Kaplan GRE Problem Solving Prep

18

A group of 30 tourists paid a total of $240 for admission to a museum exhibit. If the admission price for each adult was $10 and the admission price for each child was $5, how many adults were admitted to the exhibit? 12 18 20 22 24

5

A group of x friends buys 20 T-shirts that cost $4 each. They spend $1 per T-shirt to print a design and a total of $5 to promote their T-shirt business. They sell all 20 shirts for $18 each and split the profit equally. If each friend's share of the profit is $51, how many friends are in the group?

3,120

A restaurant pays a soda company $40 for every 120 bottles of soda purchased from the soda company, and the restaurant also pays a 5 percent service fee on the total charge for the bottles of soda purchased. If a service fee of $52 was charged for the bottles of soda purchased, how many bottles of soda were purchased by the restaurant? 17 170 1,020 3,120 7,650

24,000

During a drought, the amount of water in a pond was reduced by a third. If the amount of water in the pond was 48,000 gallons immediately after the drought, how many gallons of water were lost during the drought? 6,000 12,000 18,000 24,000 30,000

43x^2

For all a and all b, a ◊ b = a^2 + 2ab + 3b^2. Which of the following is equal to (2x) ◊ (3x) ? 6x 6x^2 20x^2 31x^2 43x^2

A,D, E

For which of the following equations does the line described by the equation have a greater slope than the line described by the equation y = 0.7x + 12 ? Indicate all possible correct answers. A) 3y = 2.4x - 15 B) y=1/10x+0.9 C) 3y + 18 = x D) y = 2x - 0.4 E) y/6=4/6x+1

30

Heidi drives directly from Town A to Town B and then continues to Town C, without stopping. The distance from B to C is 30 miles longer than the distance from A to B, and she travels a total of 270 miles. Her average speed when traveling from A to B is 20 miles per hour, and she spends half as much time traveling from B to C as from A to B. What is her average speed for the entire trip? 25 30 35 40 45

7

If y * z = (y + 3)(z − 3) for all y and z and 12 * x = 60, what is the value of x ? 5 7 8 12 23

5/8 hr

Jose requires 5 hours to paint a certain room. Shavonne requires 3 hours to paint the same room. If Jose and Shavonne work together, how long will it take them to paint 1/3 of the room? 8/45 hr 3/8 hr 5/8 hr 4/3hr 15/8 hr

x+3

Paul is trading baseball cards with his friends. He gives 3 cards to each of 3 different friends and receives a total of 12 cards in return. If Paul started with x cards, how many cards does he have after trading with his friends? x + 3 x + 6 x + 9 x + 12 x - 3

16

There is a total of 256 people at a party at 10:00 p.m. If every 15 minutes after that, half the people present leave, how many people will still remain at 11:05 p.m.? 128 64 32 16 8

C

Trevor drives the first leg of a trip, a distance of c miles, over a period of d hours. Then he drives the second leg of the trip, a distance of f miles, at an average rate of r miles per hour. What is Trevor's average speed for the entire trip in terms of variables c, d, f, and r ?

6

What is the value of z if 3z + 12 = 54 - 4z ? 6 7 12 14 42

7x^2

What is y in terms of x if 8y − 17x2 = 4x2 + 5y ? -7x^2 1/7x^2 3x^2 4x^2 7x^2

x > −6

Which of the following is the solution to the inequality 3x + 25 < 7x + 49 ? x < 6 x > 4 x > 3 x > −3 x > −6

A, B

Which of the following values of x would make the inequality 125+8≤−2x−4 true? Indicate all possible correct answers. −43/5 −36/5 −27/5 −22/5 −17/5 −11/5

72

Working alone, machine A can complete a job in 48 hours. Working alone, machine B can complete the job in y hours. After machines A and B worked on the job together for 12 hours, machine B completed the job by working alone for 42 hours. What is the value of y ? 54 72 75 84 90

-3, 3

f(x) = x^2 - 9 If f(p) = 0, which of the following could be the value of p ? Indicate all such values. -9 -3 0 3 9 81

-3/2, 4

g(x) = x^2 - 5x If a is a variable such that g(2a) = 24, which of the following could be the value of a ? Indicate all possible correct answers. -3 -2 −3/2 1/2 4

3(2x + 5)(x - 2)

6x^2 + 3x - 30 = 3(2x + 5)(x - 2) 3(2x - 5)(x + 2) 3(2x - 2)(x + 5) 3(3x - 10) 3(3x^2 - 10)

40

A car traveled 24 miles in 48 minutes. What must the car's average speed be, in miles per hour, over the next 48 miles be so that the car's average speed over the total distance of 72 miles is 36 miles per hour? 30 37 40 42 48

B, D, E

A gym charges a monthly membership fee of 2x dollars and a per-session charge for personal training of 3x dollars. Which of the following is equivalent to the cost of a membership at the gym for 12 months? Indicate all that apply. A) 3-month membership and 3 training sessions B) 3-month membership and 6 training sessions C) 6-month membership and 2 training sessions D) 6-month membership and 4 training sessions E) 9-month membership and 2 training sessions F) 9-month membership and 4 training sessions

20 cents

A phone card charges a flat fee for the first minute of a phone call, plus an additional charge per each extra minute of the call. For a caller using the phone card, an 11-minute call costs 55 cents, and a 23-minute call costs 97 cents. How much does the phone card charge for the first minute of a call? 3.5 cents 7 cents 10 cents 16.5 cents 20 cents

2.5%

A photographer purchases 30 rolls of black-and-white film and 25 rolls of color film. If the cost of each roll of color film is twice of the cost of each roll of black-and-white film, what percent of the total cost of the film is the price of a roll of color film? 0.5% 1.0% 2.0% 2.5% 3.0%

120

A safe holds only 8-ounce tablets of gold and 5-ounce tablets of silver. If the safe is full, with 130 ounces of gold and silver total, what is the greatest amount of gold that can be in the safe, in ounces? 40 80 120 128 130

$5.00

A snack bar sells bottles of soda and hamburgers. All bottles of soda are sold for the same price, and all hamburgers are sold for the same price. Five bottles of soda and eight hamburgers cost $34.00, while four bottles of soda and five hamburgers cost $23.00. How much would the snack bar charge for one bottle of soda and one hamburger? $3.00 $4.25 $4.75 $5.00 $5.50

75s

A soda-bottling machine can bottle 4,500 liters per minute. How many liters can it bottle in s seconds? 4,500s 75s 75/s 27,000/s 4,500/s

80

A street vendor sells two different newspapers, one for 25 cents and the other for 40 cents. If she sold 100 newspapers for $28, how many newspapers did she sell at 25 cents? 80 60 50 40 20

9 hours 20 minutes

Amy can grade 100 tests in 7 hours. If Amy and Jan can grade 100 tests in 4 hours working together, how many hours would it take Jan to grade 100 tests if she worked alone? 3 hours 10 minutes 5 hours 22 minutes 7 hours 30 minutes 9 hours 20 minutes 9 hours 33 minutes

y/3

Andrea is currently x years old, and David is currently 5 times Andrea's age. If in y years, David will be twice as old as Andrea, then which of the following must equal x ? y/10 y/5 y/3 y/2 3y

6 2/3

Angelo ran 6 miles per hour for 3 miles, and then he ran 8 miles per hour for 2 miles. What was his average speed for the entire run, in miles per hour? 6 1/3 6 2/3 6 4/5 7 1/3 7 2/3

65 5/11

At 12:00 on a standard mechanical clock, the hour hand and the minute hand are directly atop one another pointing to the top of the clock. The hour hand completes one revolution every 12 hours, and the minute hand completes one revolution every 60 minutes. Both hands move in a clockwise direction around the clock. How many minutes will it take before the minute hand next crosses the hour hand? 60 64 5/12 65 65 5/11 66

$4.50

At Best Burgers restaurant, 2 hamburgers and 5 orders of fries cost the same as 4 hamburgers and 2 orders of fries. If a single order of fries costs $1.50, what is the cost of 2 hamburgers? $2.25 $3.00 $4.50 $5.00 $6.00

$117

At store T, the price of every computer is the same and the price of every television is the same. If at store T, the total price of 26 televisions and 18 computers is $936 more than the total price of 18 televisions and 26 computers, how much more than the price of a computer is the price of a television? $36 $52 $78 $104 $117

828

Damond and Elissia both collect stamps. If Damond gives Elissia 72 stamps, then Damond will have 4 times the number of stamps that Elissia has. If Damond gives Elissia 129 stamps, then Damond will have 3 times the number of stamps that Elissia has. How many more stamps than Elissia does Damond now have? 288 387 672 750 828

787

If #y# = y^2 + 3 for all numbers y, and w = #5#, then what is the value of #w# ? 481 628 787 841 964

-1

If (a+3)/2+a+3=3 then a = -3 -32 -1 0 1

3

If 12r < 96 and 3r > -9, then r could be any of the following EXCEPT: -2 0 3 7 8

x < 3

If 2x - 16 > 3x - 19, then which of the following must be true? x > 3 x < 3 x < -3 x > 7 x < 16

4y - 1

If 3x + 1 = 12y - 2, what is the value of x in terms of y ? 4y 4y-2/3 4y - 1 12y - 1 (12y-1)/3

0

If 4 + x = 5x + 4, then x = 0 4/5 1 5/4 4

468

If 40 fence posts are placed in a line, and the distance between the centers of adjacent posts is 12 feet, what is the distance, in feet, between the centers of the posts at each end of the line? 240 456 468 480 492

x > 1

If 4x + 1 > 5, then which of the following must be true? x < -2 x < -1 x < 1 x > 1 x > 2

12

If 8x − 24 = 5x + 12, then x = 12/5 3 6 8 12

64

If 9u^2 − 12uv + 4v^2 = 4, then what is the value of (3u − 2v)^6 ? 8 16 48 64 256

12xz/y

If a rocket can travel x/5 miles every y seconds, how many miles can it travel in z minutes? xy/5z xz/5y xyz/6 12xy/z 12xz/y

-5 < a < 5

If a^2- 25 < 0, then which of the following must be true? a < -5 a > 5 a > 25 a < -5 or a > 5 -5 < a < 5

(nm)/12

If all pieces of candy for sale in a store cost the same, and 12 pieces of this candy cost n cents, then how much will m pieces of the candy cost, in cents? n/(12m) (12m)/n (nm)/12 m/(12n) 12nm

9

If one-half of a number plus three is equal to the number minus one, then the number is 4 8 9 10 12

1/q

If pqr ≠ 0 and if x = rq , y = pq , and z=rqp, then xyz= 1/p p q 1/q 1

105

If x = −6 and y = 4, what is the value of (3x + 25)(2y + 7) ? −185 105 180 270 405

2z > x + y

If x > y > z, then all of the following could be true EXCEPT: y + z < x 2x > y + z 2z > x + y xy > yz x + y > 2y + z

-2.2

If x^2 − y^2 = 3, and x is 5 larger than y, then what is the value of y ? -2.8 -2.2 2.2 2.8 3.2

20

In his coffee shop, Joe wants to make a special blend of Guatemalan and Ecuadorian coffees. If Guatemalan coffee costs $6 per pound, Ecuadorian coffee costs $8 per pound, and 30 pounds of the blend is to cost $200, how many pounds of Guatemalan coffee does Joe need to use? 20 16 12 10 It cannot be determined from the information given.

$546

In the previous week, the amount of commission that a salesperson earned on Monday was 3/7 of the amount of commission that the salesperson earned on Tuesday, the amount of commission that the salesperson earned on Tuesday was 7/10 of the amount of commission that the salesperson earned on Wednesday, and the salesperson earned the same amount of commission on Wednesday, Thursday, and Friday. If the salesperson earned a total of $7,280 in commission on Monday, Tuesday, Wednesday, Thursday, and Friday of the previous week, how much commission did the salesperson earn on Monday of the previous week? $546 $780 $1,274 $1,560 $1,820

3 hours 36 minutes

It takes Daniel 9 hours to clean an office building, and it takes Mark 6 hours to clean the same building. How long would it take the two of them, working together at their respective rates, to clean the building? 3 hours 3 hours 36 minutes 4 hours 45 minutes 6 hours 7 hours 30 minutes

(3x-5)/4

Items A and item B weigh a total of x pounds. If the weight of item A is 5 pounds less than 3 times the weight of item B, then what is the weight, in pounds, of item A, in terms of x ? (3x+5)/4 (3x-5)/4 (3x)/4 (7x+5)/3 (x+5)/4

$4,000

Jim, Ken, and Larry each received a raise from their employer. The sum of the three raises is $12,000. Jim's raise was three times the amount of Larry's raise. Ken's raise was twice the amount of Larry's raise. How much was the raise given to Ken? $1,000 $2,000 $3,000 $4,000 $6,000

12

Jose's house is 7 miles from Takisha's house. If Jose drives at an average speed of 35 miles per hour, how many minutes would it take him to travel between his and Takisha's house? 10 12 15 16 20

2n- 9

Liza took 5n photographs on a certain trip. If she gives 2 photographs to one friend, 2n + 4 photographs to another friend, and the average of those two numbers of photographs to a third friend, how many photographs will she have left? n- 1 n + 9 2n- 9 2n + 4 3n- 9

5 hr 20 min

Machine A can produce 1,000 sausages in 4 hours. Machine B can produce 1,000 sausages in 8 hours. Working together at their respective rates, how long will it take the machines to produce 2,000 sausages? 2 hr 40 min 4 hr 30 min 5 hr 20 min 6 hr 7 hr 40 min

15

Machines A, B, and C each work at a constant rate. Working alone, machine A can complete a job 75 minutes. Working alone, machine B can complete the job in 50 minutes. Working together, machines A, B, and C can complete the job in 10 minutes. How many minutes would it take machine C to complete the job working alone? 12 15 24 30 33 1/3

5, 8, 10, 12

Mark is 2 years older than Seth. Laura is twice as old as Mark. If Laura is at least 14 years old, which could be Seth's age? Indicate all possible values. 2 4 5 8 10 12

52

Person A wants to cover a box completely with gift wrap and have fewer than 5 square feet of gift wrap left over. If the box's dimensions are 2 feet × 3 feet × 4 feet, then which of the following, in square feet, would be an acceptable quantity of gift wrap to use? Select all that apply. 24 26 48 52 57 73

v=(r-x)/2

Rachel is now r years old and Victor is now v years old. In x years, Rachel's age will be twice Victor's age. Which of the following is an equation for v in terms of r and x ? v = 2r 1/2 v=r/2 v=(r-x)/2 v=(r+x)/2

2

Rhonda can complete a job in 12 hours, Steven can complete the job in 6 hours, and Theresa can complete the job in 3 hours. Rhonda, Steven, and Theresa all work at this job at a uniform rate. How many hours will it take all three of them working together to complete the job? 12/7 5/3 2 3 24/7

4

The average (arithmetic mean) of six positive numbers is 5. If the average of the least and greatest of these numbers is 7, what is the average of the other four numbers? 3 4 5 6 7

$19.75

The bursar at a university imposes a service charge of $4.75 per course for each course of 3 credit hours or less and a service charge of $5.50 for each course of more than 3 credit hours. If Victoria enrolls in two courses of two credit hours, one course of three credit hours, and one course of four credit hours, what is the total service charge to the bursar? $15.00 $19.00 $19.75 $20.50 $22.00

16

The length of a rectangle is twice the rectangle's width. What is the length of the rectangle, in feet, if the rectangle's area is 128 square feet?

580

The number of stamps that Joan has is 40 more than twice the number of stamps that Thomas has. If Joan gives Thomas 70 stamps, then Joan will have 3/2 as many stamps as Thomas. How many stamps does Joan have? 160 270 540 580 850

54

The operation # is defined for all x and all y by x # y = 5x + 2y. If z = 2 # 1, what is the value of 6 # z ? 42 48 54 72 82

−17 < a < 3

The operation Ω is defined for all x and y by x Ω y = x2 + xy. If (a + 3) Ω 8 < 84, then which of the following describes all the possible values of a ? a < −17 a > 3 3 < a < 7 3 < a < 14 −17 < a < 3

75

The price of a brand A radio is y dollars, and the price of a brand B radio is (y − 7) dollars. The total price of 272 brand A radios is equal to the total price of 300 brand B radios. What is the value of y ? 68 75 82 84 98

(3T−14)/5

The sum of two numbers is T, and one of the numbers is 7 less than 4 times the other number. If one of the numbers is subtracted from the other, which of the following represents that difference? (3T−14)/5 (T−7)/5 (4T−7)/5 (T+7)/5 (3T+14)/5

0 < z < 8

The sum of two positive numbers x and z is 50. If x is greater than 10 more than four times z, which of the following expression describes the range of possible values for z ? 0 < z < 4 0 < z < 8 0 < z < 10 8 < z < 10 8 < z < 50

59

The symbol # is defined for all x and all y by x # y = x^2 + 2y^2. What is the value of 3 # 5 ? 27 36 43 50 59

4

Twice k added to f is 19. Three k less than f is one less than zero. What is the value of k ? 3.8 4 8 11 12

$4,100

Waiter A's compensation for any week is $500 plus 15 percent of the portion of A's total receipts above $600 for that week. Waiter B's compensation for any week is 25 percent of B's total receipts for that week. For what amount of total weekly receipts would both waiters earn the same compensation? $12,200 $10,600 $8,900 $6,300 $4,100

18

What is the value of c if 5(c− 7) = 3c + 1 ? 18 24 27 30 36

4/5

Working individually, machines A, B, and C can do a certain job in 2, 3, and 6 hours, respectively. If the two faster machines worked together to do the job at their respective rates, in how many fewer hours could the job be done than if the two slower machines worked together to do the job at their respective rates? 1/3 4/11 4/5 2 4