GMAT Problem Solving

Directions and guidelines  for use – allocate 40 minutes

What follows are 20 GMAT Problem Solving questions. It is important that you attempt to solve each question within a 40 minute time period. Once you have solved each question select the best of the 5 answer choices. As you know you will be under severe time constraints when you take the actual test. Go to a quiet place where you can concentrate. It is also important that you are not overly tired when you begin.

How To Evaluate Your Results – This test is a tool to help you evaluate where you are starting from. If you answer 10 or more questions correctly, you are probably a good candidate for the “GMAT 800 Module”. If you answer fewer than 10 questions correctly, but have a strong math background and feel that you would have performed much better if you had been exposed to a strong math review before this test, you may still benefit from the “GMAT 800 Module”. (Of course you would need review your basic math skills prior to the course).

Test taking is in large part emotional – Whatever your score, it is important that you do not allow yourself to become discouraged. GMAT Problem Solving is very susceptible to improvement. The most you can say is that your performance is a measure of your GMAT Problem Solving Skills at a certain point in time.

Pre-Course Math Review – Most GMAT questions do not assume a level of math that goes beyond that which is commonly taught in high school. We do offer a Pre-Course Math Review. It is designed for people who do not have strong math backgrounds or for people who have been away from math for many years. For further information click here:

1. A chemist must add pure alcohol to a 100-liter solution that is 15
percent alcohol in order to produce a solution that is 20 percent
alcohol. How many liters of pure alcohol are needed?

(A) 9/2
(B) 5
(C) 25/4
(D) 10
(E) 100/7

2. If a high school were to sell t tickets for a charity hockey game,
the total revenue from ticket sales would be 25 percent greater than
the total costs of putting on the game. If the school sold all but 10
percent of the t tickets, the total revenue from ticket sales would be
what percent greater than the total costs of putting on the game?

(A) 2.5%
(B) 10%
(C) 12.5%
(D) 15%
(E) 16%

3. If the sum of the interior angles of polygon P is twice the sum of
the interior angles of hexagon H, how many sides does P have?

(A) 12
(B) 10
(C) 8
(D) 6
(E) 4

4. A 25-foot ladder is leaning against a wall that is perpendicular
to level ground. The top of the ladder is 4 feet below a window ledge
that is 24 feet from the ground. How many feet will the bottom of the
ladder need to be pushed in towards the wall so that the top of the
ladder touches the window ledge?

(A) 4
(B) 5
(C) 7
(D) 8
(E) 15

5. If 2x + 7y = 5 and 2y = 3x , what is the value of 2x + 3y?

(A) 1/5
(B) 2/5
(C) 3/5
(D) 12/5
(E) 13/5

6. One-quarter of the widgets produced by a certain company are
defective. Three-fifths of the defective widgets are rejected and
one-fifteenth of the nondefective widgets are rejected in error. If
all the widgets not rejected are sold, what percent of the widgets sold
by the company are defective?

(A) 5%
(B) 7.5%
(C) 10%
(D) 12.5%
(E) 15%

7. If x ≠ 0 , and x = √6xy – 9y2 , then in terms of y , x =

(A) 3y
(B) y
(C) y/3
(D) (y – y2)/4
(E) –3y

8. If x ≠ -2 and (x2 – 4)/3y = (x + 2)/6 , then, in terms of y, x =
(A) (y + 4)/2
(B) (y + 2)/2
(C) y + 2
(D) y + 4
(E) (y – 4)/2

9. How many two-digit whole numbers yield a remainder of 1 when divided
by 10 and a remainder of 3 when divided by 6?

(A) None
(B) One
(C) Two
(D) Three
(E) Four

10. A jogger running along a road at 5 kilometers per hour is overtaken
by a cyclist traveling at 30 kilometers per hour. If the cyclist stops
1 kilometer beyond where she passes the jogger, how many minutes after
the cyclist stops does the jogger reach her?

(A) 12
(B) 10
(C) 9
(D) 8
(E) 6

11. How many four digit numbers begin with a digit that represents an
even number and end with a digit that represents an even number?

(A) 20
(B) 25
(C) 250
(D) 2000
(E) 2500

12. A retailer wishes to price an item in such a way that should he
offer his customers a 20% discount on the advertised price the
resulting sale price will still net him a 20% net profit on his
wholesale cost of the item. At what price should he advertise an item
with a wholesale cost of $15.00?

(A) $24.00
(B) $22.50
(C) $21.00
(D) $18.75
(E) $18.00

13. When an object is dropped, the number of meters that it falls is
given by the formula p(t) = 0.5gt2 , where t is the time in seconds
since the object was dropped and g is 9.8. If it takes 5 seconds for
the object to reach the ground, how many meters does it fall during the
last 2 seconds?

(A) 19.6
(B) 29.4
(C) 49.0
(D) 78.4

14. If x = 1 + 1/2 + 1/4 + 1/8 and y = 1 + (1/2)x , then y exceeds
x by

(A) 1
(B) 1/2
(C) 1/4
(D) 1/8
(E) 1/16

15. If m ∆ n = mn – n + m , then for what value of n is m ∆ n equal to
m for all values of m?

(A) –1
(B) 0
(C) 1
(D) m
(E) n

16. A student answered 44 out of 50 questions on a test and achieved a
score of 32. The test was scored by subtracting twice the number of
incorrect answers from the number of correct answers. How many
questions did the student answer correctly?

(A) 16
(B) 40
(C) 42
(D) 44
(E) 46

17. What is the greatest possible product of 3 different integers, each
of which has a value between –10 and 5, inclusive?

(A) 120
(B) 200
(C) 450
(D) 500
(E) 720

18. When working alone, Rich can complete a certain job in 10 hours.
When working together with Steve, the two can complete the same job in
6 hours. How many hours would it take Steve, working alone, to
complete two of these jobs?

(A) 30
(B) 20
(C) 15
(D) 12
(E) 8

19. Over a three year period a salesperson had an average (arithmetic
mean) yearly income of $55,000. The salesperson earned three times as
much the second year as the first year but only half as much the third
year as the second year. What was the salesperson’s income the third

(A) $10,000
(B) $15,000
(C) $30,000
(D) $45,000
(E) $55,000

20. How many integers n greater than 10 and less than 100 are there
such that, if the digits of n are reversed, the resulting integer is n
+ 18?

(A) 5
(B) 6
(C) 7
(D) 8
(E) 9

1. C
2. C
3. B
4. D
5. E
6. D
7. A
8. A
9. D
10. B
11. D
12. B
13. D
14. E
15. B
16. B
17. C
18. A
19. D
20. C

Copyright © John Richardson 2003, 2004, 2005, 2006, 2007, all rights reserved.

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