D
20. 85% of what number is 136? A. 160 B. 170 C. 180 D. 190 E. 220
Answer Key 20. A
3. Which of the following is not a fraction equivalent to 3/4? A. 6/8 B. 9/12 C. 12/18 D. 21/28 E. 27/36
Answer Key 3. C
3. Divide x^5 by x^2 A. x^7 B. x^4 C. x^10 D. x^3 E. x^2.5
Answer Key 3. D
35. A salesman sold 20 cars in the month of July, and 40 cars the month of August. What is the percent increase in the number of cars the salesman sold? A. 50% B. 100% C. 150% D. 200% E. 250%
Answer Key 35. B
37. If 8x + 5 = 21, then 3 x + 4 = A. 2 B. 5 C. 10 D. 16 E. 17
Answer Key 37. C
38. If 3x + 5x = -8, then x + 1 = A. -2 B. -1 C. 0 D. 1 E. 2
Answer Key 38. C
4. Solve: 0.25 + 0.65 A. 1/2 B. 9/10 C. 4/7 D. 2/9 E. 5/16
Answer Key 4. B
4. Find 8.23 x 109 A. 0.00000000823 B. 0.000000823 C. 8.23 D. 8230000000 E. 823000000000
Answer Key 4. D
6. What number is 5% of 2000? A. 50 B. 100 C. 150 D. 200 E. 250
Answer Key 6. B
7. What is the next number in the sequence? 6, 12, 24, 48, ___ A. 72 B. 96 C. 108 D. 112 E. 124
Answer Key 7. B
8. There are 8 ounces in a 1/2 pound. How many ounces are in 7 3/4 lbs? A. 12 ounces B. 86 ounces C. 119 ounces D. 124 ounces E. 138 ounces
Answer Key 8. D
18. You purchase a car making a down payment of $3,000 and 6 monthly payments of $225. How much have you paid so far for the car? A. $3225 B. $4350 C. $5375 D. $6550 E. $6398
B
3. Which of the following values is NOT equal to 34(58 + 9)? A. 34 x 67 B. 58(34+9) C. 34 x 58 + 34 x 9 D. 1,972 + 306 E. (9 + 58) 34
B & D
The manager of a concert venue noted that for every 100 admission tickets sold, the venue sells 12 compact discs at $15.00 each, 8 t-shirts at $20.00 each, and 5 concert posters at $12.00 each. What is the average (arithmetic mean) of these merchandise sales per ticket sold? $3.00 $3.76 $3.81 $4.00 $4.40
D
Frankie and Georgia are driving along the same road. If Frankie is driving at a speed of 52 miles per hour and Georgia is 30 miles behind him, driving at a speed of 58 miles per hour, how long will it take before Georgia catches up with Frankie?
Georgia is driving 6 miles per hour faster, so she's catching up at rate. To cover 30 miles at 6 miles per hour, it will take: 30/6 = 5 hours.
If N + K = M, what is the value of K? 1) N = 10 2) M + 10 = N
Given: N + K = M K = M - N The first thing we would like to find out is: K = ? The second is to ask what is M - N = ? (Note that N + K = M is given in the problem, while K = M - N is the same thing just reversed). 1) n = 10 Not the answer, since it doesn't help you establish the value of K. 2) However, when you look at M + 10 = N and realize that it is: M - N = -10 Since K is -10, the answer to the problem is B.
Probability of 2 heads in tossing 2 coins: Event: HH Desired outcome: HH Number of desired outcomes: 1 Total Possible outcomes: HH, TH, HT, TT Number of total possible outcomes: 4
Pr(HH) = 1/4
One third of data sufficiency questions are yes/no.
Some DS questions are a range of values.
#42, Page 278 Kaplan Textbook Did Jon complete a journey of 40 kilometers in less time than it took Ann to complete the same journey? 1. Jon traveled at an average speed of 30 km per hour for the first 10 km and then at an average speed of 15 kmH for the rest of the journey. 2. Ann traveled at an average speed of 20 kmH for the entire journey.
c.
even x even =
even
If x + 1/3 = 5/x-1, what is the value of x?
x + 1/3 = 5/x-1 (x + 1)(x - 1) = 3 x 5 Note that the left side is the difference of two squares, so: (x^2 - 1) = 15 x^2 = 16 Now take the square root of both sides and: x = 4 or -4
x + y = -1 Quantity A: x Quantity B: y
you cannot determine
Test day tip: Sometimes it is easier to subtract the probability of an event NOT occurring from 1, rather than to directly find the probability of the event occurring.
...
1% is expressed as a decimal as . . .
.01
34. What is the cost in dollars to steam clean a room W yards wide and L yards long it the steam cleaners charge 10 cents per square foot? A. 0.9WL B. 0.3WL C. 0.1WL D. 9WL E. 3WL
34. A
A train travels at an average rate of 35 miles per hour for 2.5 hours. What distance does it cover in that time?
35 = d/2:5 d = 35(2.5) = 87:5
35. Find 8.23 x 10^9 A. 0.00000000823 B. 0.000000823 C. 8.23 D. 8230000000 E. 823000000000
35. D
The factors, or divisors, of an integer are the positive integers by which it is evenly divisible (leaving no remainder). What are the factors of 36?
36 has nine factors: 1, 2, 3, 4, 6, 9, 12, 18, and 36. We can group these factors in pairs: (1)(36) 5 (2)(18) 5 (3)(12) 5 (4)(9) 5 (6)(6)
36. During a 5-day festival, the number of visitors tripled each day. If the festival opened on a Thursday with 345 visitors, what was the attendance on that Sunday? A. 345 B. 1,035 C. 1,725 D. 3,105 E. 9,315
36. E
Which of the following could be the units digit of 57^n when n is a positive interger?
7^2 = 49 7^3 = 343 7^4 = 2401 7^5 = 16,807 7^6 = 117,649 7^7 = 823,543 7^8 = 5,764,801 7^9 = 40,353,607 So, the only ending digits (the "units digit") that you get is 1, 3, 7, or 9
A fair coin is tossed 5 times. What is the probability that it lands heads up at least twice?
A coin has two sides, so there is a 50% or 1/2% chance it will land on either side on a toss. (I have a note that "32" is the number used when doing coin questions, and "36" for dice questions). 25 or (1/2 * 1/2 * 1/2 * 1/2 * 1/2) = 1/32 P (2 or more landings on heads) = 1 - (possibility 0 heads + possibility of 1 heads) = 1 - [1/32 + 5/32] = 32/32 - 6/32 = 26/32 = 13/16
29. A men's basketball team won 24 games and lost 32. What is the ratio of games lost to the number of games played? A. 32:24 B. 4:3 C. 3:4 D. 4:7 E. 3:7
Answer Key 29. D Remember, they played 56 games. 32/56 = 4/7
3. If r = 5 z then 15 z = 3 y, then r = A. y B. 2 y C. 5 y D. 10 y E. 15 y
Answer Key 3. A
8. 41% equals: A. 4.1 B. .41 C. .041 D. .0041 E. .00415
Answer Key 8. B
1. Two angles of a triangle each measure 70°. What is the measure of the third angle in degrees? A. 40° B. 80° C. 100° D. 120° E. 140°
Answer Key 1. A
1. What will it cost to carpet a room with indoor/outdoor carpet if the room is 10 feet wide and 12 feet long? The carpet costs 12.51 per square yard. A. $166.80 B. $175.90 C. $184.30 D. $189.90 E. $192.20
Answer Key 1. A
1. Round 907.457 to the nearest tens place. A. 908.0 B. 910 C. 907.5 D. 900 E. 907.46
Answer Key 1. B
1. Add 0.98 + 45.102 + 32.3333 + 31 + 0.00009 A. 368.573 B. 210.536299 C. 109.41539 D. 99.9975 E. 80.8769543
Answer Key 1. C
1. Describe the following sequence in mathematical terms. 144, 72, 36, 18, 9 A. Descending arithmetic sequence B. Ascending arithmetic sequence C. Descending geometric sequence D. Ascending geometric sequence E. Miscellaneous sequence
Answer Key 1. C
1. How long will Lucy have to wait before for her $2,500 invested at 6% earns $600 in simple interest? A. 2 years B. 3 years C. 4 years D. 5 years E. 6 years
Answer Key 1. C
1. If a discount of 20% off the retail price of a desk saves Mark $45, how much did he pay for the desk? A. $145 B. $160 C. $180 D. $210 E. $215
Answer Key 1. C
1. x + y = 15 x - y = 24 Column A: (y) Column B: (-5) A. if the quantity in Column A is greater B. if the quantity in Column B is greater C. if the two quantities are equal D. if it is impossible to determine which quantity is greater
Answer Key 1.A
1. 104 is not equal to which of the following? A. 100,000 B. 0.1 x 10^5 C. 10 x 10 x 10 x 10 D. 10^2 x 10^2 E. 10,000
Answer Key 1.A
10. Over the course of a week, Fred spent $28.49 on lunch. What was the average cost per day? A. $4.07 B. $3.57 C. $6.51 D. $2.93 E. $5.41
Answer Key 10. A
10. What is the cost in dollars to steam clean a room W yards wide and L yards long it the steam cleaners charge 10 cents per square foot? A. 0.9WL B. 0.3WL C. 0.1WL D. 9WL E. 3WL
Answer Key 10. A
10. How long will Lucy have to wait before her $2,500 invested at 6% earns $600 in simple interest? A. 2 years B. 3 years C. 4 years D. 5 years E. 6 years
Answer Key 10. C
10. Divide x^5 by x^2 A. x25 B. x10 C. x7 D. x3 E. x2.5
Answer Key 10. D
10. Of the following units, which would be most likely to measure the amount of sugar needed in a recipe for 2 dozen cookies A. degrees Celsius B. milliliters C. quarts D. kilograms E. cups
Answer Key 10. E
11. A roast was cooked at 325° F in the oven for 4 hours. The internal temperature rose from 32° F to 145° F. What was the average rise in temperature per hour? A. 20.2° F/hr B. 28.25° F/hr C. 32.03° F/hr D. 37° F/hr E. 37.29° F/hr
Answer Key 11. B
11. Which of the following numbers could be described in the following way: an integer that is a natural, rational and whole number? A. 0 B. 1 C. 2.33 D. -3 E. none of the above
Answer Key 11. B
11. Which of the following fractions are correctly placed from the least in value to the greatest in value? A. 1/4, 17/25, 3/4, 11/16 B. 17/25, 1/4, 11/16, 3/4 C. 1/4, 17/25, 11/16, 3/4 D. 1/4, 17/25, 3/4, 11/16 E. 3/4, 17/25, 11/16, 1/4
Answer Key 11. C
12. A room measures 11 ft x 12 ft x 9 ft. What is the volume? A. 1188 ft3 B. 32 ft3 C. 120 ft3 D. 1300 ft3 E. 1350 ft3
Answer Key 12. A
12. A computer is on sale for $1600, which is a 20% discount off the regular price. What is the regular price? A. $1800 B. $1900 C. $2000 D. $2100 E. $2200
Answer Key 12. C
12. Find the mode of the following list of numbers: 2, 4, 6, 4, 8, 2, 9, 4, 3, 8 A. 2 B. 3 C. 4 D. 5 E. 6
Answer Key 12. C
13. A vitamin's expiration date has passed. It was supposed to contain 500 mg of Calcium, but it has lost 325 mg of Calcium. How many mg of Calcium are left? A. 135 mg B. 175 mg C. 185 mg D. 200 mg E. 220 mg
Answer Key 13. B
13. A car dealer sells a SUV for $39,000, which represents a 25% markup over the dealer's cost. What was the cost of the SUV to the dealer? A. $29,250 B. $31,200 C. $32,500 D. $33,800 E. $33,999
Answer Key 13. B $31,200 is the dealer cost x is the cost of the car x + 0.25x = $39,000 1.25x = $39,000 $39,000/1.25 x = $31,200
13. In the fraction 3/x, x may not be substituted by which of the following sets? A. {1, 2, 4} B. {-2,-3,-4} C. {1, 3, 7} D. {0, 10, 20} E. {1.8, 4.3}
Answer Key 13. D
13. You need 4/5 cups of water for a recipe. You accidentally put 1/3 cups into the mixing bowl with the dry ingredients. How much more water in cups do you need to add? A. 1/3 cups B. 2/3 cups C. 1/15 cups D. 7/15 cups E. 7/16 cups
Answer Key 13. D
14. 3⁄4 - 1⁄2 = A. 1⁄4 B. 1/3 C. 1⁄2 D. 2/3 E. 2/5
Answer Key 14. A
14. Sarah needs to make a cake and some cookies. The cake requires 3/8 cup of sugar and the cookies require 3/5 cup of sugar. Sarah has 15/16 cups of sugar. Does she have enough sugar, or how much more does she need? A. She has enough sugar. B. She needs 1/8 of a cup of sugar. C. She needs 3/80 of a cup of sugar. D. She needs 4/19 of a cup of sugar. E. She needs 1/9 of a cup of sugar.
Answer Key 14. C
14. The electric company charges 3 cents per kilowatt-hour. George used 2800 kilowatt-hours in April, 3200 kilowatt- hours in May, and 3600 kilowatt-hours in June. What was his average cost of electricity for the 3 months? A. $72 B. $88 C. $96 D. $102 E. $113
Answer Key 14. C
14. After having to pay increased income taxes this year, Edmond has to sell his BMW. Edmond bought the car for $49,000, but he sold it for a 20% loss. What did Edmond sell the car for? A. $24,200 B. $28,900 C. $35,600 D. $37,300 E. $39,200
Answer Key 14. E
15. At a company fish fry, 1/2 in attendance are employees. Employees' spouses are 1/3 of the attendance. What is the percentage of the people in attendance who are not employees or employee spouses? A. 10.5% B. 16.7% C. 25% D. 32.3% E. 38%
Answer Key 15. B
15. At a company fish fry, 1⁄2 in attendance are employees. Employees' spouses are 1/3 of the attendance. What is the percentage of the people in attendance who are not employees or employee spouses? A. 10.5% B. 16.7% C. 25% D. 32.3% E. 38%
Answer Key 15. B
15. 7 1/2 - 5 3/8 = A. 1 1/2 B. 1 2/3 C. 2 1/8 D. 3 1/4 E. 3
Answer Key 15. C
15. You need exactly a 1680 ft3 aquarium for your fish. At the pet store you see four choices of aquariums, but the volume is not listed. The length, width, and height are listed on the box. Which of the following aquariums would fit your needs? A. 12 ft x 12 ft x 12 ft B. 13 ft x 15 ft x 16 ft C. 14 ft x 20 ft x 6 ft D. 15 ft x 16 ft x 12 ft E. 15 ft x 12 ft x 12 ft
Answer Key 15. C
16. If 6 is 24% of a number, what is 40% of the same number? A. 8 B. 10 C. 15 D. 20 E. 25
Answer Key 16. B
16. In a college, some courses contribute more towards an overall GPA than other courses. For example, a science class is worth 4 points; mathematics is worth 3 points; History is worth 2 points; and English is worth 3 points. The values of the grade letters are as follows, A= 4, B=3, C=2, D=1, F=0. What is the GPA of a student who made a "C" in Trigonometry, a "B" in American History, an "A" in Botany, and a "B" in Microbiology? A. 2.59 B. 2.86 C. 3.08 D. 3.33 E. 3.67
Answer Key 16. C
17. There are 8 ounces in a 1⁄2 pound. How many ounces are in 7 3/4 lbs? A. 12 ounces B. 86 ounces C. 119 ounces D. 124 ounces E. 138 ounces
Answer Key 17. D
18. A lamp is marked with a sale price of $23.80, which is 15% off of the regular price. What is the regular price? A. $26 B. $28 C. $30 D. $32 E. $43
Answer Key 18. B
19. A mattress store sells their stock for 15% off of retail. If someone pays cash, they take an additional 10% off of the discounted price. If a mattress's retail price is $750, what is the price after the store discount and the cash discount? A. $550.75 B. $562.50 C. $573.75 D. $637.50 E. $675.00
Answer Key 19. C
19. What is the next number in the following pattern? 1, 1/2, 1/4, 1/8, ___ A. 1/10 B. 1/12 C. 1/14 D. 1/15 E. 1/16
Answer Key 19. E
2. A customer pays $1,100 in state taxes on a newly purchased car. What is the value of the car if state taxes are 8.9% of the value? A. $9.765.45 B. $10,876.90 C. $12,359.55 D. $14,345.48 E. $15,745.45
Answer Key 2. C
2. At a certain high school, the respective weights for the following subjects are: Mathematics 3, English 3, History 2, Science 2 and Art 1. What is a student's average whose marks were the following: Geometry 89, American Literature 92, American History 94, Biology 81, and Sculpture 85? A. 85.7 B. 87.8 C. 88.9 D. 89.4 E. 90.2
Answer Key 2. C
2. Find 0.12 ÷ 1 A. 12 B. 1.2 C. .12 D. .012 E. .0012
Answer Key 2. C
2. Multiply 10^4 by 10^2 A. 10^8 B. 10^2 C. 10^6 D. 10^-2 E. 10^3
Answer Key 2. C
2. If Jack needs 2 1 ⁄ 2 pints of cream to make a dessert. How many pints will he need to make 3 desserts? A. 2 1 ⁄ 2 B. 3 C. 4 D. 5 E. 7 1
Answer Key 2. E
2. Which of the following is not a whole number followed by its square? A. 1, 1 B. 6, 36 C. 8, 64 D. 10, 100 E. 11, 144
Answer Key 2. E
2. If the perimeter of a rectangular house is 44 yards, and the length is 36 feet, what is the width of the house? A. 10 yards B. 18 yards C. 28 feet D. 32 feet E. 36 yards
Answer Key 2.A
20. Of the following units which would be more likely used to measure the amount of water in a bathtub? A. kilograms B. liters C. milliliters D. centigrams E. volts
Answer Key 20. B
20. Which of these percentages equals 1.25? A. 0.125% B. 12.5% C. 125% D. 1250% E. 1250.5%
Answer Key 20. C
22. Which of the following is a true statement? A. The product of two negative numbers is negative. B. The product of one negative and one positive number is positive. C. When dividing a positive number by a negative number, the results are negative. D. When dividing a negative number by a positive number, the results are positive. E. When dividing a negative number by a negative number the results are negative.
Answer Key 22. C
25. The fine for a driver riding in the carpool lane without any passengers is $133. A driver is issued a bench warrant for $2,294.25, which includes a 15% fee for late charges and court costs. How many tickets has the driver not paid? A. 10 B. 12 C. 13 D. 14 E. 15
Answer Key 25. E
26. Brett started a race at 6:30 A.M., and he did not cross the finish line until 1:05 P.M. How long did it take for Brett to finish the race? A. 6 hours and 15 minutes B. 6 hours and 35 minutes C. 7 hours and 5 minutes D. 7 hours and 15 minutes E. 7 hours and 35 minutes
Answer Key 26. B
28. Multiply 2.345 x 0.023: A. 0.53935 B. 0.053935 C. 0.0053935 D. 10.195652 E. 101.95652
Answer Key 28. B
3. (9 ÷ 3) x (8 ÷ 4) = A. 1 B. 6 C. 72 D. 576 E. 752
Answer Key 3. B
3. A discount store takes 50% off of the retail price of a desk. For the store's holiday sale, it takes an additional 20% off of all furniture. The desk's retail price was $320. How much is the desk on sale for during the holiday sale? A. $107 B. $114 C. $128 D. $136 E. $192
Answer Key 3. C
3. A nurse has to record her temperatures in Celsius but her thermometer reads Fahrenheit. A patient's temperature is 100.7° F. What is the temperature in °C? A. 32° C B. 36.5° C C. 38.2° C D. 213.3° C E. 223.7° C
Answer Key 3. C
3. Ginger over the course of an average work-week wanted to see how much she spent on lunch daily. On Monday and Thursday, she spent $5.43 total. On Tuesday and Wednesday, she spent $3.54 on each day. On Friday, she spent $7.89 on lunch. What was her average daily cost? A. $3.19 B. $3.75 C. $3.90 D. $4.08 E. $4.23
Answer Key 3. D
3. How many years does Steven need to invest his $3,000 at 7% to earn $210 in simple interest? A. 1 year B. 2 years C. 3 years D. 4 years E. 5 years
Answer Key 3.A
30. Which of the following choices is equivalent to 5/6? A. 5/12 B. 10/6 C. 20/30 D. 15/24 E. 15/18
Answer Key 30. E
31. Jill earns $120 for 8 hours of work. At the same pay rate, how much will she earn for 15 hours of work? A. $180 B. $225 C. $245 D. $280 E. $310
Answer Key 31. B
31. Of the following fractions, which is less than 2/3? A. 7/8 B. 5/6 C. 3/4 D. 3/5 E. 5/7
Answer Key 31. D
33. Sue receives a base salary of $90 weekly plus a 12% commission on all sales. Sue had $3,000 in sales this week. How much did she make total? A. $375 B. $450 C. $480 D. $510 E. $525
Answer Key 33. B
34. If the perimeter of a rectangular house is 25 1/3 yards, and the length is 22 feet. What is the width? A. 16 feet B. 35 feet C. 37 feet D. 40 feet E. 42 feet
Answer Key 34. A
35. Jimmy made a 15% profit on the sale of a custom designed boat, and the original cost of the boat was $15,000. The boat sold for how much? A. $17,250.00 B. $16,540.44 C. $16,230.34 D. $15,980.55 E. $15,870.88
Answer Key 35. A
36. A recent study showed that an increase in body weight by 10 kilograms resulted in a 0.15% increase in heart disease. What fraction is equal to 0.15%? A. 3/2000 B. 2/750 C. 7/4000 D. 5/3462 E. 1/500
Answer Key 36. A
36. If one side of a square is 5 units, what is the area of the square? A. 10 B. 15 C. 20 D. 25 E. 30
Answer Key 36. D
37. 6.334 x 10^4 = A. 0.0006334 B. 0.06334 C. 6334 D. 63340 E. 633400a
Answer Key 37. D
38. In triangle ABC, AB = BC and (C's measure is 65°). What is the measure of angle B? A. 40° B. 50° C. 60° D. 65° E. 75°
Answer Key 38. B
39. Two angles in a triangle equal 120°. What is the measure of the third angle? A. 60° B. 70° C. 80° D. 90° E. 120°
Answer Key 39. A
39. If the average arithmetic mean of 8, 12, 15, 21, x and 11 is 17 then what is x? A. 3 B. 15 C. 17 D. 35 E. 42
Answer Key 39. D
4. Sabrina's boss states that she will increase Sabrina's salary from $12,000 to $14,000 per year if she enrolls in business courses at a local community college. What percent increase in salary will result from Sabrina taking the business courses? A. 15% B. 16.7% C. 17.2% D. 85% E. 117%
Answer Key 4. B
4. What is 1230.932567 rounded to the nearest hundredths place? A. 1200 B. 1230.9326 C. 1230.93 D. 1230 E. 1230.933
Answer Key 4. C
4. What is 35% of a number if 12 is 15% of a number? A. 5 B. 12 C. 28 D. 33 E. 62
Answer Key 4. C
4. 6 x 0 x 5 A. 30 B. 11 C. 25 D. 0 E. 27
Answer Key 4. D
4. Art realized that he had 2 more quarters than he had originally thought in his pocket. If all of the change in his pocket is quarters and it totals to $8.75, how many quarters did he originally think were in his pocket? A. 27 B. 29 C. 31 D. 33 E. 35
Answer Key 4. D
4. What is the volume of a cube whose width is 5 inches? A. 15 cubic inches B. 25 cubic inches C. 64 cubic inches D. 100 cubic inches E. 125 cubic inches
Answer Key 4. E
Column A - The area of a circle with the radius of 3 Column B - The area of a semi-circle with the radius of 4 A. if the quantity in Column A is greater B. if the quantity in Column B is greater C. if the two quantities are equal D. if it is impossible to determine which quantity is greater
Answer Key 4.A
40. Which of the following would be an appropriate unit to measure sugar for a cookie recipe? A. liters B. cups C. quarts D. kilograms E. pounds
Answer Key 40. B
5. 83,000 equals: A. 83.0 x 10^4 B. 8.3 x 10^4 C. 8.3 x 10^3 D. 83.0 x 10^5 E. 83.0 x 10^2
Answer Key 5. B
5. A computer is on sale for $1600, which is a 20% discount off the regular price. What is the regular price? A. $1800 B. $1900 C. $2000 D. $2100 E. $2200
Answer Key 5. C
5. There are 12 more apples than oranges in a basket of 36 apples and oranges. How many apples are in the basket? A. 12 B. 15 C. 24 D. 28 E. 36
Answer Key 5. C
5. Which of the following statements is false? A. In the fraction 1⁄2, one is the numerator. B. When 4.89 is rounded to the ones place, the answer is 5. C. Ten thousandths place is located 5 places to the right of the decimal D. 7/6 is described as an improper fraction.
Answer Key 5. C
5. Sally has three pieces of material. The first piece is 1 yd. 2 ft. 6 in. long, the second piece is 2 yd. 1 ft. 5 in long, and the third piece is 4 yd. 2ft. 8in long. How much material does Sally have? A. 7 yd. 1 ft. 8 in. B. 8 yd. 4 ft. 4 in. C. 8 yd. 11 in. D. 9 yd. 7 in. E. 10 yd.
Answer Key 5. D
5. Sarah volunteered from 9:27 A.M. until 12:45 P.M. Jan volunteered from 9:15 A.M. until 12:32 P.M. Column A - The amount of time Sarah volunteered. Column B - The amount of time Jan volunteered. A. if the quantity in Column A is greater B. if the quantity in Column B is greater C. if the two quantities are equal D. if it is impossible to determine which quantity is greater
Answer Key 5.A
5. Subtract the following numbers rounded to the nearest tenths place. 134.679 - 45.548 - 67.8807 A. 21.3 B. 21.25 C. -58.97 D. -59.0 E. 1
Answer Key 5.A
6. 0.00875 equals: A. 8.75 x 10^-2 B. 8.75 x 10^-3 C. 8.75 x 10^-4 D. 87.5 x 10^-3 E. 875 x 10^-4
Answer Key 6. B
6. A can's diameter is 3 inches, and its height is 8 inches. What is the volume of the can? A. 50.30 B. 56.55 C. 75.68 D. 113.04 E. 226.08
Answer Key 6. B
6. A car dealer sells a SUV for $39,000, which represents a 25% profit over the cost. What was the cost of the SUV to the dealer? A. $29,250 B. $31,200 C. $32,500 D. $33,800 E. $33,999
Answer Key 6. B
6. Find the square of 25/9 A. 5/3 B. 3/5 C. 7 58/81 D. 15/2 E. 650/81
Answer Key 6. C
6. Which of the following correctly identifies 4 consecutive odd integers where the sum of the middle two integers is equal to 24? A. 5, 7, 9, 11 B. 7, 9, 11, 13 C. 9, 11, 13, 15 D. 11, 13, 15, 17 E. 13, 15, 17, 19
Answer Key 6. C
6. If a 1 ⁄ 4 of a teaspoon is 1 ml, then how many milliliters are in 6 teaspoons? A. 10 ml B. 12.5 ml C. 15 ml D. 20 ml E. 24 ml
Answer Key 6. E
7. -37 + -47 equals: A. 64 B. -84 C. 65 D. -75 E. -66
Answer Key 7. B
7. Sarah needs to make a cake and some cookies. The cake requires 3/8 cup of sugar and the cookies require 3/5 cup of sugar. Sarah has 15/16 cups of sugar. Does she have enough sugar, or how much more does she need? A. She has enough sugar. B. She needs 1/8 of a cup of sugar. C. She needs 3/80 of a cup of sugar. D. She needs 4/19 of a cup of sugar. E. She needs 1/9 of a cup of sugar.
Answer Key 7. C
7. What percent of 90 is 27? A. 15% B. 20% C. 30% D. 33% E. 41%
Answer Key 7. C
7. After having to pay increased income taxes this year, Edmond has to sell his BMW. Edmond bought the car for $49,000, but he sold it for a 20% loss. What did Edmond sell the car for? A. $24,200 B. $28,900 C. $35,600 D. $37,300 E. $39,200
Answer Key 7. E
7. Column A - The fraction of 76 hours of a week Column B - The fraction of 10 hours in a day
Answer Key 7.A
8. If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how long would the job take if Sam, Lisa, and Tom worked together to complete it? A. 0.8 days B. 1.09 days C. 1.23 days D. 1.65 days E. 1.97 days
Answer Key 8. B
8. Of the following units which would be more likely used to measure the amount of water in a bathtub? A. kilograms B. liters C. milliliters D. centigrams E. volts
Answer Key 8. B
8. Which of the following numbers could be described in the following way: an integer that is a natural, rational and whole number? A. 0 B. 1 C. 2.33 D. -3 E. none of the above
Answer Key 8. B
8. Jim works for $15.50 per hour for a health care facility. He is supposed to get a 75 cent per hour raise at one year of service. What will his percent increase in hourly pay be? A. 2.7% B. 3.3% C. 133% D. 4.8% E. 105%
Answer Key 8. D
8. A scale on a map states that every 1⁄4 of an inch represents 20 miles. If two cities are 3 1⁄2 inches apart, how many miles are actually between the two cities? A. 14 miles B. 20 miles C. 125 miles D. 230 miles E. 280 miles
Answer Key 8. E
8. What is the mathematical average of the number of weeks in a year, seasons in a year, and the number of days in January? A. 36 B. 33 C. 32 D. 31 E. 29
Answer Key 8. E
9. In a college, some courses contribute more towards an overall GPA than other courses. For example, a science class is worth 4 points; mathematics is worth 3 points; history is worth 2 points; and English is worth 3 points. The values of the grade letters are as follows, A= 4, B=3, C=2, D=1, F=0. What is the GPA of a student who made a "C" in Trigonometry, a "B" in American History, an "A" in Botany, and a "B" in Microbiology? A. 2.59 B. 2.86 C. 3.08 D. 3.33 E. 3.67
Answer Key 9. C
9. Find 0.12 ÷ 12 A. 100 B. 10 C. 1 D. 0.01 E. 0.001
Answer Key 9. D
9. If a match box is 0.17 feet long, what is its length in inches the most closely comparable to the following? A. 5 1/16 inch highlighter B. 3 1/8 inch jewelry box C. 2 3/4 inch lipstick D. 2 3/16 inch staple remover E. 4 1/2 inch calculator
Answer Key 9. D
9. Michelle wants to expand her flowerbed by increasing the length and width each by 2 ft. What will the new area of the flower bed be if L and W represent the original dimensions of the flowerbed's length and width? A. 2 LW B. 2 (L+W) C. 2L +2W D. (L+2) (W+2) E. LW/2
Answer Key 9. D
9. If 45 is 120% of a number, what is 80% of the same number? A. 30 B. 32 C. 36 D. 38 E. 41
Answer Key 9.A
Which of the following statements must be true? Indicate all statements: 2006-07 and 2007-08 P +10 -10 T +17 -8 A. For 2008 the dollar amount of sales at Store R was greater than that at each of the other four stores. B. The dollar amount of sales at Store S for 2008 was 22 percent less than that for 2006. C. The dollar amount of sales at Store R for 2008 was more than 17 percent greater than that for 2006.
Answer choice C. (The dollar amount of sales at Store R for 2008 was more than 17 percent greater than that for 2006).
Kaplan Course Book, Page 17, problem #7. John spent 40 percent of his earnings last month on rent and 30 percent less than what he spent on rent to purchase a new dishwasher. What percent of last month's earnings did John have left over? 30% 32% 45% 68% 70%
Answer on page 37: Answer Choice B. Because there is an unspecified value in this percent question, you can pick numbers. Pick 100 for the total earnings for ease of calculation. In this case, John spent $40 on rent and $40 - $40(0.3) or $28 on his dishwasher. The amount left over was $100 - ($40 + $28) = $32, which is 32% of his month's earnings left over.
10. What is the least possible distance between a point on the circle; x^2 + y^2 = 1 and a point on the line; y = 3/4*x - 3? A) 1.4 B) sqrt (2) C) 1.7 D) sqrt (3) E) 2.0
Answer: The equation of the line will be 3x - 4y - 12 = 0. This crosses the x and y axis at (0,-3) and (4,0) The circle has the origin at the center and has a radius of 1 unit. So it is closest to the given line when, a perpendicular is drawn to the line, which passes through the origin. This distance of the line from the origin is: 12 / sqrt (9 + 16) which is: 2.4 [Length of perpendicular from origin to line ax + by + c = 0 is mod (c / sqrt (a^2 + b^2))] The radius is 1 unit. So the shortest distance is 2.4 - 1 unit = 1.4 units
if the receipts for a matinee performance at the Granada theater totaled $2,400, how many tickets were sold for that performance? (1) the average price of a ticket sold was $7.50. (2) All tickets sold cost either $10.00 or $6.00.
Average = sum of terms/number of items You already know the sum of terms (total receipts = $2,400). All that you need to find the number of items (number of tickets sold) is the other part of the equation: the average price of a ticket sold. Statement (1) gives you this so it is sufficient. Since you don't know how many $10.00 vs. $6.00 tickets were sold, statement (2) does not give you the number of tickets sold, and so is not sufficient. The answer then is choice (A).
2. Two cyclists start biking from a trail's start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles per hour. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking? A. 2 hours B. 4 ½ hours C. 5 ¾ hours D. 6 hours E. 7 ½ hours
B
41. Country X taxes each of its citizens an amount equal to 12 percent of the first $40,000 of income, plus 20 percent of all income in excess of $40,000. If a citizen of Country X is taxed a total of $8,000, what is her income? $40,000 $56,000 $64,000 $66,667 $80,000
B
5. What simple interest rate will Susan need to secure to make $2,500 in interest on a $10,000 principal over 5 years? A. 4% B. 5% C. 6% D. 7% E. 8%
B
A sporting goods store that sells tennis balls sells each of its packages of Brand X balls for a certain price and each of its packages of Brand Y balls for a certain price. If Oscar, Rennie, and Thom bought tennis balls in this store, how much did Rennie pay for 2 packages of Brand X balls and 2 packages of Brand Y balls? (1) Oscar bought 2 packages of Brand X balls and 1 package of Brand Y balls for $9.49. (2) Thom bought 1 package of Brand X balls and 1 package of Brand Y balls for $6.49.
B
#45. Tracy has 3 bags of marbles, each bag containing at least 1 blue marble, at least 1 red marble, and no marbles of another color. If tracy selects 1 marble at random from each bag, what is the probability that all 3 marbles that she selects will be red? 1. There are a total of 5 red marbles and 5 blue marbles in the 3 bags. 2. The ratios of red to blue marbles in the 3 bags are 2:1, 1:1, and 1:2
B.
GRE Book, page 146, #5 r, s, and t are three consecutive, odd integers such that r < s < t. A: r + s + 1 B: s + t - 1
B. I used Picking Numbers on this, but the solution on page 170 was their "question mark in a box" thingy where they made an equation out of the two terms.
Is | 15 - m| + |m - 15| > 15 1. m > 6 2. m < 7
B. Step 1: Determine, from the question stem, what kind of information is needed to answer this question? Everything hinges on m. Use Picking Numbers. Step 2: Evaluate each statement individually. Statement 1: Insufficient. CASE 1: m = 7 Yes; CASE 2: m = 15 NO. Statement 2: Sufficient. Any number less than 7 leads to 'yes.' Step 3: Combine the statements if necessary. Combined statements: Not needed.
Page 21, Kaplan Course Book: If integers a and b are distinct factors of 30, which of the following CANNOT be a factor of 30? I. ab + b^2 II. (a + b)^2 III. a + b I only II only III only I and II only I, II, and III
B. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. Write "CANNOT" on your scratch paper. It's a good idea to start with the statement that appears most often, so let's start with II. We see no perfect squares other than 1, which cannot be the sum of two distinct numbers on our list. So, it is eliminated, as is Answer choice A and C. Let's move on to Statement I since it appears twice. Let's use picking numbers and try a = 2 and b = 1. Together they give a result of 3, which is a factor of 30. Eliminate Answers D and E. There is no need to check Statement III.
Board member A wants to schedule a 30-minute meeting on Tuesday with himself and three other board members, B, C, and D. Is there a 30-minute period on Tuesday that is open for all four members? (1) On Tuesday A and C have an open period from 9:30 a.m to 11:00 a.m. (2) On Tuesday D has an open period from 10:30 a.m. to 1:00 p.m. and B has an open period from 8:00 a.m. to 12:00 p.m.
C
10. A student receives his grade report from a local community college, but the GPA is smudged. He took the following classes: a 2 hour credit art, a 3 hour credit history, a 4 hour credit science course, a 3 hour credit mathematics course, and a 1 hour science lab. He received a "B" in the art class, an "A" in the history class, a "C" in the science class, a "B" in the mathematics class, and an "A" in the science lab. What was his GPA if the letter grades are based on a 4 point scale? (A=4, B=3, C=2, D=1, F=0) A. 2.7 B. 2.8 C. 3.0 D. 3.1 E. 3.2
C This is a problem involving "weighted" grades. You solve it by multiplying the credit for a course times the numerical value of the grade received, then adding up all the credits and dividing it into the sum of all the grade products. Art .......... 2 credit hours times B (3 points) = 6 grade points History ...... 3 credit hours times A (4 points) = 12 grade points Science ...... 4 credit hours times C (2 points) = 8 grade points Mathematics .. 3 credit hours times B (3 points) = 9 grade points Science Lab .. 1 credit hour times A (4 points) = 4 grade points . Now add up all the credit hours (2 + 3 + 4 + 3 + 1 = 13 hours) Then add up all the grade points earned (6 + 12 + 8 + 9 + 4 = 39 grade points) . Finally divide the credit hours into the grade points and you have the grade point average (GPA) = 39/13 = 3.00. The grade point average (GPA) of this student is 3 point oh oh ... 3.00.
#46, Page 279. Each person in Room A is a student and 1/6 of the students in Room A are seniors. Each person in Room B is a student and 5/7 of the students in Room B are seniors. If 1 student is chosen at random from Room A, and 1 student is chosen at random from Room B, what is the probability that exactly 1 of the students chosen is a senior? 5/42 37/84 9/14 16/21 37/42
C.
Each of the coins in a collection is distinct, and is either silver or gold. In how many different ways could all of the coins be displayed in a row, if no 2 coins of the same color could be adjacent? 1. The display contains an equal number of gold and silver coins 2. If only the silver coins were displayed, 5,040 different arrangements of the silver coins would be possible
C.
At the zoo the ratio of sea lions to penguins is 4 to 11. If there are 84 more penguins than sea lions how many sea lions are there? 24 36 48 72 132
C. Let's start with B. If it conforms to the ratio, then if there are 36 sea lions there should be 99 penguins. The difference is 63 animals; not enough. Let's try D. If there are 72 sea lions, there will be 198 penguins or a difference of 126 animals, which is too many. Automatically we know that we have the target bracketed, and it must be 48, since it is between 36 and 72.
7. A study reported that in a random sampling of 100 women over the age of 35 showed that 8 of the women were married 2 or more times. Based on the study results, how many women in a group of 5,000 women over the age of 35 would likely be married 2 or more times? A. 55 B. 150 C. 200 D. 400 E. 600
D
If Kevin were three times as old as he currently is, he would be 50 years older than Dave. If Kevin is twenty years younger than Dave, how old is Kevin? A. 35 B. 36 C. 39 D. 41 E. 42
D = K + 20 3K = D + 50 3K = K + 20 + 50 3K = K + 70 2K = 70 K = 35 A. 35 Yea! I got this one right.
A student is entering in a college housing lottery for 2 consecutive years. What is the probability that the student receives housing through the lottery for at least 1 of these years? Eighty percent of the students in the lottery do not receive housing through the lottery for at least 1 of these years? 1. Eighty percent of the students in the lottery do not receive housing through the lottery in any given year. 2. Each year, 1 of 5 students receives housing through the lottery.
D.
The Kaplan Method of Value Questions, Page 31 of the Kaplan Coursebook. 30. If x and y are prime numbers, is y(x - 3) odd? 1. x > 10 2. y < 3
D. Step 1: Determine, from the question stem, what kind of information is needed to answer this question? We need to know if this particular expression is odd, so we need to know the rules of evens and odds. Odd x odd = odd; even x even = even, and odd x even = even. So if either y is even or if x - 3 is even, we can answer the question with a NO. Since 2 is the only prime number, that could be an issue. Step 2: Evaluate each statement individually. Statement 1: If x is a prime number greater than 10, it must be odd. And x - 3 must therefor be even. so this is sufficient. Statement 2: If y is a prime number less than 3, y must be even. So this is sufficient. Step 3: Combine the statements if necessary. Combined statements: NOT NECESSARY
If a>b>c>d on the number line, c is halfway between b and d, and b is halfway between a and d, then c-b/c-a equals 1 3/4 2/3 1/3 1/6
D. Since there are variables in the question stem, Picking Numbers will work here. Pick the c value first, since the other values are given in relation to it. If c = 4 and b = 6, then d = 2, and a = 10. Then find the value of the expression c-b/c-a; then 4-6/4-10 = -2/-6 = 1/3
Treat the two columns as if they were the two sides of an equation. Anything you can do to both sides of an equation, you can also do to both columns. You can add or subtract numbers from both columns; you can multiply or divide both columns by a positive number; you can multiply one side by some form of 1.
Do not, however, multiply or divide both columns by a negative number. The reason is that we don't know if the two columns represent an equation or an inequality. If they represent an inequality, the direction of the inequality will change if you multiply or divide by a negative number. You should always simplify the terms in a quantitative comparison by reducing, factoring, unfactoring, etc.
14. During a 5-day festival, the number of visitors tripled each day. If the festival opened on a Thursday with 345 visitors, what was the attendance on that Sunday? A. 345 B. 1,035 C. 1,725 D. 3,105 E. 9,315
E
8. John is traveling to a meeting that is 28 miles away. He needs to be there in 30 minutes. How fast does he need to go to make it to the meeting on time? A. 25 mph B. 37 mph C. 41 mph D. 49 mph E. 56 mph
E
4. Mary is reviewing her algebra quiz. She has determined that one of her solutions is incorrect. Which one is it? A. 2x + 5 (x-1) = 9, x = 2 B. p - 3(p-5) = 10, p = 2.5 C. 4 y + 3 y = 28, y = 4 D. 5 w + 6 w - 3w = 64, w = 8 E. t - 2t - 3t = 32, t = 8
E Note that all of the math in all 5 examples is correct EXCEPT for the sign in E. This is typical GMAT trickery where they give you the right answer last so you waste time working through them one at a time.
If a bicyclist increases his speed by 30% and then again by 10%, what is his total increase in speed?
For this question, try Picking Numbers. Assign the speed of 100 mph as the cyclist's speed (it doesn't have to be plausible). 100 mph x 30% = 130 mph 130 x 10% =13 mph Add 130 and 13 together and you get 143 mph or an increase of 43%. You can check your answer by using the following formula: 143 - 100/100 = 43%
Page 18, Kaplan Course Book: Each writer for a local newspaper is paid as follows: a dollars for each of the first n stories each month, and a + b for each story thereafter, where a>b (conditional). How many more dollars will a writer who submits N + a stories in a month earn than a writer who submits N + b stories? (a - b)(a + b + n) a - b a^2 - b^2 n(a - b) an + bn - an
I can see from my notes that the answer is: C. a^2 - b^2 but I'm not sure why. I'll have to rebuild the answer since it's not in the key.
Page 22, Kaplan Course Book: Backsolving. A teacher grades student's tests by subtracting twice the number of incorrect responses from the number of correct responses. If student A answers each of the 100 questions on her test and receives a score of 73, how many questions did student A answer correctly? 55 60 73 82 91
If she got 82 correct she had 18 wrong. Let's start strategically with D. D. 82 - (18 x 2) = 82 - 36 = 46 B. 60 - (40 x 2) = 60 - 80 = -20 E. 91 - (91 x 2) = 91 - 18 = 73 So, E is the answer.
x/2 must be an integer, but is x/2 even or odd?
In this case, picking two different even numbers for x can yield two different results. If you let x = 4, then x/2 = 4/2 = 2 which is even. but if you let x = 6, then x/2 = 6/2 = 3, which is odd. So x/2 could be even or odd—and you wouldn't know that if you picked only one number.
6. If Leah is 6 years older than Sue, and John is 5 years older than Leah, and the total of their ages is 41. Then how old is Sue? A. 8 B. 10 C. 14 D. 19 E. 21
In your question you want to know sue's age. all the other kids have numbers that are added to them, so it is best to let sue's age be the variable x. So let the following be true, and always write it down, it helps you remember. x = Sue's age x + 6 = Leah's age x + 6 + 5 = John's age Leah is 6 years older than Leah so she is "x + 6". John is 5 years older than Leah who is 6 years older than sue so John is x+6+5. Your equation is set up like this: Sue's age + Leah's age + John's age = 41 x + x + 6 + x + 6 + 5 = 41 Now add your common factors: 3x + 17 = 41 solve for x 3x = 41 - 17 3x = 24 x = 8 Therefore, Sue must be 8 years old. To check this you can use sue's age of 8: Sue= 8 Leah= 8 + 6 = 14 (Sue's age plus 6 years) John = 14 + 5 = 19 ( Leah's age plus 5 years) Sue+Leah+John = 41 8+14+19=41 ANOTHER WAY to solve this would be "picking numbers" and plug 8 into Sue's age. A
Is z an integer? 1. 2z is an even integer 2. 4z is an even integer
Kaplan Course Textbook, page 173 Remember, the answer is "always yes" or "always no" for data sufficiency. Statement 1: Because all even numbers can be evenly divided by 2, every even number must be 2 times some integer. Thus, if 2z is an even number, z must be an integer. If 2z = 2 then z = 1. If 2z = -122, then z = -61. We can pick any even number for 2z and we will always find that z is an integer, so statement 1 is sufficient, and we can eliminate answer choices B, C and E. Statement 2 looks similar. If 4z = 4, z =1, which is an integer. But if 4z =6, then z = 1.5, which is not an integer. We can't then say that z is always or never an integer and so it is insufficient. Answer A
A certain quantity of 40% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced? (A) 1/4 (B) 1/3 (C) 1/2 (D) 2/3 (E) 3/4
Let X be the fraction of solution that is replaced. Then: X * 25% + (1 - X) * 40% = 35% Solving, you get X = 1/3
If q and r are both odd numbers, which of the following must also be odd? q - r (q + r)^2 q(q + r) (qr)^2 q + r
Let's pick numbers! How about: q = 3 r = 5 So, starting from the bottom we plug into E: 3 + 5 = 8 (that's even) (3 x 5)^2 = 225 (that's odd) We were looking for odd, so stop right here. This is your answer.
If j and k are integers, and 2j + k = 15 which of the following MUST be true? j + k is odd j + k is even j is odd k is odd k > j
Let's start with E and do some picking numbers: k = 1 and j = 7. Plug those into our formula and we get 2 (7) + 1 = 15. Kaplan says E is out, but I can't figure out why. Let's try D. K is odd. Well, let's try to make k even. You can try but it can't be done. That's because 2j has to be even, and when you add tow even numbers together the sum is always even. So there's no way to make j even and have 2j+ k = 15. Once you realize that you search is over and D is your answer.
When you know the sales price of an item and the markup how do you find the dealer cost?
Let's use the SUV example. The SUV sales price was $39,000 and the markup was 25%: $39,000 ÷ 1.25 = $31,200 Note that you divide in both cases where you are trying to determine the price.
"Jacob is now 12 years younger than Michael"
M = J + 12 Think of it this way: If Jacob is 3 years old and Michael is 15 years old, then 15 = 3 + 12
How many randomly assembled people do you need to have a better than 50% probability that at least 1 of them was born in a leap year?
Probability of a randomly selected person to have NOT been born in a leap yr = 3/4. Take 2 people, probability that none of them was born in a leap year: 3/4 * 3/4 = 9/16. The probability at least one born in leap year: 1- 9/16 = 7/16 < 0.5 Take 3 people, probability that none born in leap year: 3/4 * 3/4 * 3/4 = 27/64. The probability that at least one born is: 1 - 27/64 = 37/64 > 0.5 Thus min 3 people are needed.
If Charles and Sarah's current age are C years and S years, respectively, which of the following expresses the statement, "Six years from now, Charles will be at least as old as Sarah was 2 years ago."
Six years from now, Charles' age will be C+6. Two years ago Sarah's age was S-2. Because in 6 years Charles will be at least as old as Sarah was 2 years ago. C+6 ≥ S-2
Example 2: Column A: 2/7 - 1 Column B: 1/3 - 1
Solution: Immediately eliminate choice D because there are only numbers involved. Also, since (-1) appears in both expressions, we can ignore it. Now we only have to decide which is bigger, 2/7 or 1/3. Since 1/3 can also be written as 2/6, 2/7 is obviously smaller. Therefore, the answer is B.
Example 4: Column A: 9(3 + 24) Column B: (9×3) + (9×24)
Solution: Notice first that D cannot be the answer. Now notice that A is simply the factored form of B. The answer is C. You are not expected to multiply out numbers like these.
Page 18, Kaplan Course Book: If x ≠ 0 and 4x = 3y, which of the following is NOT true? x + y/y = 7/4 y/y-x = 4 x - y/y = 1/4 2x/3y = 1/2 x + 3y/x = 5
Start at the bottom and work upward: E, D, C, B, and finally A. First of all, this question begs for picking numbers: 4x = 3y, we could make x = 3 and y = 4 and thus make the equation 12 = 12. 3 + 4/4 = 7/4 4/4 - 3 = 4 3 - 4/4 ≠ 1/4 (ANSWER!) 2(3)/3(4) = 1/2 3 + 3(3)/3 = 5 Answer C
The Kaplan Method of Value Questions, Page 30 of the Kaplan Coursebook. 29. Is 4 + n/6 an integer? 1. n is a multiple of 3 2. n divided by 6 has a remainder of 0
Step 1: Determine, from the question stem, what kind of information is needed to answer this question? First of all, you can ignore the 4 in the question stem. Also, we need the value of n Step 2: Evaluate each statement individually. Statement 1: Insufficient Statement 2: Sufficient. n is a multiple of 6. Step 3: Combine the statements if necessary. Combined statements:
Beware of answer choices that are structurally different from others.
Step 1: Determine, from the question stem, what kind of information is needed to answer this question? Step 2: Evaluate each statement individually. Statement 1: Statement 2: Step 3: Combine the statements if necessary. Combined statements:
The Kaplan Method of Data Sufficiency, Page 27 of the Kaplan Coursebook. 24. A certain company produces exactly three products: X, Y and Z. In 1990 what was the total income for the company from the sale of its products? 1) In 1990, the company sold 8,000 units of product X, 10,000 units of Y, and 16,000 units of product Z. 2) In 1990 the company charged $28 per unit for product X, and twice as much for Product Z.
Step 1: Determine, from the question stem, what kind of information is needed to answer this question? In this case we need six things: three prices and three quantities. Step 2: Evaluate each statement individually. Statement 1: Insufficient. (1) provides only three pieces of information. Statement 2: Insufficient. (2) provides only two pieces of information. Step 3: Combine the statements if necessary. Combined statements: insufficient. When combined, the two statements only provide five of the six required pieces of information.
The Kaplan Method of Data Sufficiency, Page 27 of the Kaplan Coursebook. 23. If b is a positive integer, how many factors does b have? 1) b has the same number of factors as 3^5 2) b is the product of a prime number and the square of a different prime number.
Step 1: What kind of information is needed to answer this question? We need to know something about b. Step 2: Evaluate each statement individually. Statement 1: Sufficient: The number of distinct factors that 3^5 has can be determined. Statement 2: Sufficient: Try b = (2)(3)^2 = 18 or b = (3)(5)^2 = 75 or any other case that meets the requirement of 2. Each time, you'll find that b has 6 factors. Step 3: Not necessary.
Example 1: When to use the Fundamental Counting Rule: In the Identity Theft example, we see that for someone to guess your SSN, they would have to have your name and guess the 9 digit number.
That's unlikely, since 10 x 10 x 10 x 10 x 10 x 10 x10 x 10 x 10 = 1,000,000,000,000 or a one in a billion change of getting that right. It's important to note that this is not written as 9! since that would be 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 which is 362,880. We're counting the total number of possible outcomes and it doesn't matter if a number is used or not or in what order they come.
If six business partners are having a dinner at a round table, how many seating arrangements are possible?
The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects, instead of n!, we have (n‐1)! Thus, the answer is 5! or 120
Multiply 0.029 by 10^3
The exponent is 3, so move the decimal point three places to the right. (0.029)10^3 = 0029. = 29 if you had been told to multiply 0.029 by 1,000, you could have counted the number of zeros in 1,000 and done exactly the same thing.
In a basketball contest, players must make 10 free throws. Assuming a player has 90% chance of making each of his shots, how likely is it that he will make all of his first 10 shots?
The probability of making all of his first 10 shots is given by: (9/10)* (9/10)* (9/10)* (9/10)* (9/10)* (9/10)* (9/10)* (9/10)* (9/10)* (9/10) = (9/10)^10 = 0.348 => 35%
If a truck driver travels 455 miles at an average speed of 70 miles per hour, then takes a one-hour break, then travels another 315 miles at the same speed, what is his average speed for the entire 770-mile trip, including the break?
The total time spent on the road is 770/70 = 11 hours, which means that including the break his total time is 12 hours. Average speed, then, is: 770/12 = 64 1/6
11. Simon arrived at work at 8:15 A.M. and left work at 10: 30 P.M. If Simon gets paid by the hour at a rate of $10 and time and ½ for any hours worked over 8 in a day. How much did Simon get paid? A. $120.25 B. $160.75 C. $173.75 D. $180 E. $182.50
There are 12 hours if one works from 8:30AM-8:30PM He worked and additional 2.25 since he started at 8:15AM and ended at 10:30OM I got .25 for the 15 minutes by performing the following calculation 15/60=1/4 hour. He gets paid straight time for 8 hours and is calcuated by the number of hours x the wage per hour = $10(8) = $80 We next need to calculate how much money he made at a rate of 1.5 over the eight hours. His total number of hours worked was 14.25. Subtract 14.25-8=6.25 The number of hours over eight is 6.25 the new rate is (1.5)($10) Multiply 6.25(1.5)($10)=$93.75 The total amount he made that day is $80+93.75=$173.75 C
A train leaves New York for Boston. Five minutes later another train leaves Boston for New York at double the speed. Which train will be closer to New York when they encounter?
They will be the same distance from New York. (This is a trick question).
p. 275 of Kaplan textbook. Each of 6 adjacent cages in a zoo holds either 1 lion or 1 tiger. If there are 3 tigers, how many arrangements (order matters, i. e. permutation) of the animals are possible, if the tigers must occupy the 3 cages on the right and all 6 animals are distinguishable? A 12 B 24 C 36 D 40 E 48
Tigers = 3 N! or 3 * 2 * 1 = 6 Lions = 3 N! or 3 * 2 * 1 = 6 (6)(6) = 36 C. 36
A cyclist bikes x distance at 10 miles per hour and returns over the same path at 8 miles per hour. What is the cyclist's average rate for the round trip in miles per hour?
Time out = d/r = x/10 hrs Time in = d/r = x/8 hrs Round-trip DATA: distance = 2x ; time = [(x/10) + (x/8)] (18x/80) = (9x/40) hrs So average rate for the round trip = d/r = (2x)/(9x/40)= 80x/9x 80/9 = 8.8888888... mph Rounding down you get 8.9 mph ------------------ A cyclist bikes x distance at 10 mph and returns over the same path at 8 mph. What is the cyclists average rate for the round trip in miles per hour. x miles/10mph + x miles/8mph =[8x+10x]/[80] =18x/80 =(9/40)x hrs (This is total roundtrip time) -------- Total distance is 2x miles --------- Rate = distance/time = (2x)/[(9/40)x]= 80/9 mph Cheers, Stan H. Answer by Edwin McCravy(6567) (Show Source): You can put this solution on YOUR website! A cyclist bikes x distance at 10 mph and returns over the same path at 8 mph. What is the cyclist's average rate for the round trip in miles per hour. First, I'll tell you what it is NOT. It it NOT the average of the two rates, or it is NOT 9 mph, but a little bit less. Since she travels a distance of x miles at 10 mph then, using TIME = DISTANCE/RATE, it took her x/10 hours to travel the x miles going. Since she then travels a distance of x miles at 8 mph then, using TIME = DISTANCE/RATE, it took her x/8 hours to travel the x miles returning. Her total distance was 2x miles and her total time was x/10 + x/8. To simplify that we must get an LCD of 40 x/10 + x/8 = 4x/40 + 5x/40 = 9x/40 AVERAGE RATE = (TOTAL DISTANCE TRAVELED)÷(TOTAL TIME TRAVELED) so AVERAGE RATE = (2x)÷(9x/40) = (2x)·[40/(9x)] = (80x)/(9x) = 80/9 = 8 8/9 mph, which is a little less than the average of her two speeds. Edwin
Probability = number of desired outcomes/total number of outcomes The sum of the probabilities of all possible outcomes is 1
To find the probability of each of a series of independent events occurring, multiply the probabilities of all the events
Jacob is now 12 years younger than Michael. If 9 years from now Michael will be twice as old a Jacob, how old will Jacob be in 4 years?
We should begin by writing an equation for Michael's and Jacob's ages now: M=J+12. Write an equation for Michael's and Jacob's ages in 9 years: M+9 = 2(J+9). We now have two distinct equations with two unknowns that we can solve. We can substitute the first equation into the second for M, yielding the equation (J+12)+9 = 2(J+9). Solving this equation, we have: (J+12)+9 = 2(J+9), J + 12 + 9 = 2J + 18, J - J + 21 - 18 = 2J - J + 18 - 18 3 = J Jacob is 3 years old, but in 4 years he will be 7 years old.
The ratio of x to y is 5:4. the ratio of y to z is 1:2. What is the ratio of x to z?
We want the y's in the two ratios to equal each other, because then we can combine the x:y ratio and the y:z ratio to form the x:y:z ratio that we need to answer this question. to make the y's equal, we can multiply the second ratio by 4. When we do so, we must perform the multiplication on both components of the ratio. since a ratio is a constant proportion, it can be multiplied or divided by any number without losing its meaning, as long as the multiplication and division are applied to all the components of the ratio. In this case, we find that the new ratio for y to z is 4:8. We can combine this with the first ratio to find a new x to y to z ratio of 5:4:8. therefore, the ratio of x to z is 5:8.
All employees are in either Dept. X or Dept. Y. Dept. X is more than twice as big and the average salary is $25,000. Average salary in Dept. Y is $35,000. What is the company average? 26,000 28,000 29,000 30,000 31,000 32,000 34,000
Weighted average problem: Add the amounts times their weights and divide by the weights. (2)(25,000) + (1)(35,000)/2 + 1 = 85,000/3 = $28,333 Answer choice B. (note that since this example says "more than twice as big" you could also select Answer A if multiple answers are allowed).
9. Which of the following is equal to 5.93 x 10^-2? A. 0.0593 B. 0.00593 C. 593 D. 5930 E. 59300
Which of the following is equal to 5.93 x 10-2? 10^(-2) is equivalent to .01 therefore: 5.93 x .01 = 0.0593 A.
The average annual rainfall in Boynton for 1976 to 1979 was 26 inches per year. Boynton received 24 inches of rain in 1976, 30 inches in 1977, and 19 inches in 1978. How many inches of rainfall did Boynton receive in 1979?
You know that total rainfall equals 24 + 30 + 19 + (number of inches of rain in 1979). You know that the average rainfall was 26 inches per year. You know that there were 4 years. So, plug these numbers into any of the three expressions of the average formula to find that sum of terms = (Average)(number of terms) 24 + 30 + 19 + inches in 1979 = (26)(4) 73 + inches in 1979 = (26)(4)73 + inches in 1979 = 104 Inches in 1979 = 31
2. If a circle has the diameter of 8, what is the circumference? A. 6.28 B. 12.56 C. 25.13 D. 50.24 E. 100.48
c
23. What is 1/9 of 9? A. 1/9 B. 0 C. 1 D. 2 E. 3
c
#35, Page 275. The members of the board of directors forma a committee of x people. If all board members are eligible, the membership of the committee can be arranged in how many different combinations? Since it's a combination, order doesn't matter, so N!/K!(n-k)! 1. the board must contain 3 members. 2. the board contains 8 members
c.
#50, Page 281, Kaplan Textbook. The only contents of a bag are 4 pens that write blue and 3 pens that write green. If 4 pens are chosen at random, what is the probability that 2 of the pens write blue and 2 of the pens write green? 2/7 1/2 18/35 4/7 9/14
c.
Robert tossed a fair coin 3 times. What is the probability that the coin landed heads up exactly twice? 0.125 0.250 0.375 0.750 0.875
c.
Options x chances =
n
odd x odd =
odd
21. A building that is 150 ft tall casts a shadow of 20 feet long. At the same time a tree casts a shadow of 2 ft. How tall is the tree? A. 10 B. 15 C. 20 D. 25 E. 30
Answer Key 21. B
21. If a match box is 0.17 feet long, what is its length in inches the most closely comparable to the following? A. 5 1/16 inch highlighter B. 3 1/8 inch jewelry box C. 2 3/4 inch lipstick D. 2 3/16 inch staple remover E. 4 1/2 inch calculator
Answer Key 21. D
23. What is the fractional equivalent of 12.5%? A. 1/4 B. 2/9 C. 1/5 D. 1/8 E. 2/7
Answer Key 23. D
24. Change 4 3/5 to an improper fraction. A. 23/5 B. 7/5 C. 12/20 D. 20/12 E. 12/5
Answer Key 24. A
7. If the area of a square flowerbed is 16 square feet, then how many feet is the perimeter of the flowerbed? A. 4 B. 12 C. 16 D. 20 E. 24
Answer Key 7. C
7. What is the median of the following list of numbers? 4, 5, 7, 9, 10, 12 A. 6 B. 7.5 C. 7.8 D. 8 E. 9
Answer Key 7. D
4. Find the slope of 9x + 12y = 4 A: 3/4 B: 4/3 C: -3/4 D: -4/3
C. The formula for slope is y = mx + b, in which m is slope.
Caution: When statements look similar at first glance, there will most likely be a key difference between them.
"Always no" is a sufficient as "always yes."
Picking numbers hint from Page 16 of the Kaplan Course Book: When you see a percent question with unspecified values, pick _____ for the unknown value. It will make calculations much easier.
100
Exterior angles all sum to:
360
20. If 3x = 6x - 15, then x + 8 = A. 5 B. 10 C. 11 D. 12 E. 13
3X = 6X - 15 3X - 6X = -15 -3X = -15 X = -15/-3 X = 5 ANSWER. 5 + 8 = 13 ANSWER.
Simplify 3^2 + 3^2
3^2 + 3^2 = 9 + 9 = 18 or 3^2 + 3^2 = 1 * 3^2 + 1 * 3^2 = (1 + 1) * 3^2 = 2 * 3^2 = 3^3 = 3 * 3 * 3 = 9
Ice cream cone options: Flavors are options, each scoop is a chance to choose 5 flavors, 2 scoops :
5 x 5 = 25
A car got 33 miles per gallon using gasoline that cost $2.95 per gallon. What is the approximate cost of the gas used to drive 350 miles. 10 20 30 40 50
(350/33)(2.95) = 30 more or less
What is a profit of $5 on a $15 sweater as a percent of cost?
(5/15)(100) = 33.333 or 33% Note that you have to convert from a decimal to a percent
The basic work formula is:
(a)(b)/a+b
Pasta Selection: Noodles: angel hair, penne, elbow, bowtie Meat: ground beef, sausage, meatballs, no meat Sauce: alfredo, marinara How many dishes have angel hair and meatballs?
1 * 1 * 2 = 2
1/16 - 3/4 + 1 7/8 =
1/16 - 3/4 + 1 7/8 = 1/16 - 3/4 + 15/8 = 1/16 - 3/4(4) + 15/8(2) = 1/16 - 12/16 + 30/16 = -11/16 + 30/16 = 19/16
"A coat which is 40% off it's original price, now costs $160. What is the original price?" Then first of all, if it is 40% off already, then 60% (100% - 40%) of what is $160? is =160 of = x % = 60 160/x = 60/100 16000 = 60x x = $ 266.67
160 is indeed 40% of 400
The sum of angles along a straight line sum to
180
An integer is divisible by 6 if it is divisible by:
2 and 3
If Oscar can build 24 feet of fencing per day, how many days would it take Oscar to build a 144 foot long fence?
24 = 144/t 24t = 144 t = 144/24 = 6
An integer is divisible by 3 if its digits add up to a multiple of:
3
Sandwiches: Bread Types: white, wheat, ciabatta Cheeses: American, swiss, provolone Type: turkey, roast beef, ham, veggie How many possible sandwiches?
3 * 3 * 4 = 36
32. If 8x + 5x + 2x + 4x = 114, then 5x + 3 is: A. 12 B. 25 C. 33 D. 47 E. 86
32. C
How long would it take someone walking at a rate of 4 miles per hour to cover a distance of 27 miles?
4 = 27/t 6.75 hours
9. Compare two quantities A and B 5 < x < 7 2 < y < 4 A) x + y B) 7 A: A is greater than B B: B is greater than A C: A and B are equal D: There is not enough information provided to determine the relationship between A and B.
9. A. The lowest possible value for x and y still adds up to more than 7.
A certain insect can crawl 900 feet in 12 hours. What is the insect's average distance per hour over that time?
900/12 = 75f/h
1. If Lynn can type a page in p minutes, what piece of the page can she do in 5 minutes? A. 5/p B. p - 5 C. p + 5 D. p/5 E. 1- p + 5
A
13. If r = 5 z, then 15 z = 3 y, then r = A. y B. 2 y C. 5 y D. 10 y E. 15 y
A
#43, Page 278 Kaplan Textbook If the average of four numbers is 10, how many of the numbers are greater than 10? 1. Precisely 2 of the numbers are equal to 10. 2. The largest of the 4 numbers is 10 greater than the smallest of the 4 numbers.
A.
5. If a > 0, then (8a)(2a) A: 16a B: 162a C: 22a D: 23a
A.
GRE Book, page 148, #9 If y = 3x and z = 2y, what is x + y + z in terms of x? 10x 9x 8x 6x 5x
A.
Factor: x2 + 5x - 6
A: (x - 6)(x + 1) B: (x - 3)(x + 2) C: (x + 9)(x - 6) D: (x + 6)(x - 1)
If you can simplify the question stem, you'll be able to move through the choices much more quickly.
Always yes or always no is sufficient. Sometimes yes and sometimes no is insufficient.
Page 33 of the Kaplan Coursebook. Scratchwork on the GMAT:
Analytical Writing Data Sufficiency Reading Comprehension Eliminating Answers
12. In the number 743.25 which digit represents the tenths space? A. 2 B. 3 C. 4 D. 5 E. 6
Answer Key 12. A
12. If the average person drinks 8, (8oz) glasses of water per day, a person who drinks 12.8 oz of water after a morning exercise session has consumed what fraction of the daily average? A. 1/3 B. 1/5 C. 1/7 D. 1/9 E. 1/10
Answer Key 12. B
15. On a map, 1/3 inch equals 15 miles. The distance between two towns on a map is 3 2/3 inches. How many miles are actually between the two towns? A. 11 B. 16 C. 88 D. 132 E. 165
Answer Key 15. E
16. James invested $4,000 at 5% interest per year; how long will it take him to earn $200 in simple interest? A. 1 year B. 2 years C. 3 years D. 4 years E. 5 years
Answer Key 16. A
5. 7.95 ÷ 1.5 A. 2.4 B. 5.3 C. 6.2 D. 7.3 E. 7.5
Answer Key 5. B
9. Column A: 500% of 6 Column B: 600% of 5
Answer Key 9. C
9. What is the next number in the following pattern? 1, 1/2, 1/4, 1/8, ___ A. 1/10 B. 1/12 C. 1/14 D. 1/15 E. 1/16
Answer Key 9. E
$10, $11, $11, $12, $12, $14, $16, $17, $21, $22 The various prices that a certain product were sold for at retailers in City X is shown above. How many prices were greater than the median price but less than the mean price? (A) None (B) One (C) Two (D) Three (E) Four
B
9. The city council has decided to add a 0.3% tax on motel and hotel rooms. If a traveler spends the night in a motel room that costs $55 before taxes, how much will the city receive in taxes from him? A. 10 cents B. 11 cents C. 15 cents D. 17 cents E. 21 cents
D
If a>b>c>d on the number line, c is halfway between b and d, and b is halfway between a and d, the c-d/c-a = 1 3/4 2/3 1/3 1/6
D
GRE Book, page 146, #4 x + y = -1 A: x B: y
D.
2. Factor: x^2 + 5x - 6 A: (x - 6)(x + 1) B: (x - 3)(x + 2) C: (x + 9)(x - 6) D: (x + 6)(x - 1)
D. Be sure that your factors will convert back to the polynomial when multiplied according to FOIL.
What are the three equations for rate? Distance = Time = Rate =
Distance = Rate x Time Time = Distance/Rate Rate = Distance/Time
$160 = 60% of original price. What was the original price?
Divide $160 by .60 to get the original price of $266.67
even + even =
Even
25. Which fraction is equal to 0.20%? A. 1/20 B. 1/40 C. 1/50 D. 1/400 E. 1/500
First change the percent to a decimal by dividing by 100. 0.20% = 0.002 0.002 = 1/500 E
The sum of the even numbers between 1 and n is 79 * 80, where n is an odd number, then n = ?
First term a=2, common difference d=2 since even number therefore sum to first n numbers of arithmetic progression would be: n/2(2a+(n-1)d) n/2(2*2+(n-1)*2) n(n+1) and this is equal to 79*80 therefore n=79 which is odd...
4. The sales price of a car is $12,590, which is 20% off the original price. What is the original price? A. $14,310.40 B. $14,990.90 C. $15,290.70 D. $15,737.50 E. $16,935.80
Let's say the original price of the car is X and we know that if we take 20% off the original price, we are only paying 80% of the original price. Our original price was 100% and (20% + 80% = 100%) Percentages are expressed in decimals, so 80% = .8 and .8x means 80% of original price .8x = 12,590 (80% of the original cost is $12,590) Divide both sides by .8 x=15,737.50 So the originial price of the car was $15,737.50 D
Peter read P books last year and Nikki read N books last year. If Peter read 35 more books than Nikki, how is this expressed?
P = N + 35
Page 94 of the Kaplan Coursebook.
Page 94.
Stacie is currently three times as old as Matthew. If fifteen years are added to Matthew's age and fifteen years are subtracted from Stacie's age, their ages would be equal. How old is Matthew?
S = 3M M + 15 = S - 15 M + 15 = 3M - 15 30 = 2M 15 = M Matthew is 15 years old.
One die, what is the number showing?
S = [1, 2, 3, 4, 5, 6] n=6
If Eileen drives at an average speed of 50 miles per hour for 3 hours and an average speed of 60 miles per hour for the next 2 hours, what is her average speed for the entire trip?
The distance for the first three hours is 3(50) = 150, and the distance for the final two hours is: 60(2) = 120. Total distance over total time, then, is: 150+120/5 = 270/5 = 54
Sample Space is . . .
The set of all possible outcomes
If a word problem says "Bob's age is twice Jim's age"
You write that as: B = 2J Think of it this way: If Bob is 50 and Jim is 25, then B = 2J, right?
Is Z an interger? (1) z/3 is an integer (2) z/2 is not an integer
a. Statement 1 means that "z is a multiple of 3 or 0" and Statement 2 means "z is not a multiple of 2"
6,930 is a multiple of 5, since:
it ends in zero.
n
size of the space (how many outcomes)
Probability is . . .
the likelihood of an event occurring.
2. If y(x - 1) = z, then x = A. y - z B. z/y + 1 C. y(z-1) D. z(y-1) E. 1 - zy
x = z/y + 1
5. If 5 ounces is equal to 140 grams, then 2 pounds of ground meat is equal to how many grams? A. 863 B. 878 C. 896 D. 915 E. 932
x grams/32 oz = 140 gr/5 oz x = 32[140/5] x = 896 grams
Picking numbers hint from Page 15 of the Kaplan Course Book: Phrases such as ______ are critical on GMAT math questions.
"the remainder"
The Kaplan Method of Data Sufficiency, Page 27 of the Kaplan Coursebook. 22. Team X won 40 basketball games. What percent of its basketball games did Team X win? 1) Team X played the same number of basketball games as Team Y. 2) Team Y won 45 games, representing 62.5 percent of the basketball games it played.
#22. What kind of information is needed? The question stem tells us information on games won. So if we can determine the number of games Team X played, we could determine its winning percentage. 1) Insufficient. We know nothing of Team Y. Eliminate answer choices B, C, and E. 2)
When you know the sales prices of a $100,000 house and want to figure a 6% commission?
$100,000 x 0.06 = $6,000 Note that when you are determining the percentage, you multiply.
The national income of Country X is $1,800,000,000. If Country X has a population of 3 million, what is its per capita national income?
$600 per person
2. If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together? A. 2 hours and 24 minutes B. 3 hours and 12 minutes C. 3 hours and 44 minutes D. 4 hours and 10 minutes E. 4 hours and 33 minutes
(a)(b)/a+b (4)(6)/4 + 6 24/10 2.4 hours or 2 hours and 24 minutes A
One-half of Mario's age three years from now, plus one-third of his age four years now is equal to thirty-seven. How old is Mario now? A. 35 B. 37 C. 39 D. 41 E. 43
.5(M + 3) + .333(M + 4) = 37 .5M + 1.5 + .333M + 1.332 .8333M + 2.832 = 37 .8333M = 34.168 M = 41 D. 41 Yea! I got this one right.
An integer is divisible by 5 if its last digit is:
0 or 5
Sandwiches: Bread Types: white, wheat, ciabatta Cheeses: American, swiss, provolone Type: turkey, roast beef, ham, veggie How many sandwiches have ciabatta bread?
1 * 3 * 4 = 12
Kaplan's answer choice method
1 2 TEN or 1, 2, Together, Either, or Neither
How many meters will a satellite travel in 1 minute if it travels at an average speed of 18 meters per second?
1 minute = 60 seconds 18 = d/60 d = 18(60) = 1080
The Kaplan Method of Value Questions, Page 28 of the Kaplan Coursebook. 25. What is the value of x? 1) x^2 - 9 = 16 2) 3x(x - 5) = 0
1) 1) x^2 - 9 = 16 Is insufficient since x^2 could be 5 or -5. 2) 3x(x - 5) = 0 Is insufficient it could be 0 or -5. Answer choice C.
What is true about every Argument Essay?
1. Every argument essay will have at least one assumption to identify, 2. There will be a flaw, 3. Your opinion will never matter, 4. You will use the same skills as critical reasoning.
How do you examine the statements in Data Sufficiency?
1. Look at the first statement. If sufficient, the answer is either A or D. If insufficient, the answer must be B, C, and E. 2. Look at the second statement. If insufficient the answer is either C or E. 3. Combine them.
Check your knowledge of Odd/Even rules 1. Odd + Odd = ? 2. Odd - Even = ? 3. Even + Odd = ? 4. Odd x Odd = ? 5. Odd / Even = ? 6. Odd x Even = ?
1. Odd+Odd = 1+1 = 2 (Even) 2. Odd - Even = 3 - 2 = 1 (Odd) 3. Even + Odd = 2 + 1 = 3 (Odd) 4. Odd x Odd = 3 x 3 = 9 (Odd) 5. Odd/Even= 3/ 2 = 1.5 (Not an integer!) 6. Odd x Even = 3 x 2 = 6 (Even)
What is the Kaplan Essay template?
1. Put it in your own words. 2. Identify the first flaw (your strongest argument). 3. Identify the second flaw. 4. Suggest how to strengthen the argument. 5. Conclude you're not persuaded.
What are the three steps in Data Sufficiency?
1. Write out the grid: A D B C E 2. Write out all given information and simplify. 3. Rephrase the question to include all correct answers.
Does 2m - 3n = 0? 1) m ≠ 0 2) 6m = 9m
1. Write out the grid: A D B C E 2. Write out all given information and simplify. 3. Rephrase the question to include all correct answers. 1) m ≠ 0 Well, I have an "x" written next to this which leads me to believe that just knowing that m is not 0 doesn't help enough to make it sufficient 2) 6m/3 = 9m/3 is what I have written down, so apparently the first step toward solving this was to to reduce it to 2m = 3n Miller wrote "match" next to this, so I guess if 2m = 3n then 2m - 3n = 0 Again, it doesn't seem necessary to solve the problem, just see if you actually need the information from 2 to solve it. Answer choice "B"
A certain group of car dealers agree to donate x dollars to a Red Cross chapter for each car sold during a 30 day period. What is the total amount that was expected to be donated? 1) A total of 500 cars were expected to be sold 2) 60 more cars were sold than expected, so that the total amount actually donated was $28,000
1. Write out the grid: A D B C E 2. Write out all given information and simplify. 3. Rephrase the question to include all correct answers. 1) n = 500 2) (60 + n)x = $28,000 n = the number of cars sold x = the amount of money per car (x)(n) = ? I see in my notes that the correct answer is C, which is "together". If I recall, it doesn't matter whether we actually find out how much money was expected to be donated or not, just that we know that both parts are needed in order to find the answer.
When a player in a certain game tossed a coin a number of times, 4 more heads than tails resulted. Heads or tails resulted each time the player tossed the coin. How many times did heads result? 1) The player tossed the coin 24 times 20 The player received 3 points each time heads resulted and 1 point each time tails resulted, for a total of 52 points.
1. Write out the grid: A D B C E 2. Write out all given information and simplify. 3. Rephrase the question to include all correct answers. Given: H = T + 4 1) T + H = 24 2) 3H + T = 52 Both answers are checked, so I assume this was C or "together"
0.5% is expressed as a fraction as . . .
1/200 (believe it or not). Note that 0.5% is 0.005 if expressed as a decimal.
12/25 + 13/5 =
12/25 + 65/25 = 77/25
Sandwiches: Bread Types: white, wheat, ciabatta Cheeses: American, swiss, provolone Type: turkey, roast beef, ham, veggie Probability of choosing a sandwich with ciabatta bread?
12/36 = 1/3
A fair coin is tossed 5 times. What is the probability that it lands heads up at least twice? 1/16 5/16 2/5 13/16 27/32
13/16
"40% of what amount is $160?" Let me give you a short way or formula. "is/of = %/100" is = 160 of = x % = 40
160/x = 40/100 160 * 100 = x * 40 16,000 = 40x 16,000/40 = x x = $400 is the answer
In 8 hours, a factory produces 176,000 wing nuts. How many wing nuts does the factory produce per hour?
176,000/8 =22,000 wingnuts
Bob, Harry, and Mark are searching for golf balls that they can resell. So far, they have collected a total of 180 golf balls from one's day work. Bob found three times the amount that Harry found, and Harry has found 25 fewer than Mark has found. How many golf balls has Mark found? A. 31 B. 48 C. 56 D. 60 E. 64
180 = B + H + M B = 3H H = M - 25 Another "double switch" problem. 180 = 3 M - 25 + M - 25 + M 180 = 5M - 50 230 = 5M 230/5 = 5M/5 M = 56 C. 56 Yea! I got this one right.
An integer is divisible by 2 if its last digit is divisible by:
2
Tossing two coins: 2 options and 2 tosses (H or T) Options for coin 1: 2 Options for coin 2: 2 x 2 x 2 then multiply across
2 * 2 = 2^2 = 4
Tossing three coins:
2 options (H or T) 3 tosses 2 times itself 3 times: 2 * 2 * 2 = 2^3 = 8
Six coins:
2 options for each coin: 2 x 2 x 2 x 2 x 2 x 2 2 * 2 * 2 * 2 * 2 * 2 = 2^6 = 64
Pasta Selection: Noodles: angel hair, penne, elbow, bowtie Meat: ground beef, sausage, meatballs, no meat Sauce: alfredo, marinara What is the probability of ordering a pasta dish with angel hair and meatballs?
2/32 = 1/16
A bowl has only 5 apples and 5 bananas. If one piece of fruit is selected from the bowl at random, and a second piece is selected from the bowl without replacing he first, what is the probability that both pieces of fruit chosen were apples? 1/10 2/9 1/5 2/5 1/2
2/9
Example 4: Kentucky Derby Exacta Bet: If you bet on the Kentucky Derby and want to pick the win and place horses of a 20 horse race, what are the odds you'll be a winner?
20! (20 - 2)! 20! (18)! 20 x 19 380 Yikes! The odds of winning are 380 to 1. Better hope there's some good money in the parimutuel pool. But what if we decided we wanted to win some big money and bet the Trifecta, where you have to pick the order of the first three finishing horses.
But what if we decided we wanted to win some big money and bet the Trifecta, where you have to pick the order of the first three finishing horses. How would those odds compare with the Exacta?
20! (20 - 3)! 20! (17)! 20 x 19 x 18 6,840 The odds of winning the Trifecta are 6,840 to 1. And, duh, as if I needed to say it, this is a permutation, since order matters.
Catherine went to the store to buy hamburgers and hot dogs for a barbeque. However, when she arrived home she realized that she forgot a bag, containing 14 hamburgers, at the store. Because of this she now has 1/3 as many hamburgers as hotdogs. However, before she lost the bag she had a combined total of 214 hamburgers and hotdogs. What was the original number of hamburgers purchased? A. 64 B. 56 C. 48 D. 36 E. 27
214 = H The answer is A
25. Of the following units, which would be most likely to measure the amount of sugar needed in a recipe for 2 dozen cookies? A. degrees Celsius B. milliliters C. quarts D. kilograms E. cups
25. E
26. Jim has 5 pieces of string. He needs to choose the piece that will be able to go around his 36-inch waist. His belt broke, and his pants are falling down. The piece needs to be at least 4 inches longer than his waist so he can tie a knot in it, but it cannot be more that 6 inches longer so that the ends will not show from under his shirt. Which of the following pieces of string will work the best? A. 3 4/5 feet B. 3 2/3 feet C. 3 3/8 feet D. 3 1/4 feet E. 2 1/2 feet
26. C
27. After purchasing a flat screen television for $750, John realizes that he got a great deal on it and wishes to sell it for a 15% profit. What should his asking price be for the television? A. $800.30 B. $833.60 C. $842.35 D. $862.50 E. $970.25
27. D
28. If 300 jellybeans cost you x dollars. How many jellybeans can you purchase for 50 cents at the same rate? A. 150/x B. 150x C. 6x D. x/6 E. 1500x
28. A
GRE Text, Page 297, problem 8. How many 3 digit positive integers are odd and do not contain the digit "5"?
288 distinct 3-digit positive odd integers without the digit 5 Start with all three digit numbers (100 through 999): 999-100+1 = 900 Remove the evens (50% of those remaining): 900 * 0.50 = 450 Remove those beginning with 5 (ie. the "500's"). There are 50 odd integers in the 500's, so we are left with: 450 - 50 = 400 Remove those *ending* in 5. Since only the odds remain, 1 out of 5 will end in "5". So remove 20%: 400 * (1-0.20) = 400 * .80 = 320 Remove those with 5 in the middle. In this case, 1 out of 10 numbers will have a 5 in the middle, so remove 10%: 320 * (1-0.10) = 320 * .90 = 288
Example 2: Historical Events: Here we have three occurrences: a) Boston Tea Party, b) Teapot Dome, and c) The Civil War. If one were to guess the answer how they occurred in chronological order the answer would be:
3 x 2 x 1 = 6 possible answers. Since you have only one guess, the probability of getting the correct answer simply by chance is 1/6 or 0.167. Note that in this case you use the factorial since answer choices/occurrences are used as you complete your answer.
The weighted average formula for, say, mileage is . . .
3(50) + 2(60)/2+3 = 270/5 = 54 Very similar to the work formula.
6,930 is not a multiple of 4 since:
30 is not a multiple of 4.
30. Lee worked 22 hours this week and made $132. If she works 15 hours next week at the same pay rate, how much will she make? A. $57 B. $90 C. $104 D. $112 E. $122
30. B
An airplane travels a 1,200 mile route in 4 hours. What is the airplane's average speed for the trip?
300 miles per hour
An integer is divisible by 4 if its last two digits are a multiple of:
4
Pasta Selection: Noodles: angel hair, penne, elbow, bowtie Meat: ground beef, sausage, meatballs, no meat Sauce: alfredo, marinara How many possible pasta dishes are there?
4 * 4 * 2 = 32
4(1/3 + 1/12) = ?
4(1/3 + 1/12) 4 (1/3 * (4) + 1/12) 4 (4/12 + 1/12) 4 * 5 1 12 20 12 1 8/12 or 1 2/3
7. Alfred wants to invest $4,000 at 6% simple interest rate for 5 years. How much interest will he receive? A. $240 B. $480 C. $720 D. $960 E. $1,200
4,0000 x .06 x 5 = $1,200 E
40. Sarah has a 20 dollar bill and a 5 dollar bill. If she purchases two items, one for $11.23 and the other for $8.32, then how much money does she have left over? A. $3.75 B. $5.45 C. $6.34 D. $7.77 E. $8.12a
40. B
A bowl contains only 5 apples and 5 bananas. If one piece of fruit is selected from the bowl at random, and a second piece is selected from the bowl without replacing the first, what is the probability that both pieces of fruit chosen are apples?
5 apples 5 bananas 10 total pieces of fruit 1st apple = 5 = 1 10 2 New total = 9 total fruit: 4 apples and 5 bananas or 4/9 1 4 = 4 2 * 9 18 2/9
Example 7: The Florida Lottery: You play the Florida Lottery by selecting six numbers between 1 and 53. Obviously you only pick one number once. So, what are your odds of winning, since there is only one winner?
53! . 6! (53 - 6)! 53! . 6! (47)! 53 x 52 x 51 x 50 x 49 x 48. 6 x 5 x 4 x 3 x 2 x 1 16, 529, 385, 600. 720 22, 957, 480 to 1 are the odds of winning the Florida Lottery. Note that this is the same format of problem as the Lisa Plant problem with the apartment cabling, only there you subtract 1 at the end. In the Kaplan booklet they show this as a Combination problem and the formula as the Combination formula. Of course, there is no replacement in this particular case (the Florida Lottery) and you don't care what order the numbers are in.
6,930 is a multiple of 3, since:
6 + 9 + 3 + 0 = 18, which is a multiple of 3.
Convert 6 miles per hour to feet per second
6 miles/1 hour 5280/1 miles 1 hour/3600 seconds Now multiply across and get: 31,680/3,600 = 8.8 fps
29. If 6 is 24% of a number, what is 40% of the same number? A. 8 B. 10 C. 15 D. 20 E. 25
6 ÷ 0.24 = 25 25 x .4 = 10 29. B
1/2 + 1/3 + 1/4 = ?
6/12 + 4/12 + 3/12 = 13/12
6/21 + 7/3 =
6/21 + 7/3 (7/7) = 6/21 + 49/21 = 55/21
A pool drains at a rate of 600 gallons of water per hour. How many gallons of water will be drained from the pool in 1 1/4 hours?
600= g/1 1/4 g = 600(5/4) = 150(5) = 750
Page 15, Kaplan Textbook #2: Company Z spent 1/4 of its revenues last year on marketing and 1/7 of the remainder on maintenance of its facilities. What fraction of last year's original revenues did Company Z have left after its marketing and maintenance expenditures? 5/14 1/2 17/28 9/14 9/11
9/14 Let's say the company's revenue was 28/28. If they spent 1/4 of that on marketing or 7/28 they would have 21/28 left. If they spent 1/7 of the $21 on maintenance it would be $3. The math would be $21 - $3 = 18 So, 18/28 is 8/14s or answer D.
Is ax = 3 - bx? 1) x(a+b) = 3 2) a = b = 1.5 and x =1
A D B C E 1) ax = 3 - bx could be rewritten as: ax + bx = 3 This is the same as x(a + b) = 3 So answer choice 1 works 2) a = b = 1.5 and x =1 This means that x(a + b) = 3 is the same thing as 1(1.5 + 1.5) = 3 which as we already saw above is a valid answer. So answer choice 1 works, too Thus, the answer is D, or "either"
Find the slope of 9x + 12y = 4.
A: 3/4 B: 4/3 C: -3/4 D: -4/3
Convert 65% to a fraction.
A: 4/5 B: 13/20 C: 3/4 D: 7/10
60% of 3 is:
A:1 1/2 B: 1 4/5 C: 1 3/4 D: 1 5/8
AB + CD = AAA, where AB and CD are two-digit numbers and AAA is a three digit number; A, B, C, and D are distinct positive integers. In the addition problem above, what is the value of C? (A) 1 (B) 3 (C) 7 (D) 9 (E) Cannot be determined
AB + CD = AAA Since AB and CD are two digit numbers, then AAA must be 111. Therefore 1B + CD = 111 B can assume any value between 3 and 9 If B = 3, then CD = 111-13 = 98 and C = 9 If B = 9, then CD = 111-19 = 92 and C = 9 So for all B between 3 & 9, C = 9 Therefore the correct answer is D (C = 9)
The average annual rainfall in Boynton for 1976 to 1979 was 26 inches per year. Boynton received 24 inches of rain in 1976, 30 inches in 1977, and 19 inches in 1978. How many inches of rainfall did Boynton receive in 1979?
Another way to find a missing number is to understand that the sum of the differences between each term and the mean of the set must equal zero. plugging in the numbers from the previous problem, for example, we find that (24 - 26) + (30 - 26) + (19 - 26) 1 (inches in 1979 - 26) = 0 (22) + (4) 1 (27) 1 (inches in 1979 - 26) = 0 -5 + (inches in 1979 - 26) = 0 inches in 1979 = 31 It may be easier to comprehend why this is true by visualizing a balancing, or weighting, process. the combined distance of the numbers above the average from the mean must be balanced with the combined distance of the numbers below the average from the mean.
Page 18, Kaplan Course Book: In order to fulfill a local school's request for cakes B mothers agreed to bake an equal number of cakes. If P of the mothers did not bake any cakes, which of the following represents the additional number of cakes that each of the other mothers had to bake in order for the school's request for x cakes to be fulfilled? px/B px/B(B-p) x/B - p p/B - px p/B(B - p)
Answer B. Let's try: x = 80 B = 10 p = 2 If all 10 mothers bake their share, then each mother must bake 8 cakes. If two mothers don't bake any cakes, then each of the remaining 10 - 2 = 8 mothers must bake 80/8 = 10 cakes. So the additional number of cakes that each mother must bake is 10 - 8 - 2. Only answer choice B equals 2 when x = 80, B = 10, and p = 2.
22. Which of the following fractions is the equivalent of 0.5%? A. 1/20 B. 1/200 C. 1/2000 D. 1/5 E. 1/500
Answer Key 22. B
24. Over the course of a week, Fred spent $28.49 on lunch. What was the average cost per day? A. $4.07 B. $3.57 C. $6.51 D. $2.93 E. $5.41
Answer Key 24. A
10. Melinda's lights went out. She has 3 pairs of red socks in her drawer, 2 pairs of black socks, and 5 pairs of white socks. What is the minimum number of pairs she must remove from the drawer to ensure that she has a pair of each color? A. 3 B. 5 C. 7 D. 9 E. 10
Answer Key 10. D
11. 5 is 2/3% of n Column A: n Column B: 15
Answer Key 11. A
18. 22% of $900 = A. 90 B. 198 C. 250 D. 325 E. 375
Answer Key 18. B
32. A hockey team won 6 games and lost 8. What is the ratio of wins to number of games? A. 6/8 B. 8/6 C. 3/7 D. 8/14 E. 6/7
Answer Key 32. C
5. 35% of what number is 70? A. 100 B. 110 C. 150 D. 175 E. 200
Answer Key 5. E
6. -32 + 7 equals: A. -25 B. 25 C. -26 D. 26 E. 27
Answer Key 6. A
6. If 34% of 360 equals 7.5% of h, what is h? Column A: h Column B: 1634
Answer Key 6. B
6. What is the absolute value of -9? A. -9 B. 9 C. 0 D. -1 E. 1a
Answer Key 6. B
Brian has $1 more than four times the amount of money Anna has. If three times the amount of money that Brian has is subtracted from twice the amount of money that Anna has, the result is $-43. How much money does Brian have? A. $19 (B) $18 (C) $17 D. $16 (E) $15
Answer: C
The temperature in Boston on Saturday was eight degrees less than four times the temperature on Friday. If six times the temperature on Saturday was subtracted from twice the temperature on Friday, the result is four degrees. What was the temperature on Saturday? (A). 3 degrees (B) 2 degrees (C) 1 degree (D) 0 degrees (E) -1 degree
Answer: D
10. If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how long would the job take if Sam, Lisa, and Tom worked together to complete it? A. 0.8 days B. 1.09 days C. 1.23 days D. 1.65 days E. 1.97 days
B
15. Lee worked 22 hours this week and made $132. If she works 15 hours next week at the same pay rate, how much will she make? A. $57 B. $90 C. $104 D. $112 E. $122
B
If x > 0, what is the value of x? 1) x > 5 2) 40 - x^2 = 4
B. Note that when you see a squared exponent, there are two possible answers (+/-). In this case, +/- 6
1. Convert 65% to a fraction. A: 4/5 B: 13/20 C: 3/4 D: 7/10
B. Convert the percentage to the fraction 65/100, then simplify by dividing numerator and denominator by 5.
Page 18, Kaplan Course Book: If x/3 is an integer, each of the following must also be an integer EXCEPT: x+6/6 x-9/3 x+9/3 8x/24 x^4 - 81/81
Because there are variables in both the questions and answer choices, picking numbers works well. Pick a number for x that is divisible by 3, in order to make x/3 an integer. When x = 3 the answer choices become: 3+6/6 = 3/2 3-9/3 = -2 3+9/3 = 4 8(3)/24 = 1 3^4 - 81/81 = 0 Of these choices, A is the non-integer.
Integer x is evenly divisible by 2. Is x/2 even?
By definition, any multiple of 2 is even, so integer x is even.
17. You need to purchase a textbook for nursing school. The book cost $80.00, and the sales tax where you are purchasing the book is 8.25%. You have $100. How much change will you receive back? A. $5.20 B. $7.35 C. $13.40 D. $19.95 E. $21.25
C
Tara drove at an average speed of 50 miles per hour for the first 50 miles of her trip and then at an average speed of 75 miles per hour for the remaining 50 miles of her trip. If she made no stops during the trip, what was Tara's average speed, in miles per hour, for the entire trip? 50 55 60 65 70
C
If a word problem says "Eight years from now, Clara's age will be 4 times Ed's age" what do you write?
C + 8 = 4(E + 8) Let's break it down: Clara in eight years is "C + 8" Here's the tricky part: Ed's age will also be "+ 8" or "E + 8" because in eight years Clara will be eight years older, but so will Ed. Is that so hard to wrap your mind around? But one more thing: you put that "E + 8" in parenthesis and multiply it by 4, since Clara's age will be 4 times whatever Ed's is.
9. A bag contains 3 red, 4 black and 2 white balls. What is the probability of drawing a red and a white ball in two successive draws, each ball being put back after it is drawn? (A) 2/27 (B) 1/9 (C) 1/3 (D) 4/27 (E) 2/9
Case I: Red ball first and then white ball P1 = 3/9*2/9= 2/27 Case 2: White ball first and then red ball P2 = 2/9*3/9 = 2/27 Therefore total probability: p1 + p2 = 4/27
If there is no diagram on a geometry problem, it may mean that a drawing would make the answer obvious. So, draw one yourself. Column A: On a CUBE, the number of faces that share an edge with any one face. Column B: The number of sides of a SQUARE.
Considering our drawings above, you can see that any one face shares an edge with 4 other faces. Obviously, the number of sides of a square is 4. Hence, the answer is C.
15. What will it cost to tile a kitchen floor that is 12 feet wide by 20 feet long if the tile cost $8.91 per square yard? A. $224.51 B. $237.60 C. $246.55 D. $271.38 E. $282.32
Convert the 12x20 feet into units of yards: Area (in yards) = 4(20/3) = 80/3 sq yards 80/3 * 8.91 = $237.60 Ans: B
19. If edging cost $2.32 per 12-inch stone, and you want a double layer of edging around your flower bed that is 6 yards by 1 yard. How much will edging you flower bed cost? A. $32.48 B. $64.96 C. $97.44 D. $129.92 E. $194.88
Convert the flower bed from yardage to feet by multiplying by 3 (3 feet in a yard) Length = 6*3 or 18 feet Width = 1*3 or 3 feet then use the formula: Perimeter = 2*length + 2*width Perimeter = 2(18)+2(3) perimeter = 36 + 6 Perimeter = 42 feet But you want a double layer of edging, so you will need: 2 * 42 feet of edging 84 feet of edging If edging costs 2.32 per foot (12"stone = 1 foot) 84 feet * $2.32 = $194.88 total
1. If the average of three numbers is V. If one of the numbers is Z and another is Y, what is the remaining number? A. ZY - V B. Z/V - 3 - Y C. Z/3 - V - Y D. 3V- Z - Y E. V- Z - Y
D
22. The cost to ride on a ferry is $5.00 per vehicle and driver with an additional cost of 50 cents per passenger. If the charge to get on the ferry is $6.50, how many people were in the vehicle? A. 1 B. 2 C. 3 D. 4 E. 5
D
26. Find the missing term in the following sequence: 4, 9, 19, __, 79 A. 36 B. 37 C. 38 D. 39 E. 40
D
4. Two angles of a triangle measure 15° and 85 °. What is the measure for the third angle? A. 50° B. 55° C. 60° D. 80° E. 90°
D
When you know the amount of the discount and the discounted price . . .
Divide the price by the reciprocal of the amount of the discount. Example: a suit is on sale for 60% off for $160. What was the original price? 160 ÷ .4 = $400 However, if the discount was 40% the price of the suite would be $266.67. Note that you divide in both cases where you are trying to determine the price. This is similar to #355
The most efficient way to backsolve is to plug in either B or D first. You will have a 40% chance of determining the correct answer with your first effort.
Don't assume that the information is given to you in the most helpful order.
Another way to do the multiplication rule:
Draw one blank for each time a choice will be made. Ask yourself how many options for that space, and write the number down in the space. Do the same for each space and then multiply all the numbers.
6. Which of the following is not a rational number? A. -4 B. 1/5 C. 0.8333333... D. 0.45 E. the square root of 2
E
If an item is purchased for x percent less than its retail price, and then sold for y percent less than its retail price, what was the retail price of the item? (1) x - y = 10 (2) y = 5
E
Running at the same constant rate, identical machine "a" can produce a total of 120 bolts per minute. At this rate, how many bolts could 4 such machines produce in 5 minutes? a/6 a/600 150/a 480/a 2,400/a
E
Steve and Carl each received an increase in salary. Which one received the larger percent increase? (1) Steve's salary increased by $1,000 per month. (2) Carl's salary increased by $1,200 per month
E
Eric is thirty-four years younger than Lauren. In four years, Lauren will be twice as old as Eric. How old is Lauren now? A. 64 B. 65 C. 66 D. 67 E. 68
E = L - 34 L = 2E + 4 L = 2(L - 34) + 4 L = 2L - 68 + 4 L = 64 A. 64 Yea! I got this one right.
8. A person buys a share for $50 and sells it for $52 after a year. What is the total profit made by him from the share? (I) A company pays annual dividend (II) The rate of dividend is 25% (A) Statement (I) ALONE is sufficient, but statement (II) alone is not sufficient (B) Statement (II) ALONE is sufficient, but statement (I) is not sufficient (C) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient (D) Each statement ALONE is sufficient (E) Statements (I) and (II) TOGETHER are NOT sufficient
E, since you don't know what the stock price was when the 25% dividend was paid.
What is the distance from Town A to Town B, in miles? 1. If Steve had traveled from Town A to Town B at an average speed that was 10 miles per hour faster, he would have traveled for 5 fewer hours. 2. If Steve had traveled from Town A to Town B at an average speed that was 50 percent greater, the amount of time he would have traveled would have been the time it actually took reduced by 1/3 of the the time it actually took.
E.
The Kaplan Method of Value Questions, Page 31 of the Kaplan Coursebook. 31. Is 0 < a/b < 1? 1. ab > 1 2. a - b < 1
E. Step 1: Determine, from the question stem, what kind of information is needed to answer this question? Here a statement would be sufficient yes if it showed that a/b is always a positive fraction less than 1, and sufficient if it showed that a/b is always something other than a positive fraction less than 1. Maybe Picking Numbers would simplify this. Step 2: Evaluate each statement individually. Statement 1: Insufficient. CASE 1: (-3)(-2) > 1 No CASE 2: (2)(3) > 1 Yes Statement 2: Insufficient. The same cases from 1 apply here. Step 3: Combine the statements if necessary. Combined statements: Insufficient. Since the same cases applied to both statements, combining the statements in Step 3 adds no new information to the analysis.
Eight years ago, Julie was four times as old as Bob was then. If Julie is now six years older than Bob, how old is Julie? A. 6 B. 10 C. 12 D. 16 E. 30
Equation #1: J - 8 = 4(B - 8) Equation #2: J = B + 6 B + 6 - 8 = 4B - 32 B - 2 = 4B - 32 30 = B3 10 = B 10 + 6 = 16, so Julie is 16 years old D. 16 Yea! I got it right!
A girl is three times as old as her younger sister. In four years, she will be twice as old as her younger sister. How old is the girl now? A. 4 B. 12 C. 15 D. 18 E. 21
Equation 1: G = 3S Equation 2: 4 + G = 2(4 + S) Plug in the numbers: 4 + 3S = 8+ 2S S = 12 B. 12 Yea! I got this one right.
Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections of the 4 items can she make? A 9 B 12 C 14 D 15 E 60
First of all, this is an "unordered formula" question. The formula that we will use with BOTH of the two items to determine how many can be selected: N! K! (N-K)! Board games: 6! 3! (6 - 3)! 6! 3! (3)! 6 x 5 x 4 x 3 x 2 x 1 3 x 2 x 1 (3 x 2 x 1) 6 x 5 x 4 = 120 = 20 3 x 2 x 1 6 Balls: 3! 1! (3 - 1)! 3! 1! (2)! 3 x 2 x 1 = 6 = 3 2 x 1 2 So 20 x 3 = 60 or Answer Choice D
y = x2 + 1 Column A: x y Column B: x + y
First plug in some easy numbers like 3 for x and 4 for y. Then Column A is 12 and Column B is 6. We can now eliminate choices B and C. Now try some of the numbers we mentioned above that have special properties. Try 0 for x and 0 for y since there is no condition that x and y must be different. Then Column A and Column B are both 0. By finding just one situation in which A is not greater than B, we've eliminated choice A. Hence, the answer is D.
Jacob is now 12 years younger than Michael. If 9 years from now Michael will be twice as old as Jacob, how old will Jacob be in 4 years?
First set up the problem. The first sentence is written "Jacob is now 12 years younger than Michael" but written "Michael = Jacob + 12" The second sentence is written "M + 9" or Michael in nine years equals Jacob in nine years times two ("twice as old"). M = J + 12 M + 9 = 2(J + 9) Now just do the algebra: J + 12 + 9 = 2J + 18 J + 21 = 2J + 18 J + 21 = 2J + 18 3 = J 4 + 3 = 7 Jacob will be 7 years old in 4 years.
24. In his pocket, a boy has 3 red marbles, 4 blue marbles, and 4 green marbles. How many will he have to take out of his pocket to ensure that he has taken out at least one of each color? A. 3 B. 7 C. 8 D. 9 E. 11
He will have to remove all 4 blue, followed by all 4 green, followed by at least 1 red. That would be the maximum number of draws to get at least one of each color: In other words, you have to assume that you will be exceedingly unlucky while drawing marbles so that not until the last possible moment will you have drawn enough. Ans: 9 This is similar to problem 182.
Test Day Tip: On GMAT questions that ask test takers to calculate a percent increase, a common trap answer is for test takers who calculate the final amount as a percent of the original
Hint: Don't lose sight of what is being asked.
12. How many cubed pieces of fudge that are 3 inches on an edge can be packed into a Christmas tin that is 9 inches deep by 12 inches wide by 8 inches high with the lid still being able to be closed? A. 18 B. 24 C. 32 D. 36 E. 43
I've seen two answers for this, the first of which (while elegant) ignores the fact that you can't squish the fudge. The volume of the fudge is 3*3*3 = 27 cubic inches. The volume of the pan is 9*12*8 = 864 cubic inches 864/27 = 32 Ans: C (I believe this is wrong) I drew it out and came up with 24 pieces.
At Store T, the dollar amount of sales for 2007 was what percent of the dollar amount of sales of 2008?
If A is the dollar amount of the sales at Store T for 2007, then 8 percent of A, or 0.08A, is the amount of decrease from 2007 to 2008. Thus A-0.08A = 0.92A is the dollar amount for 2008. Therefore, the desired percent can be obtained by dividing A by 0.092A, which equals: A/0.92A = 1/0.92 = 1.087 or 108.7%
One of the benefits of knowing the Data Sufficiency answer choices well is that, each time you evaluate a statement, you can eliminate a few choices. Consider the following:
If Statement (1) is sufficient, (B), (C), and (E) are eliminated. If Statement (1) is insufficient, (A) and (D) are eliminated. If Statement (2) is sufficient, (A), (C), and (E) are eliminated. If Statement (2) is insufficient, (B) and (D) are eliminated.
Here are two more ways you can eliminate choices. These are a little more complicated, and I'll focus on them in future tips.
If Statements (1) and (2) say the exact same thing, (A), (B), and (C) are eliminated. If a statement repeats something that the question tells you, or provides no information whatsoever, that statement's choice [(A) or (B)] and (C) are eliminated.
"40% of what amount is $160?" How can you back into the original price?
If you know that $160 is 40% of the original price, then doubling it will get you to 80%, right? 160 x 2 = 320 And if $160 is 40%, then $80 would be the last 20%, wouldn't it? So . . . . 160 + 160 + 80 = $400
Hint: In "must be/could be' questions, test takers must use the answer choices. So picking nubers
In "could be" questions test takers can usually avoid checking all of the answer choices
In a certain bag, what is the ratio of the number of red marbles to the total number of marbles? (1) the ratio of the number of red marbles to the number of blue marbles in the bag is 3:5. (2) there are only red and blue marbles in the bag. Information to answer the question, so the answer is (C).
In this case, statement (1), by itself, is insufficient. You cannot convert a part to part ratio (red marbles to blue marbles) to a part to whole ratio (red marbles to all marbles) because you don't know whether there were any other colored marbles in the bag. Only when you combine the two statements do you have enough
Of the 25 people in Fran's apartment building, what is the ratio of people who use the roof to total residents? (1) there are 9 residents who use the roof for tanning and 8 residents who use the roof for gardening. (2) the roof is only used by tanners and gardeners.
In this question we do not know if there is any overlap between tanners and gardeners. How many, if any, residents do both? Since we don't know, the answer is (E).
18. A cyclist bikes x distance at 10 miles per hour and returns over the same path at 8 miles per hour. What is the cyclist's average rate for the round trip in miles per hour? A. 8.1 B. 8.3 C. 8.6 D. 8.9 E. 9.0
It is a question of average Speed. It has to be solved in three parts. 1. Going from A to B 2. Going from B to A 3. Average Speed 1. Going from A to B Distance = d1 = x miles Speed = s1 = 10 miles per hour Time = t1 = Distance/ Speed = x/10 2. Going from B to A Distance = d2 = x miles Speed = s2 = 8 miles per hour Time = t2 = Distance/ Speed = x/8 3. Average Speed = Total Distance/Total Time Total Distance = x + x = 2x Total Time = x/10 + x/8 = x (1/10 + 1/8) = x ( 4 + 5)/40 = 9x/40 Speed = 2x/(9x/40) = (2x * 40)/9x = 80x/9x = 80/9 = 8.9 [email protected]
If the question asks about two people (or two paintings, or whatever) in the future or the past, then you have to (?) For example, "In ten years, Jeff will be three times as old as Pat is then" would be written:
J + 10 = 3(P + 10) 1) raise or lower both sides of the equation by the same amount and, 2) multiply the lesser side by whatever factor is stated in the problem to increase it so that it matches the other side of the equation.
Jeff is five times as old as Pat. In ten years, Jeff will be three times as old as Pat is then. What is the sum of their current ages?
J = P x 5 J + 10 = 3(P + 10) P5 + 10 = 3(P + 10) P5 + 10 = P3 + 30 P2 = 20 P = 10 Pat is 10 years old, so Jeff must be 50. Their combined ages are 60.
Jane makes toy bears. If she has an assistant she can make 80% more bears per week & works 10% fewer hours. How much does the assistant increase her productivity?
Jane could make 100 bears. If she has an assistant this is increased by100 bears x 80% = 80 bears. So, 100 bears + 80 bears = 180 total bears Production time of 100 hours x 10% reduction is 10 hours 100 hours - 10 hours = 90 hours of work time Her original bears per hour = 100/100 Jane's new bears per hour = 180 bears/90 hours = 2 2 x 100% = 200% increase in productivity
Janelle and Karl both sell insurance. This year, Janelle has sold $60,000 less than Karl has. If Janelle sells $3,200 per day and Karl sells $2,000 per day, how many days will it take before Janelle catches up with Karl and moves $12,000 ahead?
Janelle sells $1,200 per day more. To catch up, she needs to sell $60,000 more than Karl, and to get $12,000 ahead, she needs to sell a total of $72,000 more. To sell $72,000 more at a rate of $1,200 more per day, it will require 72,000/1,200 = 720/12 = 60 days.
r, s, and t are three odd consecutive integers such that: r < s < t Quantity A: r + s + 1 Quantity B: s + t - 1
Just a note: the first time I did this I didn't notice the "consecutive" and "odd" parts. I would have gotten it wrong. The correct answer is B.
8. Jim is able to sell a hand-carved statue for $670 which was a 35% profit over his cost. How much did the statue originally cost him? A. $496.30 B. $512.40 C. $555.40 D. $574.90 E. $588.20
Let original cost be "x" x + 0.35x = 670 1.35x = 670 x = $496.30 A
1. An instrument store gives a 10% discount to all students off the original cost of an instrument. During a back to school sale an additional 15% is taken off the discounted price. Julie, a student at the local high school, purchases a flute for $306. How much did it originally cost? A. $325 B. $375 C. $400 D. $408 E. $425
Let x = original cost Let .90x = the amount the student pays (100%-10% = 90%) Let .85(.90x) = the sales price (100%-15%=85%) If the sales price = 306, then .85(.90x)=306 .765x=306 x=$400 So the original cost was $400 This makes sense because $40 was taken off for the student discount, bringing the sales price to $360 and an additional 15% of 360 = $54, so $360-$54 = $306
3. Jim can fill a pool carrying buckets of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ½ hours. How quickly can all three fill the pool together? A. 12 minutes B. 15 minutes C. 21 minutes D. 23 minutes E. 28 minutes
Let's deal in minutes Let x=amount of time it takes all three working together to fill the pool. Jim fills at the rate of 1/30 pool per min Sue fills at the rate of 1/45 pool per min Tony fills at the rate of 1/90 pool per min Together they fill at the rate of 1/30 + 1/45 + 1/90= 3/90 + 2/90 + 1/90=6/90 =1/15 pool per min, so our equation to solve is: (1/15)x=1 (1 pool that is) multiply each term by 15 x=15 min is the time it takes all three working together. Check: Jim: (1/30)*15=1/2 Sue: (1/45)*15=1/3 Tony (1/90)*15=1/6 1/2 +1/3 +1/6 =3/6 + 2/6 + 1/6=6/6 1=1
16. In a writing competition, the first place winner receives 1⁄2 of the prize money. The second runner up receives 1⁄4 of what the winner won. What was the total amount of prize money distributed if the winner receives $6,000? A. $6,000 B. $8,500 C. $12,000 D. $15,000 E. $18,500
Looks as though this problem gave you MORE information than necessary. From the first sentence alone you can get your answer of $12,000. Ans: C
If 9 years from now Michael will be twice as old as Jacob, how old will Jacob be in 4 years?
M + 9 = 2(J + 9) THIS IS IMPORTANT: PARENTHESIS ONLY GO AROUND ONE SIDE OF THE EQUATION. IF YOU PUT THEM ON BOTH YOU'LL GET THE WRONG ANSWER.
Of the 5 wires that lead into an apartment, 2 are for cable TV service and 3 are for phone. Using these wires, how many distinct combinations of 3 wires are there such that at least 1 of the wires is for cable TV? 6 7 8 9 10
N K! (N-K)! N = the big number K = the small number N = 5 K = 3 5 x 4 x 3 x 2 x 1 --------------- 3 x 2 x 1 (5-3) 20 2 = 10 10 - 1 = 9 or answer choice D
Megan is nine years older than Brian. Thirteen years ago, Megan was twice as old as Brian. How old is Brian? A. 22 B. 24 C. 26 D. 28 E. 30
Note: In the second sentence it says "thirteen years ago" which means that you only subtract 13 from one side of the equation. Equation #1: M = B + 9 Equation #2: M = 2B -13 Solve by substitution: B + 9 + 13 = 2B - 13 + 13 B + 22 = 2B B - B + 22 = 2B - B 22 = B A. 22 Yea! I got it right!
Column A: 100 × 7.39 Column B: 739
Now it's obvious that the two quantities are equal. The answer is C.
The probability of an outcome . . .
Number of desired outcomes/ Number of total possible outcomes
On Roman numeral questions, test the options that appear most often in the answer choices and try to eliminate answer choices that way.
On "which of the following questions" the answers are weighted disproportionately toward D and E.
What are the probability and sample space for a single coin toss?
One coin: S = [H, T] n=2
Example 6: Drug Clinical Trial. In this case there are two possibilities: that order counts and that order doesn't count. In this case the question stem offers that in a clinical drug trial the company might want to test people one at a time (in sequence) and cancel the test if anyone has a strong negative reaction. (We'll call it the Merck v. Pfizer drug trials). Thus, order counts:
Order counts, so it's a permutation: n! . (n - r)! 10! . (10 - 8)! 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1. 2 x 1 Of course, here you can cancel out the "2 x 1" in both the numerator and denominator. 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 = 1,814,400 As you begin to see, the longer the string of multiplications in the numerator the bigger the answer will be. In the other example, the drug maker (Pfizer) doesn't really care if there is a negative reaction or not and just administers all the tests on on the same day. Order doesn't count, thus it's a combination: n! . r!(n - r)! 10! . 8!(10 - 8)! 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1. 8!(2)! Of course, here again you cancel out the upper and lower terms: 10 x 9 2 x 1 90 2 And so the answer is 45. Here's the interesting thing: with the permutation (order matters) the answer is 1,814,400 while the combination (order doesn't matter) the answer is 45.
GRE Text, Page 297, problem 9. From a box of 10 lightbulbs, you remove 4. How many different sets of 4 lightbulbs could you remove?
Order matters, so use the n choose k formula: 10! 4! (10 - 4)! 10! 4! (6)! 10 x 9 x 8 x 7 4 x 3 x 2 x 1 5,040 24 120
3. Employees of a discount appliance store receive an additional 20% off of the lowest price on an item. If an employee purchases a dishwasher during a 15% off sale, how much will he pay if the dishwasher originally cost $450? A. $280.90 B. $287 C. $292.50 D. $306 E. $333.89
Original cost: $450 15% off original cost: 450 - .15(450) = 450(1-.15) = 450(.85) = $382.5 addition 20% discount for employee: 382.5 - .20(382.5) = 382.5(1-.20) = 382.5(.80) = $306 . Answer: D
A target shooter participates in 2 tournaments. She has a 20 percent chance of winning the first tournament and a 30 percent chance of winning the second tournament. What is the probability that she will win exactly one of them? A 6% B 14% C 28% D 38% E 50%
P (win first) x P (lose first) P (lose second) x P (win second) .2 x .7 .8 x . 3 (.2)(.7) + (.8)(.3) (note that you can reverse the W/L probabilities, only) .14 + .24 = .38 D. 38%a
Pam will be B years old in A years from now. How old will she be in C years from now. A. A + B + C B. A + B - C C. -A + B - C D. B + C E. -A + B + C
Pam will be B years old in A years from now. How old will she be in C years from now? B = 20, A = 5, C = 10 If Pam's age today is 15 years old, then 15 + 10 = 25 So if you were to plug the numbers into the equation, it would look like this: -(A) + (B) + (C) which is the answer. -(5) + (20) + (10) = 25 E. -A+B+C
y = 2x^2 + 7x -3 Which is greater: Quantity A: (x) Quantity B: (y)
Picking numbers is the way to solve this: Solve the equation by substituting 0 for x: y = 2(0)^2 + 7(0) - 3 y = - 3 Now substitute 1 for x: y = 2(1)^2 + 7(1) - 3 y = 2+ 7 - 3 y = 9-3 y = 6 In the first case x (or 0) was greater than y (-3). In the second case, x (or 1) was less than y (6). Because the it depends on what number you input, the correct answer choice is D, "cannot be determined."
Probability of 2 heads or two tails in tossing 2 coins: Event: HH or TT Number of desired outcomes:2 Number of total outcomes: 4
Pr(2H or 2T) = 2/4 = 1/2
Probability of heads and tails in tossing two coins: Event: HT or TH Desired outcomes: HT, TH Number of desired outcomes: 2 Number of total outcomes:4
Pr(H and T) = 2/4 = 1/2
Probability of heads in tossing 1 coin: Event: H Desired outcome: H Number of desired outcomes: 1 Total Possible outcomes: H, T Number of Possible outcomes: 2
Pr(H) = 1/2
Emma spent $75 on a used bike and $27 repairing it. She sold it at a 40% profit. Quantity A: the sales price Quantity B: $140
Quantity A
In 2009 the property tax on each home in Town X was p percent of the assessed value of the home, where p is a constant. The property tax in 2009 on a home in Town X that had an assessed value of $125,000 was $2,500. Quantity A: The property tax in 2009 on a home valued at $160,000 Quantity B: $3,000
Quantity A
A certain hose fills a tank at a rate of 16 gallons per minute. If the tank has a capacity of 960 gallons, how long would it take the hose to fill the tank?
R = d/t 16 = 960/t 60 minutes
A and B ran a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30th of a minute. What is B's speed in m/s? (A) 12 (B) 14 (C) 16 (D) 18 (E) 20
Race 1: Ta = tb-6 ( because A beats B by 6 sec) Race 2: Ta = tb+2 ( because A loses to B by 2 sec) By the formula D= S * T we get two equations 480/Sa = 432/Sb -6 1) 480/Sa = 336/Sb +2 2) Equating these two equations we get Sb = 12 ta,Sa stand for time taken by A and speed of A resp.
Rectangle R has a length of 30 and a width of 10; square S has length 5. The perimeter of S is what fraction of R?
Rectangle: 30 + 10 + 30 + 10 = 80 Square: 5 + 5 + 5 + 5 = 20 The question asks for a fraction, so that would be 20/80. (2/8 and 1/4 are also acceptable answers)
Stephen is twelve years older than his nephew, Anthony. Fifteen years ago, Stephen was twice as old as Anthony. How old is Stephen now? A. 27 B. 37 C. 35 D. 39 E. 49
S = A + 12 S - 15 = 2(A - 15) A + 12 - 15 = 2(A - 15) A - 3 = 2A - 30 A - 3 = 2A - 30 A = 27 So we know that Anthony is 27; if Stephen is 12 years older than him, he must be 39. D. 39 Yea! I got this one right.
Two dice (add the numbers showing):
S = [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12] n = 11
What are the probability and sample space for two coins?
S = [HH, TH, HT, TT] n=4
What are the probability and sample space for three coins?
S= [HHH, HHT, HTH, HTT, THH, THT, TTH, TTT] n=8 2 outcomes x 2 outcomes x 2 outcomes = 8 = 2^3
S
Sample Space (list of outcomes)
13. Sarah is twice as old as her youngest brother. If the difference between their ages is 15 years. How old is her youngest brother? A. 10 B. 15 C. 20 D. 25 E. 30
Sarah is twice as old as her youngest brother. If the difference between their ages is 15 years. How old is her youngest brother? Let x = age of youngest brother then Sarah age = 2x from: "difference between their ages is 15 years" we get: 2x - x = 15 x = 15 Ans: B
John can weed the garden in 3 hours. If Mary can weed the garden in 2 hours, how long will it take them to weed the garden at this rate, working independently?
Set John's time per unit of work as A, and Mary's time per unit of work as B. There is no need for the variable C, since there are only two people. Plugging in, you find that: 1/3 + 1/2 = 1/t 2/6 + 3/6 = 1/t 5/6 = 1/t t = 6/5 hours
For quantitative comparisons involving variables, it is usually easier to just plug in numbers. Example 6: k < 0 [(k×1/2)÷3] × 6 2(k×3) ÷ 6
Solution: First remember that k<0 is a condition that applies to both columns. If you are comfortable with algebra, you can easily see that Column A is just (k/6)6 = k and Column B is 6k/6 = k. Hence, the answer is C. If you are not comfortable with your algebra, just plug a number in for k that satisfies the condition k<0. Let's pick -2 so we can get rid of the fraction in Column A. For Column A we get: [(k×1/2)÷3]×6 =[(−2×1/2)÷3]×6 =[−1÷3]×6 = -6/3 = -2 Column B 2(k × 3) ÷ 6 = 2(−2 × 3) ÷ 6 = 2(-6) ÷6 = -6/3 = -2 As we mentioned earlier, you must be careful when plugging in on quantitative comparisons. Because of choice D, you must determine whether a quantity is always greater than, less than, or equal to another quantity. It's not enough to determine if it sometimes is. You must determine whether a choice must be correct, not just whether it could be correct.
x > y Column A: x^2 Column B: y^2 When plugging in on quantitative comparisons, you need to use numbers with special properties that will reveal situations in which the relationship between two quantities doesn't hold.
Solution: In order to satisfy the given condition, plug in 3 for x and 2 for y. Then Column A is 9 and Column B is 4 which means Column A is bigger. But now you must plug in something different like a negative number. Plug in -2 for A and -3 for B. Now Column B is bigger than Column A. So, the answer is D. Numbers to use are: 0, 1, fractions, negative numbers, and negative fractions. Some examples of these special properties are: (1) 0 times any number is 0 (2) 0 is 0 (3) 1 is 1 (4) squaring a fraction between 0 and 1 results in a smaller fraction (5) a negative number times a negative number is a positive number (6) a negative fraction squared is a positive fraction
Column A: Area of circle with diameter 12 Column B Surface area of a sphere with diameter 12
Solution: Just picture a soccer ball and a paper plate. The answer is B. Quantitative comparisons are supposed to be fast. If you find yourself setting up an elaborate calculation or equation, you are on the wrong track. Look for a shortcut.
Column A: 25× 7.39 Column B: 739/4
Solution: Notice that D cannot be the answer. Do not do the division or multiplication in this problem. Try to simplify it. Multiplying both sides by 4, we get:
The Kaplan Method of Value Questions, Page 31 of the Kaplan Coursebook.
Step 1: Determine, from the question stem, what kind of information is needed to answer this question? Step 2: Evaluate each statement individually. Statement 1: Statement 2: Step 3: Combine the statements if necessary. Combined statements:
The Kaplan Method of Value Questions, Page 29 of the Kaplan Coursebook. 27. If z is an integer, what is the units digit of z^3? 1. z is a multiple of 5. 2. The square root of z is an integer
Step 1: Determine, from the question stem, what kind of information is needed to answer this question? What we need to know here is exactly the identity of z. So here we can use Picking Numbers. Step 2: Evaluate each statement individually. Statement 1: Insufficient. Case 1: if z = 25, then the units digits of z^3 is 5. Case 2: if z = 100, then units digit of z^3 is 0 Statement 2: Insufficient. Case 1: if z = 25, then the units digits of z^3 is 5. Case 2: if z = 100, then units digit of z^3 is 0 Step 3: Combine the statements if necessary. Combined statements: Insufficient. If z = 25, then both statements are true and the answer to the question is 5. If z = 100, then both statements are true and the answer to the question is 0. Since more than one answer to the question is possible, the two statements taken together are insufficient.
The Kaplan Method of Data Sufficiency, Page 26 of the Kaplan Coursebook. 21. If 2b - 2a^2 = 18 what is the value of b? Step 1: From the question stem, determine what type of information would be needed to answer the question. Step 2: Evaluate each statement separately. 1) a^2 = 1,156 2) a > 0 Step 3: Evaluate the statements in combination if necessary.
Step 1: From the question stem, determine what type of information would be needed to answer the question. 1. The value of b 2. The value of a or a^2 Step 2: Evaluate each statement separately. 1. a^2 = 1,156 2. a > 0 In looking at the two statements, we can see that the square root of 1,156 is 34, while a > 0 doesn't help much. Answer A
The Factorial Rule: A collection of n different items can be arranged in order n! different ways. This factorial rule reflects the fact that the first item may be selected in n different ways, the second item may be selected in n-1 ways, and so on.
The Permutations Rule: In another example on this page they offer, what if you wanted to visit all 50 state capitals but only had time to visit four. The math they would be 50!/46! = 50 x 49 x 48 x 47 = 5,527,200. In other words, you have lots of options in how you would go about visiting any four of the state capitals out of the possible 50. And as we already know, the 46 in the denominator cancels out all numbers 46 and lower in the numerator, leaving just four (Pierre, Bismark, Santa Fe, and Frankfort) state capitals to compute. This is the procedure when items are all different. In other words, you only go to Bismark, North Dakota one time. In order for this permutations rule to work, you need three things: there have to be n different items available, you have to select k of the n items (without replacement or revisiting), and each different rearrangement counts as a different sequence (ABD is counted differently that CBA). With this permutation example, order matters.
The youngest of 4 children has siblings who are 3, 5, & 8 years older than she. If the average (arithmetic mean) age of the 4 siblings is 21, what is the age of the youngest sibling?
The age of the youngest sibling is = x. So, her siblings are: x+3, x+5, and x+8. And, their average age is 21, so x, x+3, x+5, and x+8 = 21 The average formula is: Average = Sum of Terms Number of Terms x + (x+3) + (x+5) + (x+8) = 21 4 x + x+3 + x+5 + x+8 = 21 4 4x + 16 = 21 In order to reduce this, multiply each side by 4 4 4x + 16 = 84 In order to reduce this, subtract 16 from each side 4x = 68 In order to reduce this, divide each side by 4 x = 17 The age of the youngest sibling is 17 (the others are 20, 22, and 25 or 21)
GRE Text, Page 297, problem 7. Martha invited 4 friends to go with her to the movies. There are 120 different ways in which they can sit together in a row of 5 seats, one person per seat. In how many of those ways is Martha sitting in the middle seat?
The answer is 24. Now, I went overboard when I started on this problem. But as it turns out, it's very simple and easy. They TELL you that there are 120 ways for the kids to be arranged. All you have to imagine is that in 24 of those 120 Martha will be in each one of the seats in each arrangement. They just happen to want to know about the "middle seat" event, so it's 1/5 of the total of 120.
Example 3: Routes to the National Parks (or the "traveling salesman" problem). If you want to see six national parks, how many routes can you take?
The answer is 6! or 6 x 5 x 4 x 3 x 2 x 1 = 720 possible route combinations.
If a, b, and c are positive integers such that a is divisible by b and c is divisible by a, which of the following is NOT necessarily an integer? a + c/b c-a/b ca/b c + b/a cb/a
The best way to answer this quest is by Picking Numbers so that a is divisible by b and c is divisible by a. For instance we could make b = 2, a = 4, and c = 8. Now let's plug these numbers into the answer choices and wee whether we come up with an answer that is not an integer: 4 + 8/2 = 6 8 - 4/2 = 2 (8)(4)/2 = 16 8 + 2/4 = 5/2 Well, looks like we found it! (8)(2)/4 Who cares? It's D. But the answer is 4, anyway.
A train travels at a speed of 60 miles per hour for the first 180 miles of its trip, then it travels at a speed of 45 miles per hour for the remaining 180 miles of its trip. What is the train's average speed for the entire trip?
The first 180 miles take 180/60 = 3 hours. The second 180 miles take 18045 = 4 hours. Total distance over total time is: 180+180/4+3 =360/7 =51 3/7
One used car salesman receives a commission of $200 plus 4 percent of $1,000 less than the car's final sales price. Another car salesman earns a straight commission of 6 percent of the car's final sales price. What would be the final sales price of a car if both salesmen would earn the same commission for selling it? $5,000 $6,000 $8,000 $10,000 $12,000
The first salesman receives a flat sum no matter how low the sales price. The second gets a larger percentage so if prices escalate, he makes more money. Start with B. If the car sells for $6,000 he gets 4% of $5,000 and $200 or $200 + $200 = $400. The second salesman would get $360. Based on what we know from the first paragraph, we need a higher sales price since #1 IS HIGHER THAN #2. Let's go to D. A car selling for $10,000 would yield $200 plus 4% of $9,000 or $360. $200 plus $360 is $560. Salesman number two would get 6% of $10,000 or $600. So what we need is a lower sales price, since the numbers skewed the other way and now #2 IS HIGHER THAN #1. So, without even taking the time to work it out, we know the answer is C.
Which is greater? A. 2^30 - 2^29/2 B. 2^28
The first step is to get rid of the fraction, so multiply both sides by 2. A. 2^30 - 2^29 B. 2^29 Note that this has the effect of increasing the B value's exponent by one. Now add 2^29 to both sides. A. 2^30 B. 2^29 + 2^29 Now things get a little tricky: 2^29 + 2^29 = 1 · 2^29 + 1 · 2^29 = (1 + 1) · 2^29 = (2) · 2^29 = (2)(2^29) = 2^30 So, now look at the problem: A. 2^30 B. 2^30 Answer choice C.
Page 23, Kaplan Course Book: Backsolving. The combined weight of three people is 475 pounds. If the heaviest person is one-third heavier than the second-heaviest person, and the second-heaviest person is one-fifth heavier than the lightest person, what is the weight, in pounds, of the lightest person? 125 150 175 200 225
The question is: who is the lightest person? Start with A: If the lightest person weighs 150 pounds, the the second-heaviest person weighs on-fifth more than that, or 180 pounds and the heaviest person weights one third more than that or 240 pounds. Thus the three together weigh 150 + 180 + 240 = 570 pounds. That's more than the number we were looking for. Since A is the only choice that is lighter, we know it's the correct answer.
In how many different ways can a group of 8 people be divided into 4 teams of 2 people each? 90 105 168 420 2520
The solution to this problem is the number of combinations. First we get one team out of 8 . The number of ways to do this would be . The next combination is 2 out of 6 or , and so on. Having all four combinations multiplied, we need to divide the total number by the number of ways the teams can be chosen, since we are not interested if the team with two certain people is chosen first, second or third. Therefore, the answer is 105 or B.
Xavier and Yoelle are proofreading a 144-page manuscript. Xavier starts at the first page and works at a rate of 20 pages per hour and Yoelle starts at the last page and works at a rate of 16 pages per hour. When Xavier and Yoelle have read the entire manuscript between them, how many pages will Xavier have read?
Their combined rate is 36 pages per hour. Therefore it takes them 144/36 = 4 hours to read the whole thing. Xavier is reading at 20 pages per hour x 4 hours = 80 pages.
Ana and Bradley are 12 miles away from each other on opposite ends of a straight path. If Ana walks toward Bradley at a rate of 4 miles per hour and Bradley walks toward Ana at a rate of 5 miles per hour, how long will it take before they meet?
Their combined rate is 4 + 5 = 9 miles per hour. Thus, we want to find how long it takes to cover 12 miles at 9 miles per hour: 9 = 12/x 9x = 12 x = 12/9 = 4/3 hours
21. The number of milliliters in 1 liter is: A. 10,000 B. 1,000 C. 0.1 D. 0.01 E. 0.001
There are 1000 milliliters in 1 liter.
12. Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color? A. 4 B. 8 C. 12 D. 13 E. 16
There are 3 different colors: Red, Green, and Blue She wants to have one of each color: 1 blue + 1 red + 1 green = 3 Thus 16 - 3 = 13. She must take out 13 jellybeans. Answer choice D This is similar to problem 281.
2. Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color? A. 4 B. 8 C. 12 D. 13 E. 16
There are 3 different colors: Red, green, blue. She wants to have one of each color. 1 blue + 1 red + 1 green = 3 Thus 16 - 3 = 13. She must take out 13 jellybeans. Answer Key 2. D
Carrie has twenty five less than fifteen times the amount of money Bill has. If three times the amount of money that Carrie has is subtracted from twelve times the amount that Bill has, the result is $9. How much money does Carrie have? (A) $1 (B) $2 (C) $3 (D) $4 (E) $5
There are two Variables here: C and B (for Carrie and Bill). There are two Equations, shown in two different colors. The first is: Carrie has (or is equal to) Bill's money multiplied by 15 and then subtract 25. The second equation is: $9 is the result, or is equal to, 12 times Bill's minus 3 times Carrie's money. These equations would be written: C = 15B - 25 $9 = 12B - 3C Now substitute the first equation into the second equation: $9 = 12B - 3(15B - 25) $9 = 12B - 45B + 75 Now subtract $75 from both sides $66 = -33B Now divide both sides by 33 $2 = Bill's amount of money Note that the question was, "How much money does Carrie have?" So insert $2 into the first equation: C = 15($2) - 25 C = $30 - $25 Carrie's money = $5, which is the answer E (E) $5 Yea! I got it right!
The average of 63, 64, 85, and x is 80. What is the value of x?
Think of each value in terms of its position relative to the average, 80. 63 is 17 less than 80. 64 is 16 less than 80. 85 is 5 greater than 80. So these three terms are a total of 17 + 16 - 5, or 28, less than the average. Therefore, x must be 28 greater than the average to restore the balance at 80. so x = 28 + 80 = 108.
17. You are lying 120 ft away from a tree that is 50 feet tall. You look up at the top of the tree. Approximately how far is your hear from the top of the tree in a straight line? A. 50 feet B. 75 feet C. 120 feet D. 130 feet E. 150 feet
This is a Pythagorean theorem problem. The Pythagorean theorem says that in a right triangle the sum of the squares of the two legs is equal to the square of the hypotenuse. In equation form this is: a^2 + b^2 = c^2 The distance from you to the base of the tree is 120 feet. This is one leg. The tree forms a right angle with the ground, and the tree is 50 feet tall. This is the second leg of the right triangle. The straight line distance from you to the top of the tree is the hypotenuse. If you substitute 120 feet and 50 feet for the two legs of the triangle in the Pythagorean equation you get: 120^2 + 50^2 = c^2 Square the two terms on the left side to get: 14400 + 2500 = c^2 Add the two terms on the left side to reduce the equation to: 16900 = c^2 Solve for c, the unknown straight line distance from you to the top of the tree by taking the square root of both sides and you get (on your calculator): 130 = c So the answer is that you are 130 feet from the top of the tree. Hope this helps you to understand the problem and one way that you can solve it.
If the dollar amount of sales at Store P was $800,000 for 2006, what was the dollar amount of sales at that store for 2008? Percent change from 2006 to 2007 was +10. Percent change from 2007 to 2008 was -10.
This is one of those two stage percent problems. Multiply $800,000 x .1 = $880,000 Multiply $880,000 x .9 = $792,000.
In 1998 the profits of Company N were 10 percent of revenues. In 1999, the revenues of Company N fell by 20 percent, but profits were 15 percent of revenues. The profits in 1999 were what percent of profits in 1998? 80% 105% 120% 124.2% 138%
This mirrors the "toy bears" problem. 1998 1999 Revenues $100 100 x .8 = $80 Profits $100 x .1 = $10 $80 x .15 = 12 12/10(100) = 120% From page 37 of the answer key: Because there are percents in the answer choices and an unspecified value in the question stem, you can pick numbers. Pick 100 for the 1998 revenues. That means that profits were 10. Profits in 1999 were 80 and profits were 15% of that, or 12. So the question becomes 12 is what percent of 10. The percent that 12 is of 10 is 12/10(100) = 12 x 10% = 120%
"If the longer piece is 5 inches less than twice the shorter piece."
This would be written: L = 2s - 5 or Longer equals ("is") twice the shorter piece less 5 inches.
"The longest piece is 3 feet more than twice the shortest piece."
This would be written: L = 2s + 3 or Longest equals ("is") 3 plus twice the shortest piece.
"The temperature in Boston on Saturday was eight degrees less than four times the temperature on Friday."
This would be written: S = 4F - 8 or Saturday equals ("was") four times Friday minus eight degrees.
A theatre charges $12 for seats in the orchestra and #8 for tickets in the balcony on a certain night. On a certain night, a total of 350 tickets were sold for a total cost of $3,320. How many more tickets were sold for seats in the balcony that night than seats in the orchestra?
Tickets: Orchestra tickets + Balcony tickets = 350 tickets Money: $12o + $8b = $3,320 $8(Orchestra + Balcony) = 350 tickets $8Orchestra + 8Balcony = $2,800 8 Orchestra + 8 Balcony = $2,800 -8 Orchestra + 8 Balcony (strikethrough) = $2,800 40 = 570/4 = 0 = 130 Orchestra + Balcony = 350 130 + Balcony = 350 Subtract 130 from each side of the equation and you get: Balcony = 220 220 - 130 = 90
Example: If the price of a $120 dress is increased by 25%, what is the new selling price?
To find the new whole, you'll first have to find the amount of increase. the original whole is 25%. plugging in, we find that: increase/120(100%) = 25% increase/120 = 25/100 increase = the amount of increase is $30, so the new selling price is: $120 + $30, or $150.
Percents and Data Sufficiency: Data sufficiency questions (covered in session 2) test your knowledge of percents in a different way. the crux of these problems, as a rule, is finding all the pieces of the percent formula. You can use the percent formula to pinpoint exactly what you need to achieve sufficiency. Example: By what percent did the price of stock X increase? (1) the price after the increase was $12. (2) the stock increased in price by $1.50
To prove sufficiency you would have to be capable of filling in all parts of the equation. Statement (1) informs you of the price after the increase. this does not give you either the amount of increase or the original price, so it is not sufficient. statement (2) informs you of the increase in price, but not the original price, so it, too, is not sufficient. Combining the statements, however, gives you the increase in price, $1.50, and the original price, $12.00 - $1.50 = $10.50. So the correct answer is choice (C).
A ratio is the proportional relationship between two quantities. the ratio, or relationship, between two numbers, for example, 10 and 15, may be expressed with a colon between the two numbers (10:15), in words ("the ratio of 10 to 15"), or as a common fraction 10/15
To translate a ratio in words to numbers separated by a colon, replace to with a colon.
Computing Probability: Denoted Pr(name of event) Event is a set of individual outcomes. Examples: Tossing a head with one coin in one toss is an event.
Tossing either HT or HH is an event with two coins and one toss.
A factory produces 220 engines per week for six weeks. Following the installation of new equipment, the factory produces 320 engines per week for next eight weeks. What is the average number of engines produced per week over the 14-week period?
Total engines for the first six weeks is 220(6) = 1320, Total engines for the last eight weeks is 8(320) = 2560. Total engines divided by total weeks is: 2560+1320/6 + 8 = 3880/14 = 277 1/7
10. On a Map, 1 inch represents 20 miles. The distance between 2 towns is 6 1/5 inches. How many miles are actually between the two towns? A. 65 miles B. 84 miles C. 124 miles D. 138 miles E. 145 miles
We need to convert 6 1/5 into decimal inches: 1/5 = 0.2 therefore 6 1/5 is 6.2 inches. Since there is 20 miles per inch: 6.2 x 20 = 124 miles Ans: C
Is y > 4? A. 3y + 2/5 B. y
What the book advises is to put a ? between the two terms. The first step is to multiply both sides by 5 to get rid of the fraction. 3y + 2 ? 5y 2 ? 2y 1 ? y Since it was originally stated that y > 4 we can therefor e replace the ? with y < 1. But the question wants to know which is greater between A and B. By reversing the processes and multiply both sides by 2, then add 3y to both sides, then divide both sides by 5 we see that the relationship has stayed constant, and thus B is greater than A, so the answer is B.
The Combinations Rule: If there are n different items available, if we select r of the n items (without replacement), and we consider rearrangements of the same items to be the same (ABC is the same as BCA) then you can use the Combinations Rule. Examples of this are the Clinical Drug Trial and the Florida Lottery.
When different orderings of the same items are counted separately, it is a permutation. When different orderings of the same items are not counted separately, it is a combination.
Test Day Tip: On a question involving multiple changes in percent one of the trap answers will most likely simply involve adding or subtracting the percents.
When guessing on Problem Solving questions, be wary of answer choices that are structurally different from others.
"In ten years, Jeff will be three times as old as Pat is then"
Would be written: J + 10 = 3(P + 10)
A Random Experiment is . . .
an activity or process whose outcome cannot be predicted ahead of time.
odd x even =
even
rules for odds and evens odd + odd =
even
6,930 is a multiple of 6, since:
it is a multiple of 2 and 3.
Picking numbers hint from Page 15 of the Kaplan Course Book: With fractions, a ______ common denominator is often a good pick.
lowest
Example 5: IVF Gender Selection: Permutations when some of the items are identical to others. In this case 14 couples tried to have baby girls. How many ways can 11 girls and 3 boys be arranged in a sequence? In other words, find the number of permutations of 11 girls and 3 boys.
n! . n1! n2! 14! . 11! 3! 14! . 11! 3! 87,178,291,200. (39,916,800)! (6)! 14 x 13 x 12. 3 x 2 x 1 2,184. 6 364, or there are 364 ways to arrange 11 girls and 3 boys
Picking numbers hint from Page 15 of the Kaplan Course Book: Drawing a ______ can help you visualize the question more clearly.
number line
odd + even =
odd
If Charles drives at an average speed of 55 miles per hour, how long would it take him to drive 275 miles?
r = d/t 55 = 275/t 55t = 275 t = 275/55 t = 5 hours
The sum of three consecutive integers is 33. What is the first number? What is x?
x + (x + 1) + (x + 2) = 33 3x + 3 = 33 3x = 30 x = 10
Use this method to determine the number of outcomes for a triple scoop ice cream cone with no repeats of flavors, each scoop has to be a different flavor still 31 flavor options.
31 x 30 x 29 Total possible ice cream cones: 31 * 30 * 29 = 26,970
31 flavors, 2 scoops
31 x 31 = 961
31 flavors, 3 scoops:
31 x 31 x 31 or 31^3 = 29,791
31. The last week of a month a car dealership sold 12 cars. A new sales promotion came out the first week of the next month and the sold 19 cars that week. What was the percent increase in sales from the last week of the previous month compared to the first week of the next month? A. 58% B. 119% C. 158% D. 175% E. 200%
31. A
The price of a bushel of corn is currently $3.20, and the price of a peck of wheat is $5.80. The price of corn is increasing at a constant rate of 5x cents per day while the price of wheat is decreasing at a constant rate of cents per day. What is the approximate price when a bushel of corn costs the same amount as a peck of wheat? (A) $4.50 (B) $5.10 (C) $5.30 (D) $5.50 (E) $5.60
320 + 5x = 580 - .41x x = # of days after price is same; solving for x x is approximately 48, thus the required price is: 320 + 5 * 48 = 560 cents = $5.6
33. If two planes leave the same airport at 1:00 PM, how many miles apart will they be at 3:00 PM if one travels directly north at 150 mph and the other travels directly west at 200 mph? A. 50 miles B. 100 miles C. 500 miles D. 700 miles E. 1,000 miles
33. C
We don't really need to list every part of the sample space. We just need the size of the sample space. What is the shortcut for finding N?
Multiplication Rule = the method for counting outcomes. Multiply the number of options by itself the number of times a "choice" is made.
How can we count number of outcomes?
By listing all possible outcomes.
11. Jim has 5 pieces of string. He needs to choose the piece that will be able to go around his 36-inch waist. His belt broke, and his pants are falling down. The piece needs to be at least 4 inches longer than his waist so he can tie a knot in it, but it cannot be more that 6 inches longer so that the ends will not show from under his shirt. Which of the following pieces of string will work the best? A. 3 feet B. 3 ¾ feet C. 3 ½ feet D. 3 ¼ feet E. 2 ½ feet
C
13. If two planes leave the same airport at 1:00 PM, how many miles apart will they be at 3:00 PM if one travels directly north at 150 mph and the other travels directly west at 200 mph? A. 50 miles B. 100 miles C. 500 miles D. 700 miles E. 1,000 miles
C
16. If 8x + 5x + 2x + 4x = 114, then 5x + 3 is A. 12 B. 25 C. 33 D. 47 E. 86
C
20. If y = 3, then y^3(y^3 - y)= A. 300 B. 459 C. 648 D. 999 E. 1099
C
If x equally priced shares of a certain stock were valued at $25,000 on Monday, what was the value per share of the stock on Friday? (1) The value of each share increased by 3% between Monday and Friday. (2) The value of each share increased by $1.50 between Monday and Friday.
C
6,930 is a multiple of 2, since
0 is even
6,930 is a multiple of 9, since:
6 + 9 + 3 + 0 = 18, a multiple of 9.
12. The last week of a month a car dealership sold 12 cars. A new sales promotion came out the first week of the next month and the sold 19 cars that week. What was the percent increase in sales from the last week of the previous month compared to the first week of the next month? A. 58% B. 119% C. 158% D. 175% E. 200%
A
14. If 300 jellybeans cost you x dollars. How many jellybeans can you purchase for 50 cents at the same rate? A. 150/x B. 150x C. 6x D. 1500/x E. 600x
A
19. Your supervisor instructs you to purchase 240 pens and 6 staplers for the nurse's station. Pens are purchased in sets of 6 for $2.35 per pack. Staplers are sold in sets of 2 for 12.95. How much will purchasing these products cost? A. $132.85 B. $145.75 C. $162.90 D. $225.25 E. $226.75
A
5. Solve the following equation for A 2A/3 = 8 + 4A A. -2.4 B. 2.4 C. 1.3 D. -1.3 E. 0
A
9. If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks? A. 2 minutes and 44 seconds B. 2 minutes and 58 seconds C. 3 minutes and 10 seconds D. 3 minutes and 26 seconds E. 4 minutes and 15 seconds
A
If a > 0, then (8^a)(2^a) (All of the "a"s here are superscript) A: 16^a B: 16^2a C: 2^2a D: 2^3a
A
What is the GMAT answer grid?
A D B C E (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. (C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. (D) EACH statement ALONE is sufficient. (E) Statements (1) and (2) TOGETHER are NOT sufficient.
11. One inch equals 2.54 cm, How many centimeters tall is a 76 inch man? A. 20 cm B. 29.92 cm C. 193.04 cm D. 300.04 cm E. 593.04 cm
Answer Key 11. C
11. What is 35% of a number if 12 is 15% of a number? A. 5 B. 12 C. 28 D. 33 E. 62
Answer Key 11. C
12. What is the mathematical average of the number of days in a typical year, the number of days in a week, and the number of hours in a day? A. 100 B. 115 C. 132 D. 158 E. 224
Answer Key 12. C
The Kaplan Method of Value Questions, Page 29 of the Kaplan Coursebook. 28. What is the value of 4n - 5m? 1. n/5 = m/4 2. n/4 = m/5
A. Step 1: Determine, from the question stem, what kind of information is needed to answer this question? We need a single value for the expression in the question stem. Step 2: Evaluate each statement individually. Statement 1: Sufficient. After cross multiplying, the statement becomes 4n - 5m = 0 Statement 2: Insufficient. The statement provides an equation, but a second equation would be necessary to answer the question. Step 3: Combine the statements if necessary. Combined statements: NOT NECESSARY.
Compare two quantities, A and B. A) 0.076 B) 0.0748 A: A is greater than B B: B is greater than A C: A and B are equal D: There is not enough information provided to determine the relationship between A and B.
A. The larger number in the thousandths place indicates that A is larger.
3. 60% of 3 is: A:1 1/2 B: 1 4/5 C: 1 3/4 D: 1 5/8
A: 1 1/2 B: 1 4/5 C: 1 3/4 D: 1 5/8
During a sale, a store sells 20 percent of its remaining stock each day, without replacement. After 4 days, what fraction of its original stock has it sold? 1/625 256/625 61/125 64/125 369/625
E. Choose a number for the original amount of material. Since 625 shows up in the three answer choices, use 625 shirts. The answer will represent the remaining material over the original material. Organize the data in your chart: Day 1: 125 sold, 500 left Day 2: 100 sold, 400 left Day 3: 80 sold, 320 left Day 4: 64 sold, 256 left Now, don't get this far and get the wrong answer. The question wanted the fraction of the stock SOLD. The number sold was 625 - 256 = 369. The fraction of the stock sold was 369/625, or choice E.
Painting Y is four times as old as painting Z. Fifty years from now, painting Y will be three times as old as painting Z. How old is painting Y? A. 300 B. 350 C. 400 D. 450 E. 500
Ellie helped me with this one: Y = 4Z 50 + Y = 3(50 + Z) 50 + 4Z = 150 + 3Z Z = 100 Since we want to know how old painting Y is (not painting Z) and we know that y = 4Z, the answer is 100 x 4 or 400. C. 400 Yea! I got this one right.
30. Jonathan can type a 20 page document in 40 minutes, Susan can type it in 30 minutes, and Jack can type it in 24 minutes. Working together, how much time will it take them to type the same document? A. 5 minutes B. 10 minutes C. 15 minutes D. 18 minutes E. 20 minutes
Find the person in the equation who can do 100% of the work! If Jack can type the entire document in 24 minutes, then he can type 1/24 of the document in 1 minute. Working together, they can type 1/40 + 1/30 + 1/24 of the document in one minute would be written: 3/120 + 4/120 + 5/120 12/120 = 1/10 So, together, they can type 1/10 of the document in one minute. Therefore, it will take them 10 minutes to type the entire document.
A prime number is an integer greater than 1 that has only two factors: itself and 1.
The number 1 is not considered a prime, because it is divisible only by itself. The number 2 is the smallest prime number and the only even prime. (Any other even number must have 2 as a factor, and therefore cannot be prime.)
The combination formula, n!/k! (n-k)! gives the number of unordered subgroups of k items that can be selected from a group of n different items, where k < n. If n is a positive integer, n! is the product of the first positive integers. The permutation formula, n!/(n-k)!, gives the number of ordered subgroups of k items that can be made from a set of n different items, where k < n
The number of possible arrangements of n different items where each arrangement contains all n items is n! When K < N, K is always the smaller number
Jane makes toy bears. If she has an assistant she can make 80% more bears per week and work 10% fewer hours. How much does the assistant increase her productivity?
Use Picking Numbers. Let's say that Jane makes 100 bears a week and works 100 hours per week. So: 100 bears x .8 = 180 bears per week 100 hours x .9 = 90 hours per week 180/90 = 2 Having an assistant would double her productivity or increase it by 200%
Boston and New York are approximately 280 miles apart. One Train leaves Boston traveling towards New York at an average speed of 80mph. Another train leaves New York at the same time traveling toward Boston at an average speed of 60 mph. (a) How long will it take them to meet? (b) How far has each train traveled when they meet?
Use the combined speed 80 + 60 = 140 280/140 = 2 hours Then the train traveling at 80 miles an hour for 2 hours travels 160 miles. And the train traveling at 60 miles an hour for 2 hours travels 120 miles.
14. Which of the following fractions is equal to 5/6? A. 20/30 B. 15/24 C. 25/30 D. 40/54 E. 2/7
Which of the following fractions is equal to 5/6? Through elimination -- and because we can multiply numerator and denominator by 5 to get the answer. Ans: C
Compare two quantities, A and B. A) x^17 B) (x6)^3 A: A is greater than B B: B is greater than A C: A and B are equal D: There is not enough information provided to determine the relationship between A and B.
10. D. The value for B is equivalent to x18. However, depending on what x is, x17 may be greater, equal to, or less than x18.
8. Compare two quantities, A and B. Roger scored 18 points in the basketball game, 7 of them in the first half. A) Points scored by Roger in the first half. B) Points scored by Roger in the third quarter. A: A is greater than B B: B is greater than A C: A and B are equal D: There is not enough information provided to determine the relationship between A and B.
8. D. It is impossible to determine how many points Roger scored in each of the quarters of the second half.
Frank, Melissa, and Jon all have Halloween candy. All together they have 85 pieces of candy. Frank has 1/3 as much as Melissa and Jon has 15 more than Frank. How many pieces of candy does Melissa have? A. 12 B. 14 C. 29 D. 42 E. 44
85 = F + M + J J = M x .333 + 15 F = M x .333 85 = .333M + M + .333M + 15 85 = .666M + M + 15 85 = 1.666M + 15 70 = 1.666M 70/1.666 = 1.666M/1.666 42 = M This is a bit tricky since there is a "double switch." It also has a fractional multiplication, which won't be easy on the GMAT. D. 42 Yea! I got this one right.
7. Compare two quantities, A and B. 2x + 4 = 8, 5y =40 A) y/x B) 16x/y A: A is greater than B B: B is greater than A C: A and B are equal D: There is not enough information provided to determine the relationship between A and B.
C. Both A and B are equal to 4.
Tim is eight years younger than Jerry. In twelve years, Jerry will be twice as old as Tim is now. How old was Jerry six years ago? A. 22 B. 24 C. 26 D. 28 E. 30
Equation 1: J = T + 8 Equation 2: 2T = J + 12 2T = T + 8 + 12 2T = T + 20 T = 20 So we know that Tim is 20 years old now. So we know that Jerry must be 28 years old now, so six years ago Jerry must have been 22. A. 22 Yea! I got this one right.
Jeff is currently five times as old as Pat is. In ten years, Jeff will be three times as old as Pat is then. What is the sum of their current ages? A. 20 B. 40 C. 60 D. 80 E. 100
J = P x 5 10 + J = 3(10 + P) (10 + 5P) = 3(10 + P) 10 + 5P= 30 + 3P 2P = 20 P = 10 So now we know that Pat is a ten year old boy. And if Jeff is five times older than him, Jeff is 50 years old, and the sum of their ages is 50 + 10 = 60 or answer C. C. 60 Yea! I got this one right.
Working alone at its constant rate, machine A produces K car parts in 10 minutes while machine B produces K parts in 15 minutes. How many minutes does it take A and B working together to make K car parts?
K/10 + K/15 = K(1/10+1/15) = K(25/150) = K/6 Now to computer K/6, use the formula k/K/6 and cross multiply k/1 x 6/K = 6 This makes sense because two machines working at A's rate would make the same number of parts in 5 minutes while two machines working at B's rate would make the same number of parts in 7.5 minutes.
If Sara's age is exactly twice Bill's age, what is Sara's age? 1) Four years ago, Sara's age was exactly 3 times Bill's age 2) Eight years from now, Sara's age will be exactly 1.5 Bill's age
The given information in this problem is: S = 2B 1) S - 4 = 3(B -4) 2) S + 8 = 1.5(B + 8) Thus . . .
Amy is three times as old as Mary is now. In five years, the sum of their ages will be 50. How old is Amy now? A. 10 B. 20 C. 30 D. 35 E. 40
The two Variables are A (Amy's age) and M (Mary's age). The two equations are: M3 = A (If Amy is 30 years old, Mary would be 10 years old) 50 = (M + 5) + (A + 5) (If in 5 years the sum of their ages is 50, you would add 5 years Amy and 5 years to Mary). 50 = (M + 5) + (3M + 5) 50 = 4M + 10 50 -10 = 4M + 10 - 10 40 = 4M 40/4 = 4A/4 10 = M Once again, I seem to be getting the correct numerical answer, but the wrong answer for the question. I have figured out that "10" is the right answer, but it's really Mary's age, not Amy's. Amy should be 30 years old. So either Jeff has a defect in two questions or I'm missing something in my solution. Actually, I figured out what it is: the first equation should be Mary's age (10 years old) times three would be 30 years old. Amy is 30; Mary is 10. Answer: C
A cord 12 feet in length is cut into three pieces. The longest piece is 3 feet more than twice the shortest piece, and the medium-size piece is 6 feet longer than the shortest piece. What is the length of the shortest piece?
The variables are: L, M, S The equations are: 12 = L + M + S L = 2S + 3 M = S + 6 12 = 2S + 3 + S + 6 + S 12 = 4S + 9 3 = 4S 3/4 = 4S/4 3/4 = S There's no answer key here, so I'm not sure if I got it right or not. (E) 3/4
The temperature in Anchorage on Wednesday was -6 degrees. If nine times the temperature on Wednesday is subtracted from 5 times the temperature on Thursday, the result was sixty four degrees. What was the temperature on Thursday? (A)-2 degrees (B) 0 degrees (C) 2 degrees (D) 4 degrees (E) 6 degrees
There is only one Variable here: T for the temperature on Thursday. There is only one Equation, which is highlighted. It is: 64 degrees is the result (or equal to) 5 times the temperature from Thursday if you were to subtract 9 times Wednesday's temperature (-6 degrees) from it. This equation would be written: 64 = 5T - 9(-6) 64 = 5T - (-54) 64 = 5T + 54 If you subtract 54 from both sides of the equation, 10 = 5T Now divide both sides by 5 and you have 2 - T Since the question was, "What was the temperature on Thursday," the answer is C.
Which is greater? A. X^2 + 1 B. 2x - 1
This is one of those questions where you need to construct a quadratic polynomial. X^2 + 1 = 2x - 1 X^2 - 2x + 1 = - 1 (X - 1)^2 = -1 Any number squared is positive, so it has to be greater than -1. thus answer choice A.
The temperature in Anchorage on Wednesday was -6 degrees. If nine times the temperature on Wednesday is subtracted from 5 times the temperature on Thursday, the result was sixty four degrees. What was the temperature on Thursday? (A)-2 degrees (B) 0 degrees (C) 2 degrees (D) 4 degrees (E) 6 degrees
W = -6 5T - 9W = 64 5T - 9 (-6) = 64 5T - 54 = 64 5T = 10 T = 2 (C) 2 degrees Yea! I got this one right.
What is the average price of a Large Car sold at the auction?
While I can't reproduce the entire table, there were 20 Large Cars sold for a total of $120,000. Thus the average price was $6,000.
"If six times the temperature on Saturday was subtracted from twice the temperature on Friday, the result is four degrees."
While this looks more complicated, it's not. Note also that the answer is given in the question. This would be written: 4 = 2F - 6S or Four (degrees, a given) equals ("is") twice Friday's temperature minus six times the temperature Saturday.
"Amy is three times as old as Mary is now"
Would be written "M3 = A" since if Amy is 30 years old, Mary would be 10 years old. You would have to increase Mary's age by a factor of three in order for their ages to be equal.
"Stacie is currently three times as old as Matthew"
Would be written as "S = M x 3" since while Stacie is three times older than Matthew (let's say she's 30 and he's 10 years old), the equation would read "Matthew's age times three equals Stacie's age."
Sally rides her bike at a rate of Z miles in X hours. How long will it take her to ride W miles?
You should first recognize two things: that this is a Rate problem, and that they are asking for a time (How long will it take her . . .). The Rate formula is: Rate = Distance/Time "Sally rides her bike at a rate of Z miles in X hours. How long will it take her to ride W miles?" Rate = d/t We see they are asking for a time ("How long . . .") so let's solve for t. The first step is to multiply both sides of the equation by t. t * r = d ÷ t * t t * r = d Step 2 is to divide both sides by r. t = d/r So now "let's change the color of our pen and fill stuff in" t = d/r = w ÷ z/x t=d/r * w/z//x w/1 * x/z = wx/z
Coffee Shop Options: Local coffee shop offers the following options: -Iced or Hot coffee -Mocha, Latte, or Espresso -15 flavored syrups How many types of coffee could be ordered? List number of times we can choose and options. Three times to choose: __ x __ x __
___ x ___ x ___ = Total combinations 2 * 3 * 15 = 90
In 2005 Jake purchased a warehouse to start his health drink business. He purchased the warehouse for $30,000, and this was his only fixed cost in 2005. If the variable cost was $2.50 per bottle of his health drink, and he sold each drink for $5.50 how much profit per bottle did Jake make in 2005, if he produced and sold 150,000 bottles of his health drink? A. $2.00 B. $2.20 C. $2.40 D. $2.60 E. $2.80
y = 5.5(150,000) - 2.5(150,000) + 30,000 y = 825,000 - 375,000 - 30,000 y = 420,000/150000 y = $2.80 E. $2.80 Yea! I got this one right.
