GMAT Review Questions
"Aaron will jog from home at x miles per hour and then walk back home by the same route at y miles per hour. How many miles from home can Aaron jog so that he spends a total of t hours jogging and walking? (A) xt/y (B) (x+t)/xy (C) xyt/(x+y) (D) (x+y+t)/xy (E) (y+t)/x-t/y"
C
"If a number N is decreased by p percent and then the resulting value is increased by q percent, the final result is equal to N. If both p and q are positive integers, what is the value of p ? (1) p is not a multiple of 10. (2) q is not a multiple of 10."
C
"If n = 3^8 - 2^8 which of the following is NOT a factor of n? A. 97 B. 65 C. 35 D. 13 E. 5"
C
"If x/y = c/d and d/c = b/a, which of the following must be true? I. y/x = b/a II. x/a = y/b III. y/a = x/b (A) I only (B) II only (C) I and II only (D) I and III only (E) I, II, and III"
C
"In a certain deck of cards, each card has a positive integer written on it, in a multiplication game a child draws a card and multiplies the integer on the card with the next large integer. If the each possible product is between 15 and 200, then the least and greatest integer on the card would be A. 3 and 15 B. 3 and 20 C. 4 and 13 D. 4 and 14 E. 5 and 14"
C
"S is a set of points in the plane. How many distinct triangles can be drawn that have three of the points in S as vertices? (1) The number of distinct points in S is 5. (2) No three of the points in S are collinear."
C
"What is the value of (a + b)2 ? (1) a = 15/b (2) (a - b)2 = 4"
C
A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the three numbers on the balls selected from the box will be odd? A. 1/4 B. 3/8 C. 1/2 D. 5/8 E. 3/4
C
A car traveling at a constant speed took 1 minute 48 seconds to travel the distance between a certain road sign and the beginning of a roadwork area. If the distance between the road sign and the beginning of the roadwork area was 2,400 meters, then the car was traveling at what speed, in kilometers per hour? (1 kilometer = 1,000 meters) 50 60 80 90 100
C
A certain quantity is measured on two different scales, the R-scale and the S-scale, that are related linearly. Measurements on the R-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively. What measurement on the R-scale corresponds to a measurement of 100 on the S-scale? A. 20 B. 36 C. 48 D. 60 E. 84
C
A store sells a certain product at a fixed price per unit. At the product's current price, q units cost a total of exactly $300. If the price were lowered by $5 from its current value, then q + 2n units would cost exactly $300; if the price were raised by $5, then q - n units would cost exactly $300. What is the value of q? 10 15 20 25 30
C
If S is the set of integers that are both positive factors of 64 and also multiples of 8, how many elements are there in set S? 2 3 4 6 8
C
If the length of side AB is 17, is triangle ABC a right triangle? (1) The length of side BC is 144. (2) The length of side AC is 145.
C
Jim filled his dog's bowl with 80 dog food pellets. Starting at 8:00 a.m., Jim's dog ate exactly once an hour, consuming exactly half of the number of dog food pellets remaining in the bowl at each feeding session. What percent of the original 80 pellets were there in the dog's bowl right before the dog began to eat at noon of the same day? 2.75% 3.125% 6.25% 12.5% 20%
C
Quantitative :: Problem solving:: 04517 A positive integer is divisible by 3 if and only if the sum of its digits is divisible by 3. If the six-digit integer n is divisible by 3 and n is of the form 1k2, k24, where k represents a digit that occurs twice, how many values could n have? A Two B Three C Four D Five E Ten
C
What is the sum of all 50 numbers in a list? (1) The sum of the positive numbers in the list is 7.3. (2) The sum of the negative numbers in the list is 10.6 less than the sum of the positive numbers.
C
"Is the average of n consecutive integers equal to 1 ? (1) n is even (2) if S is the sum of the n consecutive integers, then 0 < S < n "
D
"Is the positive integer N a perfect square? (1) The number of distinct factors of N is even. (2) The sum of all distinct factors of N is even. "
D
"Let f( x) = x 2 + bx + c. If f(6) = 0 and f(-3) = 0, then b + c = 18 15 -15 -21 -24"
D
"The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 210? 3 14 30 42 70 "
D
"The sum of the positive integers from 1 to 27 is equivalent to the sum of the integers from -27 to 54 0 to 28 15 to 45 38 to 46 48 to 54"
D
"What is the average (arithmetic mean) of eleven consecutive integers? (1) The average of the first nine integers is 7. (2) The average of the last nine integers is 9."
D
"What is the cube root of w ? (1) The 5th root of w is 64. (2) The 15th root of w is 4."
D
A circular tabletop has a circumference of c inches, where c > 0, and an area of a square inches, where a > 0. Which of the following equations must be true? A. c - = 0 B. c2 + 4a = 0 C. 4a - c = 0 D. c2 - = 0 E. c - 2a = 0
D
Alex deposited x dollars into a new account that earned 8 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w ? A. w/(1+1.08) B. w/(1.08+1.16) C. w/(1.16+1.24) D. w/(1.08+1.08^2) E. w/(1.08^2+1.08^2)
D
Company X has 50 employees and Company Y has 60 employees. Both companies have the same number of full-time employees, but Company Y has 3 more than twice the number of part-time employees that Company X has. How many part-time employees does Company Y have? 3 7 14 17 20
D
If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many such committees are possible? 20 40 50 80 120
D
In a certain school district, math teachers are considered qualified if they have either a math degree or a teaching credential in math. If 5% of math teachers have both a math degree and a teaching credential in math, what percentage of math teachers are considered qualified? (1) Fifteen percent of math teachers lack a teaching credential in math, and 90% lack a math degree. (2) Eighty percent of math teachers have a teaching credential in math but not a math degree, and 5% have a math degree but not a teaching credential.
D
The average speed of a car decreased by 3 miles per hour every successive 8-minute interval. If the car traveled 4.8 miles in the sixth 8-minute interval, what was the average speed of the car, in miles per hour, in the first 8-minute interval? 35 40 48 51 53
D
Three straight metal rods have an average (arithmetic mean) length of 77 inches and the shortest rod has a length of 65 inches. What is the maximum possible value of the median length, in inches, of the three rods? 71 77 80 83 89
D
What is the circumference of circular region R ? (1) The area of R is 36\small \pi. (2) The area of a square region inscribed in R is 72.
D
when a certain tree was first planted, it was 4 feet tall & the height of the tree increased by a constant amount each year for the next 6 years. at the end of 6 year the tree was 1/5 taller then it was at the end of 4 year. by how many feet did the height of the tree increase each year a 3/10 b 2/5 c 1/2 d 2/3 e 6/5
D
"For the past n days, the average (arithmetic mean) daily production at a company was 50 units. If today's production of 90 units raises the average to 55 units per day, what is the value of n ? (A) 30 (B) 18 (C) 10 (D) 9 (E) 7"
E
"If a and b are nonzero integers such that 2a = 5b, then each of the following must be true EXCEPT 0 < b/a < 1 ab is positive. On the number line, b lies between 0 and a. The ratio of a to b is equivalent to 10/4. a - b is positive."
E
"If |x|y+ 9 > 0, and x and y are integers, is x < 6? (1) y is negative (2) |y| < 1"
E
"Is x < z? (1) x = (1/2)y (2) y = 0.5z"
E
"Machine A and Machine B can produce 1 widget in 3 hours working together at their respective constant rates. If Machine A's speed were doubled, the two machines could produce 1 widget in 2 hours working together at their respective rates. How many hours does it currently take Machine A to produce 1 widget on its own? A) 1/2 B) 2 C) 3 D) 5 E) 6"
E
"The perimeter of a rectangular yard is completely surrounded by a fence that measures 40 meters. What is the length of the yard if the area of the yard is 64 meters squared? 8 10 12 14 16"
E
"Two musicians, Maria and Perry, work at independent constant rates to tune a warehouse full of instruments. If both musicians start at the same time and work at their normal rates, they will complete the job in 45 minutes. However, if Perry were to work at twice Maria's rate, they would take only 20 minutes. How long would it take Perry, working alone at his normal rate, to tune the warehouse full of instruments? 1 hr 20 min 1 hr 45 min 2 hr 2 hr 20 min 3 hr"
E
For a certain art exhibit, a museum sold admission tickets to groups of 30 people every 5 minutes from 9:00 in the morning to 5:55 in the afternoon, inclusive. The price of a regular admission ticket was $10 and the price of a student ticket was $6. If on one day 3 times as many regular admission tickets were sold as student tickets, what was the total revenue from ticket sales that day? A. $24,960 B. $25,920 C. $28,080 D. $28,500 E. $29,160
E
Four extra-large sandwiches of exactly the same size were ordered for m students, where m > 4. Three of the sandwiches were evenly divided among the students. Since 4 students did not want any of the fourth sandwich, it was evenly divided among the remaining students. If Carol ate one piece from each of the four sandwiches, the amount of sandwich that she ate would be what fraction of a whole extra-large sandwich? A) (m+4)/[m(m-4)] B) (2m-4)/[m(m-4)] C) (4m-4)/[m(m-4)] D) (4m-8)/[m(m-4)] E) (4m-12)/[m(m-4)]
E
If n is a member of the set {33, 36, 38, 39, 41, 42}, what is the value of n ? (1) n is even. (2) n is a multiple of 3.
E
If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200, then x must be a multiple of which of the following? A) 3 B) 6 C) 7 D) 8 E) 10
E
Is x < z? (1) x = (1/2)y (2) y = 0.5z
E
"If a - b > a + b, where a and b are integers, which of the following must be true? I. a < 0 II. b < 0 III. ab < 0"
II only
"A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women? 1/14 1/7 2/7 3/7 1/2"
" 5! / 2!3! = 10 So, the number of ways that 2 women can be selected is 10. Now the men: Thus, the number of ways that 2 men can be selected is 3. Now we can multiply to get the total number of teams with exactly 2 women (and thus exactly 2 men): w = (10)(3) = 30. Since there are 30 possible teams with exactly 2 women, and 70 possible teams overall, w/t = 30/70 = 3/7. The correct answer is D."
"Eco Wildlife Preserve contains 5x zebras and 2x lions, where x is positive. If the lions kill z zebras, is the new ratio of zebras to lions less than 2 to 1? (1) z>x (2)z=4"
"(5x-z)/2x < 2/1 5x-z<4x is z>x?"
A string of 10 lightbulbs is wired in such a way that if any individual lightbulb fails, the entire string fails. If for each individual lightbulb the probability of failing during time period T is 0.06, what is the probability that the string of lightbulbs will fail during time period T ?
1-(0.94)^10
Lisa spends 3/8th of her salary on rent and 5/12 on food. Her roommate, Carrie earns about twice as much as Lisa, spends 1/4th of her salary on the rent and 1/2 on food. If the two women decide to contribute the rest of their salary to charity every month, what fraction of their combined monthly income will they donate.
17/72
"List S includes elements {8, 2, 11, x, 3, y} and has a mean of 7 and a median of 5.5. If x < y, then which of the following is the maximum possible value of x? A) 0 B) 1 C) 2 D) 3 E) 4"
3
The ratio of roses to tulips in a bouquet is 3 to 5. If 2 roses are added to the bouquet and 6 tulips are removed, the new ratio of roses to tulips is 5 to 6. How many tulips were in the bouquet to begin with?
30
The amount of time that three people worked on a special project was in the ratio of 2 to 3 to 5. If the project took 110 hours, how many more hours did the hardest working person work than the person who worked the least?
33 hours
Greg, Marcia, Peter, Jan, Bobby and Cindy go to a movie and sit next to each other in 6 adjacent seats in the front row of the theater. If Marcia and Jan will not sit next to each other, in how many ways different arrangements can the 6 people sit?
480
"A researcher has determined that she requires a minimum of n responses to a survey for the results to be valid. If p% of the surveyed individuals fail to respond to the survey, how many individuals, in terms of n and p, must the researcher survey to produce twice the minimum required number of responses?"
A
"If 2xy + z = 9, what is the value of the positive integer z? (1) xyz - z2 = 0 (2) x + y - 3z = -5 "
A
"If m and n are positive integers, is (√m)^n an integer? (1) (√m) is an integer. (2) (√n) is an integer."
A
"If x is a positive integer, what is the units digit of 3x? (1) x = 10k^2 + 1, where k is a positive integer. (2) The units digit of x2 is 1."
A
"In one week a construction worker worked more than 40 hours, and was paid two times his regular hourly rate for every hour worked in excess of 40 hours. If he earned $780, how many hours did he work in that week? (1) If he had worked 6 more hours that week, his earnings would have been $960. (2) If he had worked 20 fewer hours that week, his earnings would have been $390 less that week."
A
"In the quadrilateral PQRS, side PS is parallel to side QR. Is PQRS a parallelogram? (1) PS = QR (2) PQ = RS"
A
"In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3) ? (1) The x-coordinate of point R is -1. (2) Point R lies on the line y = -3."
A
"Is (x + 1)/(x - 3) < 0 ? (1) -1 < x < 1 (2) x^2 - 4 < 0"
A
"Is the integer z divisible by 6? (1) The greatest common factor of z and 12 is 3. (2) The greatest common factor of z and 15 is 3."
A
"Maryam's wallet contains a combination of $5 and $10 bills. What is the ratio of $5 bills to $10 bills? (1) The ratio of the number of bills to the total dollar value is 1/9. (2) The total dollar value of the bills is $360."
A
"Two trains, X and Y, started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; Train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had Train X traveled when it met Train Y? (A) 37.5 (B) 40.0 (C) 60.0 (D) 62.5 (E) 77.5"
A
"What is the value of 2a4b? (1) a = -2b (2) b = 4`"
A
If Anne takes 13 minutes to jog f feet, how many minutes will it take her to jog g feet at the same rate? (a) 13g/f (b) 13f/g (c) g/13f (d) 13/fg (e) fg/13
A
If m = 9/25, w = 15/32, and m + w + c = 1, which of the following gives the values of m, w, and c in increasing order? A. c, m, w B. c, w, m C. m, w, c D. w, c, m E. w, m, c
A
If x, y, and z are integers and xy + z is an odd integer, is x an even integer? (1) xy + xz is an even integer. (2) y + xz is an odd integer.
A
Of the 3,600 employees of Company X, (1/3) are clerical. If the clerical staff were to be reduced by (1/3), what percent of the total number of the remaining employees would then be clerical? 25% 22.2% 20% 12.5%
A
"If q, s, and t are all different numbers, is q < s < t ? (1) t - q = |t - s| + |s - q| (2) t > q"
A (Revised from first iteration)
How many of the integers that satisfy the inequality (x+2)(x+3) / (x-2) >= 0 are less than 5?
Answer is (D) - 4
If Bob takes 18 minutes to run x miles, how many minutes will it take him to run y miles at the same rate?
Answer=18y/x
"Company P had 15 percent more employees in December than it had in January. If Company P had 460 employees in December, how many employees did it have in January? (A) 391 (B) 400 (C) 410 (D) 423 (E) 445"
B
"For any positive integer x, the 2-height of x is defined to be the greatest nonnegative integer n such that 2^n is a factor of x. If k and m are positive integers, is the 2-height of k greater than the 2-height of m? (1) k > m (2) k/m is an even integer."
B
"If the scale model of a cube sculpture is 0.5 cm per every 1 m of the real sculpture, what is the volume of the model, if the volume of the real sculpture is 64 m3? A. 64 cm3 B. 8 cm3 C. 2 cm3 D. 4 cm3 E. 16 cm3"
B
"In order to complete a reading assignment on time, Terry planned to read 90 pages per day. However, she read only 75 pages per day at first, leaving 690 pages to be read during the last 6 days before the assignment was to be completed. How many days in all did Terry have to complete the assignment on time? (A) 15 (B) 16 (C) 25 (D) 40 (E) 46"
B
"Is P an integer? (1) 3P is an integer (2) p/3 is an integer"
B
"Lake A has a duck population of 30 females and 36 males. Lake B's duck population consists of the same ratio of females to males. If 6 new female ducks are added to Lake B and no other ducks are added or removed, the new total duck population of Lake B could be which of the following? a) 144 b) 105 c) 78 d) 51 e) 36"
B
"Line segments AB and CD are of equal length and perpendicular bisectors of one another. If a line segment is drawn connecting point A to point C, what is the measure of angle ACD? A. 0° B. 45° C. 60° D. 90° E. 180°"
B
"What is the minimal value of function f(x)? (1) f(0) = 16 (2) f(x) = (x - 4)2"
B
A camera lens filter kit containing 5 filters sells for $57.50. If the filters are purchased individually, 2 of them are priced at $10.45 each, 2 at $12.05 each, and 1 at $17.50. The amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually? 7% 8% 8.5% 10% 11%
B
An investment of $1,000 was made in a certain account and earned interest that was compounded annually. The annual interest rate was fixed for the duration of the investment, and after 12 years the $1,000 increased to $4,000 by earning interest. In how many years after the initial investment was made would the $1,000 have increased to $8,000 by earning interest at that rate? 16 18 20 24 30
B
Anne traveled from City A to City B in 4 hours, and her speed was between 25 miles per hour and 45 miles per hour. John traveled from City A to City B along the same route in 2 hours, and his speed was between 45 miles per hour and 60 miles per hour. Which of the following could be the distance, in miles, from City A to City B ? 95 115 125 160 180
B
If Pei ordered a total of 63 bottles of cola, root beer, and ginger ale for a party, how many bottles of cola did she order? (1) The number of bottles of root beer that Pei ordered was 80 percent of the number of bottles of ginger ale that she ordered. (2) The number of bottles of cola that Pei ordered was 75 percent of the total number of bottles of root beer and ginger ale that she ordered.
B
Is z equal to the median of the three positive integers x, y, and z ? (1) x < y + z (2) y = z
B
Of the 800 sweaters at a certain store, 150 are red. How many of the red sweaters at the store are made of pure wool? (1) 320 of the sweaters at the store are neither red nor made of pure wool. (2) 100 of the red sweaters at the store are not made of pure wool.
B
The cost of a certain phone call was $0.75 for the first 3 minutes and $0.20 for each additional minute after the first 3 minutes. Did the phone call last longer than 15 minutes? (1) The cost of the phone call was less than $4.16. (2) The cost of the phone call was greater than $3.35.
B
When positive integer x is divided by positive integer y, the remainder is 9. If x/y = 96.12, what is the value of y? A. 96 B. 75 C. 48 D. 25 E. 12
B
If a, b, and c are positive numbers such that a is b percent of c, what is the value of c? (1) a is c percent of b. (2) b is c percent of a.
B - statement 1 is the same as the question
"A certain high school has 5,000 students. Of these students, x are taking music, y are taking art, and z are taking both music and art. How many students are taking neither music nor art? (A) 5,000 - z (B) 5,000 - x - y (C) 5,000 - x + z (D) 5,000 - x - y - z (E) 5,000 - x - y + z"
"Easier formula to remember is Group1+ Group2- Both +Neither = Total (Source: Kaplan) So, solution is x + y - z + Neither = 5000 Neither = 5000 - x - y + z ..Choice E!"
A certain store sells small, medium, and large toy trucks in each of the colors red, blue, green, and yellow. The store has an equal number of trucks of each possible color-size combination. If Paul wants a medium, red truck and his mother will randomly select one of the trucks in the store, what is the probability that the truck she selects will have at least one of the two features Paul wants?
1/2
Kim finds a 1-meter tree branch and marks it off in thirds and fifths. She then breaks the branch along all the markings and removes one piece of every distinct length. What fraction of the original branch remains?
3/5
"Initially, the men and women in a room were in the ratio of 4 : 5. Then, 2 men entered the room and 3 women left the room. Then, the number of women doubled. Now there are 14 men in the room. How many women are currently in the room? A. 12 B. 14 C. 15 D. 24 E. 36"
43
How many circles can be drawn on the line segment above if each circle is subject to the rule that the endpoints of one of its diameters must be any two of the points A, B, C, D, E, F, G, H, J, K, L, and M? 36 66 72 78 121
66
"Is xy > y^2? (1) yx<1 (2) |x| > y"
Answer = E
"At his regular hourly rate, Don had estimated the labor cost of a repair job as $336 and he was paid that amount. However, the job took 4 hours longer than he had estimated and, consequently, he earned $2 per hour less than his regular hourly rate. What was the time Don had estimated for the job, in hours? (A) 28 (B) 24 (C) 16 (D) 14 (E) 12"
B
"Is x < 5? (1) x^2 > 5 (2) x^2 + x < 5 "
B
"Which of the following is greatest? A. 10√3 B. 9√4 C. 8√5 D. 7√6 E. 6√7"
B
"Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 4 days? (A) 24 (B) 18 (C) 16 (D) 12 (E) 8"
B
6.4 is what percent of 16,000? A. 0.004% B. 0.04% C. 0.4% D. 4% E. 4.4%
B
Does the integer k have a factor p such that 1 < p < k ? (1) k > 4! (2) 13! + 2 ≤ k ≤ 13! + 13
B
What is the value of x − y ? (1) 3x − z = 42 and y − z = 5. (2) x2 − xy − xz + yz = 84 and x − z = 12.
B
"If $ defines a certain operation, is p $ q less than 20? (1) x $ y = 2x^2 - y for all values of x and y (2) p = 4, q = 10"
C
"What is the ratio x : y: z ? (1) x + y = 2 z (2) 2x + 3y = z"
C
If xyz > 0, is x > 0 ? (1) xy > 0 (2) xz > 0
C
Is quadrilateral MNOP a square? (1) MN = NO = OP (2) Angle N and angle O are right angles.
C
Is the standard deviation of the numbers x, y, and z equal to the standard deviation of 10, 15, and 20 ? (1) z - x = 10 (2) z - y = 5
C
"Boomtown urban planners expect the city's population to increase by 10% per year over the next two years. If that projection were to come true, the population two years from now would be exactly double the population of one year ago. Which of the following is closest to the percent population increase in Boomtown over the last year? A) 20% B) 40% C) 50% D) 65% E) 75%"
D-65%
"What is the value of x? (1) x + 2y = 4 (2) 5x + y + 15 = 3x - 3y + 23"
E
A convenience store currently stocks 48 bottles of mineral water. The bottles have two sizes of either 20 or 40 ounces each. The average volume per bottle the store currently has in stock is 35 ounces. How many 40 ounce bottles are in stock? 20 24 28 32 36
E
If m, x, and y are positive integers, what is the value of x - y ? (1) 2x = m(2y) (2) m is a multiple of 4.
E
If p is an integer greater than 1, is p a prime number? (1) p is a factor of 13. (2) p is a factor of 78.
A
Which integer values of b would give the number 2002 / (10 raised to the -b) a value between 1 and 100?
-2,-3
If snow accumulation increased at a constant rate of 30 millimeters per hour during a certain snowstorm, how many seconds did it take for snow accumulation to increase by 1 millimeter?
120
if y is an integer, then the least possible value of |23-5y|
2
10 years ago, Sana was half as old as byron. if byron is now 15 years older than sana, how old will sana be in 7 years
32
"If c and d are integers, is c-3d even? (1) c and d are odd (2) c-2d is odd"
A (Shortened from first iteration)
"A rabbit on a controlled diet is fed daily 300 grams of a mixture of two foods, food X and food Y. Food X contains 10% protein and food Y contains 15% protein. If the rabbit's diet provides exactly 38 grams of protein daily, how many grams of food X are in the mixture. a)100 b)140 c)150 d)160 e)200"
B
"If 5^21 X 4^11 = 2x10^n. What is the value of n? A. 11 B. 21 C. 22 D. 23 E. 32"
B
"The sum of all the integers k such that −26 < k < 24 is (A) 0 (B) −2 (C) −25 (D) −49 (E) −51"
D
"For every integer k from 1 to 10, inclusive, the kth term of a certain sequence is given by (-1)^(k+1)*(1/2^k). If T is the sum of the first 10 terms in the sequence then T is A. Greater than 2 B. Between 1 and 2 C. Between 1/2 and 1 D. Between 1/4 and 1/2 E. Less than 1/4"
D
"If a and b are positive integers, is a/b < 9/11 ? (1) a/b < 0.818 (2) b/a > 1.223 "
D
"If x is a positive integer, what is the median of the set of consecutive integers from 1 to x inclusive? (1) The average of the set of integers from 1 to x inclusive is 11. (2) The range of the set of integers from 1 to x inclusive is 20."
D
If a is positive, what is the value of b? (1) ab = 2ab (2) |a + b| = |a − b|
D
List L: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 A group of 3 integers is to be selected one after the other, and at random and without replacement, from list L above. What is the probability that the 3 integers selected are not 3 consecutive integers? (A) 3/5 (B) 7/10 (C) 3/4 (D) 4/5 (E) 14/15
E
If |x | > 3, which of the following must be true? I. x>3 II. x2>9 III. |x-1|>2 I only II only I and II only II and III only I, II, and III
II and III only
x^y=y^x, where x is prime and y is even
If Y is even, Y^x must be even as well. It must be true then that x^y is also even. If x^y is even, X itself must be even. Since x is both even and prime, it must be true that x=2 since 2 is the only even prime
"Alexandra needs to mix cleaning solution in the following ratio: 1 part bleach for every 4 parts water. When mixing the solution, Alexandra makes a mistake and mixes in half as much bleach as she ought to have. The total solution consists of 27 mL. How much bleach did Alexandra put into the solution? "
3 ml
"A list kept at Town Hall contains that town's average daily temperature in Fahrenheit, rounded to the nearest integer, for each day of a particular completed month. Does this month have 30 or 31 days? (1) The median temperature is 73.5. (2) The sum of the average daily temperatures is divisible by 3."
A
"Company Q plans to make a new product next year and sell each unit of this new product at a selling price of $2. The variable costs per unit in each production run are estimated to be 40% of the selling price, and the fixed costs for each production run are estimated to be $5,040. Based on these estimated costs, how many units of the new product will Company Q need to make and sell in order for their revenue to equal their total costs for each production run? A. 4,200 B. 3,150 C. 2,520 D. 2,100 E. 1,800"
A
"If x is negative, is x < -3 ? (1) x^2 > 9 (2) x^3 < -9"
A
"For each student in a certain class, a teacher adjusted the student's test score using the formula y = 0.8x + 20, where x is the student's original test score and y is the student's adjusted test score. If the standard deviation of the original test scores of the students in the class was 20, what was the standard deviation of the adjusted test scores of the students in the class? A. 12 B. 16 C. 28 D. 36 E. 40"
Answer: B " (Shortened from first iteration)
"A pharmaceutical company received $3 million in royalties on the first $20 million in sales of the generic equivalent of one of its products and then $9 million in royalties on the next $108 million in sales. By approximately what percent did the ratio of royalties to sales decrease from the first $20 million in sales to the next $108 million in sales? (A) 8% (B) 15% (C) 45% (D) 52% (E) 56%"
C
"A store reported total sales of $385 million for February of this year. If the total sales for the same month last year was $320 million, approximately what was the percent increase in sales? (A) 2% (B) 17% (C) 20% (D) 65% (E) 83%"
C
"A store sells a certain product at a fixed price per unit. At the product's current price, q units cost a total of exactly $300. If the price were lowered by $5 from its current value, then q + 2n units would cost exactly $300; if the price were raised by $5, then q - n units would cost exactly $300. What is the value of q? A) 10 B) 15 C) 20 D) 25 E) 30
C
"(R is negative on number line) The number line shown contains three points R, S, and T, whose coordinates have absolute values r, s, and t, respectively. Which of the following equals the average (arithmetic mean) of the coordinates of the points R, S, and T ? A. s B. s + t - r C. (r - s - t)/3 D. (r + s + t)/3 E. (s + t - r)/3"
E
"At a certain food stand, the price of each apple is ¢ 40 and the price of each orange is ¢ 60. Mary selects a total of 10 apples and oranges from the food stand, and the average (arithmetic mean) price of the 10 pieces of fruit is ¢ 56. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is ¢ 52? A. 1 B. 2 C. 3 D. 4 E. 5"
E
"At a certain school, the ratio of the number of second graders to the number of fourth graders is 8 to 5, and the ratio of the number of first graders to the number of second graders is 3 to 4. If the ratio of the number of third graders to the number of fourth graders is 3 to 2, what is the ratio of the number of first graders to the number of third graders? A. 16 to 15 B. 9 to 5 C. 5 to 16 D. 5 to 4 E. 4 to 5"
E
"At a two-day seminar, 90 percent of those registered attended the seminar on the first day. What percent of those registered did not attend the seminar on either day? (1) A total of 1,000 people registered for the two-day seminar. (2) Of those registered, 80 percent attended the seminar on the second day."
E
"For a party, three solid cheese balls with diameters of 2 inches, 4 inches, and 6 inches, respectively, were combined to form a single cheese ball. What was the approximate diameter, in inches, of the new cheese ball? (The volume of a sphere is 43πr343πr3, where r is the radius.) (A) 12 (B) 16 (C) cube root of 16 (D) 2* cube root of 8 (E) 2* cube root of 36"
E
"If x and y are positive numbers such that x + y = 1, which of the following could be the value of 100x + 200y? I. 80 II. 140 III. 199 (A) II only (B) III only (C) I and II (D) I and III (E) II and III"
E
"If x, y, and z are positive numbers, what is the value of the average (arithmetic mean) of x and z ? (1) x - y = y - z (2) x^2 - y^2 = z"
E
"If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be (A) 2 (B) 5 (C) 6 (D) 7 (E) 14"
E
range of f(x)= (x+sq(3))^4
Range of function can never be negative. Raising anything to an even power will result in a non-negative value
From the consecutive integers -10 to 10 inclusive, 20 integers are randomly chosen with repetitions allowed. What is the least possible value of the product of the 20 integers?
-(10)^20
"Pascal has 96 miles remaining to complete his cycling trip. If he reduced his current speed by 4 miles per hour, the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50%. What is his current speed? A) 6 B) 8 C) 10 D) 12 E) 16"
"B The best way to solve this problem is to Work Backwards from the answer choices. When working backwards, start with answer (B) or (D), whichever looks easier. (Your default can be choice (B) unless that number looks annoying for some reason.)"
Idiom NOT by x BUT by y
"Think of it this way for structure - the word ""NOT"" is where the two paths diverge, and each path needs to be directly connected to the ""shared"" entry. So... The goal was scored not by Drogba, but by Donovan. Is correct, because ""the goal was scored ... (stop at ""NOT"" and start after ""BUT"") by Donovan"" is a complete statement. "
"In a certain class of students, 25% received A's on the final exam and 2/3 of these students received A's in the class as a whole. If 15 students in the class received A's on the final exam but did not receive an A in the class, how many students did not receive an A on the final exam? A) 45 B) 60 C) 105 D) 135 E) 180"
135
If xy not equal 0 and x^2*y^2 -xy = 6, which of the following could be y in terms of x? I. 1/2x II. -2/x III. 3/x A. I only B. II only C. I and II D. I and III E. II and III
Answer= E
"According to a certain estimate, the depth N(t), in centimeters, of the water in a certain tank at t hours past 2:00 in the morning is given by N(t)= -20(t - 5)^2 + 500 for 0 ≤ t ≤ 10. According to this estimate, at what time in the morning does the depth of the water in the tank reach its maximum? a) 5:30 b) 7:00 c) 7:30 d) 8:00 e) 9:00"
Answer = B
"For which of the following functions f is f(x) = f(1-x) for all x? A. f(x)=1−x B. f(x)=1−x^2 C. f(x)=x^2- (1-x)^2 D. f(x)=x^2∗(1−x)^2 E. f(x)=x / (1−x)"
D
"If x2/9 - 4/y2 = 12, what is the value of x? (1) x/3 + 2/y = 6 (2) x/3 - 2/y = 2 "
D
"If xy = 1, what is the value of 2^(x + y)^2 / 2^(xy)^2 A. 2 B. 4 C. 8 D. 16 E. 32"
D
"Working simultaneously at their respective constant rates, Machines A and B produce 800 nails in x hours. Working alone at its constant rate, Machine A produces 800 nails in y hours. In terms of x and y, how many hours does it take Machine B, working alone at its constant rate, to produce 800 nails? (A) x/(x+y) (B) y/(x+y) (C) xy/(x+y) (D) xy/(x-y) (E) xy/(y-x)"
"Say x=1 hour and y=2 hours (notice that y must be greater than x, since the time for machine A to do the job, which is y hours, must be more than the time for machines A and B working together to do the same job, which is x hours). In this case, the time needed for machine B to do the job must also be 2 hours: 1/2+1/2=1. Now, plug x=1 and y=2 in the options to see which one yields 2. Only option E fits. Answer: E. "
"Was the number of books sold at Bookstore X last week greater than the number of books sold at Bookstore Y last week? (1) Last week, more than 1,000 books were sold at Bookstore X on Saturday and fewer than 1,000 books were sold at Bookstore Y on Saturday (2) Last week, less than 20 percent of the books sold at Bookstore X were sold on Saturday and more than 20 percent of the books sold at Bookstore Y were sold on Saturday"
"y = t/q We need to determine whether x > y, or s/p > t/q, or sq > pt. Since s > t and q > p, and all values are positive, we can determine that sq is greater than pt, and thus that x > y. Answer: C "
A certain fruit stand sold apples for $0.70 each and bananas for $0.50 each. If a customer purchased both apples and bananas from the stand for a total of $6.30, what total number of apples and bananas did the customer purchase?
0.7a+0.5b=6.30.7a+0.5b=6.3 --> 7a+5b=637a+5b=63. After some trial and error you'll get that only two integer pairs of (a,b) satisfy this equation: (9,0) and (4,7) as we are told that "a customer purchased both apples and bananas" then the first pair is out and we'll have: a=4a=4 and b=7b=7 --> a+b=11a+b=11.
"100 people are attending a newspaper conference. 45 of them are writers and more than 38 are editors. Of the people at the conference, x are both writers and editors and 2x are neither. What is the largest possible number of people who are both writers and editors? 6 16 17 33 84"
16
If the sum of the last 3 integers in a set of 7 consecutive integers is 258, what is the sum of the first 4 integers?
330
On the planet Flarp, 3 floops equal 5 fleeps, 4 fleeps equal 7 flaaps, and 2 flaaps equal 3 fliips. How many floops are equal to 35 fliips?
35 fliips x 2 flaaps/3 fliips x 4 fleeps/7 flaaps x 3 floops/5 fleeps = 8 floops
"A list of measurements in increasing order is 4,5,6,8,10,x. If the median of these measurements is 6/7 times their arithmetic mean, What is the value of x? A. 16 B. 15 C. 14 D. 13 E. 12 "
A
"If money is invested at r percent interest, compounded annually, the amount of investment will double in approximately 70/r years. If Pat's parents invested $ 5000 in a long term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of investment 18 years later, when Pat is ready for college? A. $20000 B. $15000 C. $12000 D. $10000 E. $9000"
A
"If x is a positive integer, is x^2 + 6x +10 odd? (1) x^2 + 4x + 5 is odd (2) x^2 + 3x + 4 is even"
A
"Is q > t ? (1) qp^2 < tp^2 (2) qp^3 > tp^3"
A
"QUESTION 4 OF 31 A scientist is studying bacteria whose cell population doubles at constant intervals, at which times each cell in the population divides simultaneously. Four hours from now, immediately after the population doubles, the scientist will destroy the entire sample. How many cells will the population contain when the bacteria is destroyed? (1) The population just divided and, since the population divided two hours ago, the population has quadrupled, increasing by 3,750 cells. (2) The population will double to 40,000 cells with one hour remaining until the scientist destroys the sample."
A
"Raffle tickets numbered consecutively from 101 through 350 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 2 ? (A) 2/5 (B) 2/7 (C) 33/83 (D) 99/250 (E) 100/249"
A
" order to complete a reading assignment on time, Terry planned to read 90 pages per day. However, she read only 75 pages per day at first, leaving 690 pages to be read during the last 6 days before the assignment was to be completed. How many days in all did Terry have to complete the assignment on time? (A) 15 (B) 16 (C) 25 (D) 40 (E) 46"
B
"For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of all the even integers between 99 and 301? A. 10,100 B. 20,200 C. 22,650 D. 40,200 E. 45,150"
B
"If x = , then the value of is A. between −5×106 and −4×106 B. between −2.5×10−7 and −2×10−7 C. equal to −100 D. between 2×10−7 and 2.5×10−7 E. between 4×106 and 5×106"
B
"In Country C, the unemployment rate among construction workers dropped from 16 percent on September 1, 1992, to 9 percent on September 1, 1996. If the number of construction workers was 20 percent greater on September 1, 1996, than on September 1, 1992, what was the approximate percent change in the number of unemployed construction workers over this period? (A) 50% decrease (B) 30% decrease (C) 15% decrease (D) 30% increase (E) 55% increase"
B
"Is |x - y | > |x | - |y | ? (1) y < x (2) xy < 0"
B
"Pat bought 5 pounds of apples. How many pounds of pears could Pat have bought for the same amount of money? (1) One pound of pears costs $0.50 more than one pound of apples. (2) One pound of pears costs 1.5 times as much as one pound of apples."
B
"Six shipments of machine parts were shipped from a factory on two trucks, with each shipment entirely on one of the trucks. Each shipment was labeled either S1 (1/4), S2 (1/5), S3 (1/6), S4(3/20), S5(2/15), or S6 (1/10). The table shows the value of each shipment as a fraction of the total value of the six shipments. If the shipments on the first truck had a value greater than 1/2 of the total value of the six shipments, was S3 shipped on the first truck? (1) S2 and S4 were shipped on the first truck. (2) S1 and S6 were shipped on the second truck."
B
"The interior of a rectangular carton is designed by a certain manufacturer to have a volume of x cubic feet and a ratio of length to width to height of 3:2:2. In terms of x, which of the following equals the height of the carton, in feet? A. cube root of x B. cube root of (2x/3) C. cube root of (3x/2) D. 2/3 * cube root of x"
B
"s= {1,2,5,7,X} If x is a positive integer, is the mean of set S greater than 4? (1) the median of set s is greater than 2 (2) the median of set s is equal to the mean of set S"
B
"Beginning in January of last year, Carl made deposits of $120 into his account on the 15th of each month for several consecutive months and then made withdrawals of $50 from the account on the 15th of each of the remaining months of last year. There were no other transactions in the account last year. If the closing balance of Carl's account for May of last year was $2,600, what was the range of the monthly closing balances of Carl's account last year? (1) Last year the closing balance of Carl's account for April was less than $2,625. (2) Last year the closing balance of Carl's account for June was less than $2,675."
C
"If (1/3+1/4+1/5+1/6)=r(1/9+1/2+1/15+1/18), then r = A. 1/3 B. 4/3 C. 3 D. 4 E. 12"
C
"If [x] denotes the least integer greater than or equal to x, is [x] = 0? (1) -1< x< 1 (2) x < 0"
C
"On a camping trip, x campers each paid y dollars for food. What percent of the total food expenses did each camper pay? (1) If there were one fewer camper, each camper would owe 1 dollar more. (2) If there were half as many campers, each camper would owe 7 dollars more."
C
"Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 100. what is the value of x ? A) 50 B) 100 C) 200 D) 1000 E) 2000"
C
"Stores L and M each sell a certain product at a different regular price. If both stores discount their regular price of the product, is the discount price at Store M less than the discount price at Store L ? (1) At Store L the discount price is 10 percent less than the regular price; at Store M the discount price is 15 percent less than the regular price. (2) At Store L the discount price is $5 less than the regular store price; at Store M the discount price is $6 less than the regular price."
C
"What is the total number of coins that Bert and Claire have? (1) Bert has 50 percent more coins than Claire. (2) The total number of coins that Bert and Claire have is between 21 and 28."
C
"Of the students who eat in a certain cafeteria, each student either likes or dislikes lima beans and each student either likes or dislikes brussels sprouts. Of these students, 2/3 dislike lima beans; and of those who dislike lima beans, 3/5 also dislike brussels sprouts. How many of the students like brussels sprouts but dislike lima beans? (1) 120 students eat in the cafeteria (2) 40 of the students like lima beans"
D
"Team A and Team B are competing against each other in a game of tug-of-war. Team A, consisting of 3 males and 3 females, decides to lineup male, female, male, female, male, female. The lineup that Team A chooses will be one of how many different possible lineups? (A) 9 (B) 12 (C) 15 (D) 36 (E) 720"
D
"Yesterday's closing prices of 2,420 different stocks listed on a certain stock exchange were all different from today's closing prices. The number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price. How many of the stocks closed at a higher price today than yesterday? (A) 484 (B) 726 (C) 1,100 (D) 1,320 (E) 1,694"
D
"A candy wholesaler needs to quickly sell some candy bars that are nearing their expiration date, so he reduced the price of the candy bars. By what percent did he reduce the price of the candy bars? (1) The price of a candy bar was reduced by 36 cents. (2) If a candy retailer purchases a case of 144 candy bars from the wholesaler, she will save $51.84 as a result of the price reduction."
E
"In order to play a certain game, 24 players must be split into n teams, with each team having an equal number of players. If there are more than two teams, and if each team has more than two players, how many teams are there? (1) If thirteen new players join the game, one must sit out so that the rest can be split up evenly among the teams. (2) If seven new players join the game, one must sit out so that the rest can be split up evenly among the teams."
E
"Jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid, approximately how many liters of the 2 percent solution will be required? A) 18 B) 20 C) 24 D) 36 E) 42"
E
"Kevin invested $8,000 for one year at a simple annual interest rate of 6 percent and invested $10,000 for one year at an annual interest rate of 8 percent compounded semiannually. What is the total amount of interest that Kevin earned on the two investments? A. $880 B. $1,088 C. $1,253 D. $1,280 E. $1,296"
E
"On the number line, the distance between x and y is greater than the distance between x and z. Does z lie between x and y on the number line? (1) xyz < 0 (2) xy < 0"
E
"What is the number of cans that can be packed in a certain carton? (1) The interior volume of this carton is 2,304 cubic inches. (2) The exterior of each can is 6 inches high and has a diameter of 4 inches."
E
"A furniture dealer purchased a desk for $150 and then set the selling price to the purchase price plus markup that was 40 percent of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk? 1) $40 2) $60 3) $80 4) $90 5) $100"
E-100
"If R is the set of all numbers that, when squared, have a units digit of 1 or 9, then which of the following must be true about set R? I. All members of R are prime. II. If N is a member of R, -N is a member of R. III. If N is a member of R, is a member of R. Which statements are true?"
II and III only
