GMAT QUANT: PS

If Susan takes 9 seconds to run y yards, how many minutes will it take her to run x yards at the same rate?

Rule: Distance = (rate)(time) 1. Speed or rate = (y yards) / (9 seconds) Distance = x yards 2. x = (y/9)(time), time = 9x seconds / y yards 3. (9x seconds/y yards)*(1 minute/60 seconds) = 9x/60y minutes

Timothy leaves home for school, riding his bicycle at a rate of 9 miles per hour. Fifteen minutes after he leaves, his mother sees Timothy's math homework lying on his bed and immediately leaves home to bring it to him. If his mother drives at 36 miles per hour, how far (in terms of miles) must she drive before she reaches Timothy?

http://purplemath.com/modules/distance.htm

What Is The Lowest Possible Common Multiple Of 2 Distinct Integers, Each Greater Than 329?

1) Find the next term. 330 2) Multiply by 2 to get 660. 3) LCM of 330 and 660 is 660.

On a recent trip, Cindy drove her car 290 miles, rounded to the nearest 10 miles, and used 12 gallons of gasoline, rounded to the nearest gallon. The actual number of miles per gallon that Cindy's car got on this trip must have been between

1) Miles: 285-295 Gas: 11.5-12.5 2) The lowest number of miles per gasoline can be calculated using the lowest possible miles and the highest amount of gasoline and the highest miles with the lowest gasoline. 3) 285/12.5 to 295/11.5

The average of 5 consecutive odd numbers is 25. Find the smallest of these numbers.

1) Odd numbers = x, x+2, x+4, x+6, x+8 2) 5x + 20 is the sum of all the odd numbers. 3) (5x + 20) / 5 = 25 --> x = 21 4) Find the smallest number x, so 21.

If John Rolls A Plain Die Twice, What Is The Probability That Both Rolls Will Give The Same Result?

1) Probability of getting two 1's: (1/6)(1/6) = 1/36. But this is just the probability of 1's. Suppose he gets 2 and 2 or 3 and 3 or 4 and 4 etc. The probability of two 2's is 1/36 and the probability of two 3's is 1/36. The probabilities are the same. 6*(1/6) = 6/36 = 1/6.

Working individually, Deborah can wash all the dishes from her friend's wedding banquet in 5 hours and Tom can wash all the dishes in 6 hours. If Deborah and Tom work together but independently at the task for 2 hours, at which point Tom leaves, how many remaining hours will it take Deborah to complete the task alone?

1. Deb can do 1 job in 5 hours, so she can do 1/5 of the job in 1 hour. Tom can do 1/6 of the job in 1 hour. 2. (1/5) + (1/6) = 11/30 of the job in one hour. 3. (11/30) (2 hours) = 11/15 of the job in two hours. 4. Tom is leaving and so Deb has to the do the remaining 4/15 of the job. 5. Make a ratio. 1 job = 5 hours. (4/15) job = x hours? 6. (5)(4/15) = 4/3 hours is remaining for Deb to do the job alone.

What is the value of m in the equation below? (1/5)^m * (1/4)^24 = 1 / (2*(10)^47) A) 23 B) 24 C) 46 D) 47 E) 48

1. Find bases of exponents- 2, 4, 5, and 10. 2.Prime factor the bases. 4 would be 2 and 2. 10 would be 2 and 5. 3. (1/4)^24 would be rewritten as (1/2)^48. 4. Rewrite: (1/5)^m * (1/2)^48 = (1/2) * (1/(10)^47)). 5. Subtract 1/2 from both sides. (1/5)^m * (1/2)^47 = (1/(10^47)). 6. RULE: A^2 * B^2 = (A*B)^2 (1/5)^m * (1/2)^47 = (1/10)^47 (1/5) * (1/2) = (1/10), so m has to be equal to 47. ANSWER: D

If (12!) / 3^x is an integer, what is the greatest possible value of x? A) 3 B) 4 C) 5 D) 6 E) 7

1. Find the multiples of 3 in 12! 12! = 3, 6, 9, and 12. 2. Factor those out. 3 = (3)(1) 6 = (2)(3) 9 = (3)(3) 12 = (3)(4) 3. There are 5 threes. ANSWER: C.

If it takes 70 workers 3 hours to disassemble the exhibition rides at a small amusement park, how many hours would it take 30 workers to do this same job?

RULE: For problems which involve the work rates for a group of individuals (or machines), calculate first the work rate for a single person (or machine) and then multiply this rate by the number of persons (or machines) in the new group. The time necessary to complete the new task will be 1 divided by this number. 1. 70 workers take 3 hours to do 1 job, so in 1 hour, they can complete 1/3 of the job. 2. (1/70)(1/3) = 1/210 is the hourly work rate for an individual worker. 3. (30 workers)(1/210) = 1/7. Take the reciprocal, so it takes 7 hours. *Another way to set up the problem is 30H = (70)(3) --> H=7

At least 2/3 of the 40 members of a committee must vote in favor of a resolution for it to pass. What is the greatest number of members who could vote against the resolution and still have it pass?

1) (2/3)(40 members) = 27. 27 have to vote for it to pass, meaning that 13 can vote against it. 13.

M is the sum of the reciprocals of the consecutive integers from 201 to 300, inclusive. Which of the following is true?

1) 1/300 is less than 1/200. 2) Find how many integers are in between. 300-201=99 99+1=100 3) if you add 1/201 one hundred times your answer would be greater than adding 1/300 one hundred times. 1/200 * (100 integers) = 1/2 1/300 * (100 integers) = 1/3 Sum of M is between 1/3 and 1/2.

The ratio of 2 to 1/3 is equal to the ratio?

1) 2 / (1/3) = 6 2) ratio: 6:1

The price of lunch for 15 people was $207.00, including a 15 percent gratuity for service. What was the average price per person, EXCLUDING the gratuity?

1) 207 = 1.15c C= 180- this is the total before tip. 2) 180/15 = $12 per person

A Game At The State Fair Has A Circular Target With A Radius Of 10 Cm On A Square Board Measuring 30 Cm On A Side. Players Win Prizes If They Throw Two Darts And Hit Only The Circular Area On At Least One Of The Two Attempts. What Is The Probability That Jim Won The Game?

1) Find probability of hitting the circle: Area of circle = (pi)(10^2) = 100pi Area of square = (30^2) = 900 Probability = 100pi/ 900 --> pi/9 2) Probability of not hitting the circle = 1- (pi/9). Rewrite this as (9-pi) / 9. 3) For "At least questions, it is easier to calculate the odds of NOT HITTING the target on both shots, and then subtracting the probability of this happening from 1: Probability of "Good" Scenarios = 1 - Probability of "Forbidden" Scenarios. 1- ((9-pi)/9)). When you solve, you get: (18pi-pi^2)/81

A photography dealer ordered 60 Model X cameras to be sold for $250 each, which represents a 20 percent markup over the dealer's initial cost for each camera. Of the cameras ordered, 6 were never sold and were returned to the manufacturer for a refund of 50 percent of the dealer's initial cost. What was the dealer's approximate profit or loss as a percent of the dealer's initial cost for the 60 cameras?

1) Initial cost for a camera is (250/1.2). 2) For 60 cameras, that's (60)(250/1.2). 3) 54 were sold so that's (54)(250) and 6 were sold at half price so that's (6)(1/2)(250/1.2). Add them to get x. 4) (x / (60)(250/1.2)) - 1 5) 13%

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?

1) The investment doubles in 70/8 = 8.75 years or 9 years. 2) It will double twice so (5000)(2)(2) = 20000. Initial: 5000 8 years: 10000 Another 8 years: 20000

The Probability Of Winning Game A Is X And The Probability Of Winning Game B Is Y. When Playing A Single Round Of Each Of The Two Games, What Is The Probability Of Winning Exactly Once?

1) There are two scenarios: Win A and Lose B: (X)(1-Y) Win B and Lose A: (Y)(1-X) 2) Now add them because you can only win one and lose one. X- XY + Y- YX X+Y-2XY

In Town X, 64 percent of the population are employed, and 48 percent of the population are employed males. What percent of the employed people in Town X are females?

1) Use fake numbers. 2) 100 people in town X and 64% are employed so that's 64. 3) 48% are employed males so that's 48 people. 4) 64-48 = 16 employed females. 5) 16/64 = 1/4 = 25%

A committee that includes 6 members is about to be divided into 2 subcommittees with 3 members each. On what percent of the possible subcommittees that Michael is a member of is David also a member?

1) _ _ _ / _ _ _ There are 6 members that are going to be split in two committees. Michael has to be in one committee, so the probability of him getting into 1 is (3/6). Now it's David's turn. But David needs to be in the same committee as Michael. So the probability of that is (2/5) because there are 5 members left and he just needs to be with Michael's group which still has two remaining spots open. Since this is an "and" problem, you multiply. (3/6)(2/5) = 6/30 = 1/5 = 20%. This is the chance of them being in Committee A. Now what is the chance of them being in Committee B? Same chance- 20%. Then you add. 20% + 20% = 40%. 2) This is equivalent to: We have 6 chairs divided in 2 Groups: A and B each with 3 chairs. If Michael sits on the first chair in the group A, what is the possibility that David sits on any of another 2 available chairs in Group A? So: A: M _ _ / B: _ _ _ There are 2 chairs in Group A for favorable outcomes and 5 available chairs as total possible outcomes. The answer is 2/5

A Persian rug set on a dining room floor measures a inches by b inches, which includes the actual rug design and a solid colored border c inches. Which algebraic expression below represents the area of the solid colored border in square inches?

1) area of rug = (a)(b) = ab 2) area of rug - borders = (a-2c)(b-2c) 3) area of borders= (ab) - (a-2c)(b-2c) *You need to subtract both sides of the border.

Martha's Hair Saloon Has Recently Lowered The Prices Of Haircuts. If The Decrease In The Price Of A Haircut Is 20% Of The New Price Of A Haircut, What Is The Approximate Percent Decrease In The Price Of A Haircut At Martha's ?

1) decrease = 0.2(new price). Use 100 for new price. Decrease = 0.2(100) = 20 2) If the decrease from the new price to the old price is $20. Then, $20 + $100 = $120 was the original price. 3) Find percent decrease. (100-120) / 120 = 20/120 = 1/6 = 16.7%

The ratio, by volume, of soap to alcohol to water in a certain solution is 2:50:100. The solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved. If the altered solution will contain 100 cubic centimeters of alcohol, how many cubic centimeters of water will it contain?

1) original S:A = 2:50. Altered: 2 (2/50) =2/25. 2) original S:W = 2/100. Altered: (1/2)(2/100) = 1/100. 3) soap altered/ 100 = 2/25. Soap altered =8. 4) 8/ water altered = 1/100. Water altered = 800.

In the figure shown, what is the value of v+x+y+z+w? (A) 45 (B) 90 (C) 180 (D) 270 (E) 360

1. 180(n-2) to find the degrees of the pentagon. 180(5-2) = 540 degrees 2. Make triangles. a+x+z= 180 b+v+y= 180 c+x+w= 180 d+v+z= 180 e+y+w= 180 3. Sum all together. a+b+c+d+e+2v+2x+2y+2z+2w=900 4. Substitue 540 degrees for a+b+c+d+e. 2v+2x+2y+2z+2w= 360 5. Simplify to get v+x+y+z+w = 180 degrees. Answer: C.

A group of 4 junior lawyers require 5 hours to complete a legal research assignment. How many hours would it take a group of three legal assistants to complete the same research assignment assuming that a legal assistant works at two-thirds the rate of a junior lawyer?

1. 4 junior lawyers can finish a job in 5 hours. 4 junior lawyers can do (1/5) of the job in 1 hour. 2. 4x = (1/5) x→ 1/20 OR (1/4 lawyers)(1/5) = 1/20. One junior lawyer can do 1/20 of the job in 1 hour. 3. (3 assistants)(2/3 rate)(1/20) = 6/60 = 1/10. It would take the legal assistants 10 hours.

A river boat leaves Silver Town and travels upstream to Gold Town at an average speed of 6 kilometers per hour. It returns by the same route at an average speed of 9 kilometers per hour. What is the average speed for the round-trip in kilometers per hour?

1. Find a hypothetical distance using the LCM of 6 and 9. 6 = 6, 12, 18, 24... 9 = 9, 18, 24, 36... LCM= 18 2. Distance = (Rate)(Time) Upstream: 18km = (6km/hr)(time), time = 3 hours Downstream: 18km = (9km/hr)(time), time = 2 hours 3. Find average speed or rate. Rate = (Distance) / (Time) Rate = (18 + 18) / (3+2) = 36/5 = 7.2 km/hours

If a fair die is rolled three times, what is the probability that a 3 occurs on at least one roll? A) 25/36 B) 125/216 C) 91/216 D) 11/36 E) 36/216

1. Find the complement. You want there to be at least 1 three, but the complement is that there are no 3's. 2. The probability of not rolling a 3 is (5/6). 3. There are 3 rolls. (5/6)(5/6)(5/6) = 125/216. This is the probability of rolling no threes at all in the 3 rolls. 4. Subtract 1 - (125/216) because you want there to be at least 1 three. (216/216) - (125/216) = (91/216) ANSWER: C.

Given that N = a^3 b^4 c^5 where a, b and c are distinct prime numbers, what is the smallest number with which N should be multiplied such that it becomes a perfect square, a perfect cube as well as a perfect fifth power? A) a^3 b^4 c^5 B) a^5 b^4 c^3 C) a^2 b^3 c^5 D) a^7 b^6 c^5 E) a^27 b^26 c^25

1. For N to be a perfect square, prime numbers a, b, and c must all have even powers. For N to be a perfect cube, the powers must be a multiple of 3. For N to be a perfect fifth power, the powers must be a multiple of 5. 2. LCM: (even = 2)(3)(5) = 30. 3. a^ (30-3) = 27 b^ (30-4) = 26 c^ (30-5) = 25 4. Answer: E.

A certain club has 10 members, including Harry. One of the 10 members is to be chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Harry will be either the member chosen to be the secretary or the member chosen to be the treasurer? (A) 1/720 (B) 1/80 (C) 1/10 (D) 1/9 (E) 1/5

1. P(secretary): (9/10)- probability that harry is not president (1/9)- probability that harry is secretary (1)- probability that harry is not treasurer (9/10)(1/9)(1) = 9/90 = 1/10 2. P(treasurer): (9/10)- probability that harry is not president (1/9)- probability that harry is treasurer (1)- probability that harry is not secretary (9/10)(1/9)(1) = 9/90 = 1/10 3. (1/10) + (1/10) = 2/10 = 1/5 Answer: E

At a certain ice cream parlor, 1/9 of the ice cream cones sold in one week were pistachio and 1/4 of the remaining ice cream cones sold were rocky road. If n of the ice cream cones sold were rocky road, how many were pistachio? 1. (1/2)n 2. (3/4)n 3. (2/n) 4. (3 3/4) n 5. 5n

1. Pick a common multiple of both 4 and 9, so 36. 2. (1/9)(36) = 4 pistachio ice creams 3. (1/4)(32) = 8 rocky road ice creams 4. Ratio: 4 pista : 8 rocky road gets reduced to 1/2n. ANSWER: A.

A husband and wife can complete a certain task in 1 and 2 hours respectively. Their children, Rae and Herman, can complete the same task in 4 and 6 hours, respectively. What is the ratio of the couple's time working together to complete the task to the children's time working together to complete the task? A) 15 : 46 B) 3 : 10 C) 12 : 23 D) 5 : 18 E) 10 : 3

1. Rates are additive. Find rates of parents and children. Parents: (1/1) + (1/2) = 3/2 is the rate. Parents will take 2/3 of an hour to finish the work. Children: (1/4) + (1/6) = 5/12 is the rate. Children will take 12/5 of an hour to finish the work. 2. Ratios of parents:children is 2/3 : 12/5 3. Divide. (2/3) * (5/12) = 5:18 ANSWER: D

If the positive integer x is a multiple of 4 and the positive integer y is a multiple of 6, then xy must be a multiple of which of the following? I. 8 II. 12 III 18 A) II only B) I and II only C) I and III only D) II and III only E) I, II and III

1. The product of xy must be a multiple of 24. 2. Test out to see if 24 is a multiple of the choices: 24/8 =3 (works!) 24/12 =2 (works!) 24/18 = 1.333 (no) Answer: B.