GMAT Math PROBLEM SOLVING

SECTION 1 (D) $0.75

30 Minutes (20 Questions) (E) $0.90

1. The 180 students in a group are to be

seated in rows so that there is an equal
number of students in each row. Each of
the following could be the number of
rows EXCEPT
(A) 4 6. If XYZ in the figure above is a right
(B) 20 angle, what is the value of x?
(C) 30
(D) 40 (A) 155
(E) 90 (B) 145
(C) 135
2. A parking garage rents parking spaces for (D) 125
$10 per week or $30 per month. How (E) 110
much does a person save in a year by a
renting by the month rather than by the
b
week?
c
(A) $140
(B) $160 7. In the expression above, a, b, and c are
(C) $220 different numbers and each is one of the
(D) $240 numbers 2, 3, or 5. What is the least
(E) $260 possible value of the expression?

3. If y 5 x 2 2 x and x 3, then y 1
(A)
(A) 24 30
(B) 27 2
(B)
(C) 39 15
(D) 51 1
(E) 219 (C)
6
3
(D)
4. Of the following, which is the best 10
approximation to 0.0026 ? 5
(E)
6
(A) 0.05
(B) 0.06
8. A certain culture of bacteria quadruples
(C) 0.16
every hour. If a container with these
(D) 0.5
bacteria was half full at 10:00 a.m., at
(E) 0.6
what time was it one-eighth full?
5. At a certain diner, a hamburger and (A) 9:00 a.m.
coleslaw cost $3.59, and a hamburger (B) 7:00 a.m.
and french fries cost $4.40. If french fries (C) 6:00 a.m.
cost twice as much as coleslaw, how (D) 4:00 a.m.
much do french fries cost? (E) 2:00 a.m.
(A) $0.30
9. Al, Lew, and Karen pooled their funds to
(B) $0.45
buy a gift for a friend. Al contributed $2
(C) $0.60

1
GMAT Math PROBLEM SOLVING
1 2
less than of the cost of the gift and played of its games has a record of
3 3
1 17 wins and 3 losses. What is the
Lew contributed $2 more than of the greatest number of the remaining games
4
cost. If Karen contributed the remaining that the team can lose and still win at
$15, what was the cost of the gift? 3
least of all of its games?
4
(A) $24
(B) $33 (A) 7
(C) $36 (B) 6
(D) $43 (C) 5
(E) $45 (D) 4
(E) 3
10. What is the total number of integers
between 100 and 200 that are divisible 14. Dan and Karen, who live 10 miles apart
by 3? meet at a cafe that is directly north of
Dans house and directly east of Karens
(A) 33
house. If the cafe is 2 miles closer to
(B) 32
Dans house than to Karens house, how
(C) 31
many miles is the cafe from Karens
(D) 30
house?
(E) 29
(A) 6
11. Which of the following inequalities is (B) 7
equivalent to 10 2x > 18? (C) 8
(D) 9
(A) x > -14
(E) 10
(B) x > -4
(C) x > 4
15. If n is an integer and
(D) x < 4
(E) x < -4 2 3 5 7 11 13
n then which of the
77k
1 following could be the value of k?
12. In 1979 approximately of the 37.3
3 (A) 22
million airline passengers traveling to or (B) 26
from the United States used Kennedy (C) 35
Airport. If the number of such (D) 54
passengers that used Miami Airport was (E) 60
1
the number that used Kennedy 16. There were 36.000 hardback copies of a
2
Airport and 4 times the number that certain novel sold before the paperback
used Logan Airport, approximately how version was issued. From the time the
many millions of these passengers used first paperback copy was sold until the
Logan Airport that year? last copy of the novel was sold. 9 times
as many paperback copies as hardback
(A) 18.6 copies were sold. If a total of 441.000
(B) 9.3 copies of the novel were sold in all, how
(C) 6.2 many paperback copies were sold?
(D) 3.1
(E) 1.6 (A) 45.000
(B) 360.000
(C) 364.500
13. A certain basketball team that has

2
GMAT Math PROBLEM SOLVING
(D) 392.000 (C) $1.14
(E) 396.900 (D) $1.16
(E) $1.18
p
17. In the formula w t
, integers p 3x
v 20. If y 3 and is a prime integer
y
and t are positive constants. If w =2
1 greater than 2, which of the following
when v = 1 and if w when v = 64, must be true?
2 . x = y
then t = . y = 1
(A) 1 . x and y are prime integers.
(B) 2 (A) None
(C) 3 (B) only
(D) 4 (C) only
(E) 16 (D) only
(E) and
18. Last year Mrs. Long received $160 in
dividends on her shares of Company X
stock, all of which she had held for the
entire year. If she had had 12 more
shares of the stock last year, she would
have received $15 more in total annual
dividends. How many shares of the
stock did she have last year?
(A) 128
(B) 140
(C) 172
(D) 175
(E) 200

Month Average Price

per Dozen

April $1.26
May $1.20
June $1.08

19. The table above shows the average

(arithmetic mean) price per dozen of the
large grade A eggs sold in a certain store
2
during three successive months. If
3
as many dozen were sold in April as in
May, and twice as many were sold in
June as in April, what was the average
price per dozen of the eggs sold over the
three-month period?
(A) $1.08
(B) $1.10

3
GMAT Math PROBLEM SOLVING
SECTION 2 (A) 4
30 Minutes (20 Questions) (B) 4.5
(C) 6
1. The market value of a certain machine (D) 6.25
decreased by 30 percent of its purchase (E) 15
price each year. If the machine was
purchased in 1982 for its market value of 6. Of a certain high school graduating class,
$8,000, what was its market value two 75 percent of the students continued their
years later? formal education, and 80 percent of those
who continued their formal education
(A) $8,000
went to four-year colleges. If 300
(B) $5,600
students in the class went to four-year
(C) $3,200
colleges, how many students were in the
(D) $2,400
graduating class?
(E) $800
(A) 500
2. What percent of 50 is 15? (B) 375
(C) 240
(A) 30%
(D) 225
(B) 35%
(E) 180
(C) 70%
(D) 300%
7. What is the least integer greater than
1 2+0.5?
(E) 333 %
3
(A) 2
(B) 1
3. In a certain diving competition, 5 judges
(C) 0
score each dive on a scale from 1 to 10.
(D) 1
The point value of the dive is obtained by
(E) 2
dropping the highest score and the lowest
score and multiplying the sum of the
remaining scores by the degree of 8. Which of the following is equivalent to
difficulty. If a dive with a degree of 2x 4
2
for all values of x for
difficulty of 3.2 received scores of 7.5, 2 x 8x 8
8.0, 9.0, 6.0, and 8.5, what was the point which both expressions are defined?
value of the dive?
1
(A) 68.8 (A) 2
(B) 73.6 2x 6
(C) 75.2 1
(B)
(D) 76.8 9x 2
(E) 81.6 2
(C)
4. If 2x = 3y = 10, then 12xy = x6
1
(A) 1,200 (D)
x4
(B) 200
(C) 120 1
(E)
(D) 40 x2
(E) 20
9. A certain business printer can print 40
5. If Jack walked 5 miles in 1 hour and 15 characters per second, which is 4 times
minutes, what was his rate of walking in as fast as an average printer. If an
miles per hour? average printer can print 5 times as fast

4
GMAT Math PROBLEM SOLVING
as an electric typewriter, how many (C) 45
characters per minute can an electric (D) 50
typewriter print? (E) 55
(A) 2
13. 103 is how many times (0.01)3?
(B) 32
(C) 50 (A) 106
(D) 120 (B) 108
(E) 600 (C) 109
(D) 1012
10. When ticket sales began, Pat was the nth (E) 1018
customer in line for a ticket, and
customers purchased their tickets at the 14. Which of the following groups of
rate of x customers per minute. Of the numbers could be the lengths of the
following, which best approximates the sides of a right triangle?
time, in minutes, that Pat had to wait in
line from the moment ticket sales . 1, 4, 17
began? . 4, 7, 11
. 4, 9, 6
(A) (n - 1) x
(A) only
(B) n + x 1
(B) and only
n 1 (C) and only
(C)
x (D) and only
x (E) ,, and
(D)
n 1
15. When the stock market opened
n
(E) yesterday, the price of a share of stock X
x 1 1
was 10 . When the market closed,
2
11. If 6 gallons of gasoline are added to a 1
the price was 11 . Of the following,
3 4
tank that is already filled to of its which is closest to the percent increase
4
in the price of stock X?
9
capacity, the tank is then filled to (A) 0.5%
10
of its capacity. How many gallons does (B) 1.0%
the tank hold? (C) 6.7%
(D) 7.1%
(A) 20 (E) 7.5%
(B) 24
(C) 36 16. If x and y are integers and xy2 is a
(D) 40 positive odd integer, which of the
(E) 60 following must be true?
. xy is positive.
12. A bus trip of 450 miles would have . xy is odd.
taken 1 hour less if the average speed S . x + y is even.
for the trip had been greater by 5 miles
per hour. What was the average speed S, (A) only
in miles per hour, for the trip? (B) only
(C) only
(A) 10 (D) and
(B) 40 (E) and

5
GMAT Math PROBLEM SOLVING
students must contribute in order to pay
for the present?
y
(A)
R
17. The figure above shows the dimensions y
(B)
of a rectangular box that is to be Rx
completely wrapped with paper. If a xy
single sheet of paper is to be used (C)
Rx
without patching, then the dimensions
xy
of the paper could be (D)
R ( R x)
(A) 17 in by 25 in
y
(B) 21 in by 24 in (E)
(C) 24 in by 12 in R ( R x)
(D) 24 in by 14 in
(E) 26 in by 14 in

x y 3
18. 2x 2 y 6
The system of equations above has how
many
solutions?
(A) None
(B) Exactly one
(C) Exactly two
(D) Exactly three
(E) Infinitely many

19. If M and N are positive integers that

have remainders of 1 and 3,
respectively, when divided by 6, which
of the following could NOT be a
possible value of M+N?
(A) 86
(B) 52
(C) 34
(D) 28
(E) 10

20. The R students in a class agree to

contribute equally to buy their teacher a
birthday present that costs y dollars. If x
of the students later fail to contribute
their share, which of the following
represents the additional number of
dollars that each of the remaining

6
GMAT Math PROBLEM SOLVING
SECTION 3 5. If x is a number such that x2 3x + 2 =0
30 Minutes (20 Questions) and x2 x 2= 0, what is the value of x
(A) 2
1. 6.09 4.693 =
(B) 1
(A) 1.397 (C) 0
(B) 1.403 (D) 1
(C) 1.407 (E) 2
(D) 1.497
(E) 2.603 6. In traveling from a dormitory to a certain
1
city, a student went of the way by
5
2
foot, of the way by bus, and the
3
remaining 8 kilometers by car. What is
the distance, in kilometers, from the
dormitory to the city?
2. What is the area of the region enclosed (A) 30
by the figure above? (B) 45
(A) 116 (C) 60
(B) 144 (D) 90
(C) 176 (E) 120
(D) 179
(E) 284 7. A certain elevator has a safe weight limit
of 2,000 pounds. What is the greatest
3. If p = 0.2 and n = 100, then possible number of people who can
p (1 p ) safely ride on the elevator at one time
with the average (arithmetic mean)
n weight of half the riders being 180
(A) 0.002 pounds and the average weight of the
others being 215 pounds?
(B) 0.02 0.02
(C) 0 (A) 7
(D) 0.04 (B) 8
(E) 0.4 (C) 9
(D) 10
(E) 11
4. If each of 4 subsidiaries of Corporation R
has been granted a line of credit of 8. After paying a 10 percent tax on all
$700,000 and each of the other 3 income over $3,000, a person had a net
subsidiaries of Corporation R has been income of $12,000. What was the income
granted a line of credit of $112,000, what before taxes?
is the average (arithmetic mean) line of (A) $13,300
credit granted to a subsidiary of (B) $13,000
Corporation R? (C) $12,900
(A) $1,568,000 (D) $10,000
(B) $448,000 (E) $9,000
(C) $406,000
(D) $313,600 9. 1 [2 (3 [4 5] 6) 7]
(E) $116,000
(A) 2

7
GMAT Math PROBLEM SOLVING
(B) 0 the rug, in square meters?
(C) 1
(A) mn p (m + n)
(D) 2
(B) mn 2p(m +n)
(E) 16
(C) mn p2
(D) (m - p)(n - p)
10. The price of a model M camera is $209
(E) (m 2p)(n 2p)
and the price of a special lens is $69.
When the camera and lens are
15. Working alone, R can complete a certain
purchased together, the price is $239.
kind of job in 9 hours. R and S, working
The amount saved by purchasing the
together at their respective rates, can
camera and lens together is
complete one of these jobs in 6 hours. In
approximately what percent of the total
how many hours can S, working alone,
price of the camera and lens when
complete one of these jobs?
purchased separately?
(A) 18 (B) 12 (C) 9
(A) 14%
(D) 6 (E) 3
(B) 16%
(C) 29%
16. A family made a down payment of $75
(D) 33%
and borrowed the balance on a set of
(E) 86%
encyclopedias that cost $400. The
balance with interest was paid in 23
11. If 0.497 mark has the value of one
monthly payments of $16 each and a
dollar, what is the value to the nearest
final payment of $9. The amount of
dollar of 350 marks?
interest paid was what percent of the
(A) $174 (B) $176 (C) $524 amount borrowed?
(D) $696 (E) $704
(A) 6%
(B) 12%
12. A right cylindrical container with radius
(C) 14%
2 meters and height 1 meter is filled to
(D) 16%
capacity with oil. How many empty
(E) 20%
right cylindrical cans, each with radius
1
meter and height 4 meters, can be 17. If x0 and x 4 xy 4 y 2 , then, in
2
filled to capacity with the oil in this terms of y, x
container? (A) 2y
(A) 1 (B) 2 (C) 4 (B) y
y
(C)
(D) 8 (E) 16 2
4y2
13. If a sequence of 8 consecutive odd (D)
1 2y
integers with increasing values has 9 as
its 7th term, what is the sum of the (E) 2y
terms of the sequence?
(A) 22 (B) 32 (C) 36
(D) 40 (E) 44
18. Solution Y is 30 percent liquid X and 70
14. A rectangular floor is covered by a rug percent water. If 2 kilograms of water
except for a strip p meters wide along evaporate from 8 kilograms of solution
each of the four edges. If the floor is m Y and 2 kilograms of solution Y are
meters by n meters, what is the area of added to the remaining 6 kilograms of

8
GMAT Math PROBLEM SOLVING
liquid, what percent of this new solution SECTION 4
is liquid X? 30 Minutes (20 Questions)
(A) 30%
1. Which of the following is equal to 85
1 percent of 160?
(B) 33 %
3
(A) 1.88
1
(C) 37 % (B) 13.6
2 (C) 136
(D) 40% (D) 188
(E) 50% (E) 13,600

1
19. 1 1
2. The regular hourly wage for an employee
of a certain factory is $5.60. If the
employee worked 8 hours overtime and
0.03 0.37
1
(A) 0.004 earned 1 times this regular hourly
2
(B) 0.02775 wage for overtime, how much overtime
(C) 2.775 money was earned?
(D) 3.6036
(E) 36.036 (A) $67.20
(B) $55.40
(C) $50.00
(D) $44.80
(E) $12.00

20. If each side of ACD above has length

3 and if AB has length 1, what is the
area of region BCDE?
9 3. Square RSTU shown above is rotated in a
(A)
4 plane about its center in a clockwise
7 direction the minimum number of
(B) 3 degrees necessary for T to be in the
4
9 position where S is now shown. The
(C) 3 number of degrees through which RSTU
4 is rotated is
7
(D) 3 (A) 135o
2 (B) 180o
(E) 6 3 (C) 225o
(D) 270o
(E) 315o

Questions 4-5 refer to the following graphs.

9
GMAT Math PROBLEM SOLVING

4. Of the following, which is closest to the (E) 35 to 6

increase from 1975 to 1980 in the
amount received by the processor in 8. A grocer purchased a quantity of bananas
producing 6 ounces of frozen orange at 3 pounds for $0.50 and sold the entire
juice? quantity at 4 pounds for $1.00. How
many pounds did the grocer purchase if
(A) $0.03
the profit from selling the bananas was
(B) $0.05
$10.00?
(C) $0.06
(D) $0.08 (A) 40
(E) $0.13 (B) 60
(C) 90
5. In 1980, approximately what fraction of (D) 120
the cost to the consumer for the (E) 240
production of 6 ounces of frozen orange
juice went to the farmer? 9. There are between 100 and 110 cards in a
collection of cards. If they are counted
3 1 4 out 3 at a time, there are 2 left over, but if
(A) (B) (C)
11 3 9 they are counted out 4 at a time, there is
5 3 1 left over. How many cards are in the
(D) (E) collection?
9 5
(A) 101
6. 4
496 is between (B) 103
(C) 106
(A) 3 and 4 (D) 107
(B) 4 and 5 (E) 109
(C) 5 and 6
(D) 6 and 7
(E) 7 and 8

7. If x0, 2x =5y, and 3z =7x, what is the

ratio of z to y?
(A) 2 to 21
(B) 3 to 5
(C) 14 to 15
(D) 6 to 5

10
GMAT Math PROBLEM SOLVING
13. Which of the following integers does
NOT have a divisor greater than 1 that
is the square of an integer?
(A) 75
(B) 42
(C) 32
(D) 25
(E) 12

10. If A is the center of the circle shown

above and AB=BC=CD, what is the
value of x?
(A) 15
(B) 30
(C) 45 14. There are cogs around the
(D) 60 circumference of a wheel and each cog
(E) 75
is centimeter wide with a space of
16
11. Out of a total of 1,000 employees at a
certain corporation, 52 percent are centimeter between consecutive
16
female and 40 percent of these females
cogs, as shown above. How many cogs
work in research. If 60 percent of the
of this size, with the same space
total number of employees work in
between any two consecutive cogs, fit
research, how many male employees do
on a wheel with diameter 6 centimeters?
NOT work in research?
(A) 96
(A) 520
(B) 64
(B) 480
(C) 48
(C) 392
(D) 32
(D) 208
(E) 24
(E) 88
15. If rs = rs + r + s, then for what value
12. An instructor scored a students test of
of s is r s equal to r for all values of
50 questions by subtracting 2 times the
r?
number of incorrect answers from the
number of correct answers. If the (A) 1 (B) 0 (C) 1
student answered all of the questions 1
and received a score of 38, how many (D) (E) r
r 1
questions did that student answer
correctly?
16. In each production lot for a certain toy,
(A) 19 25 percent of the toys are red and 75
(B) 38 percent of the toys are blue. Half the
(C) 41 toys are size A and half are size B. If 10
(D) 44 out of a lot of 100 toys are red and size
(E) 46 A, how many of the toys are blue and
size B?
(A) 15 (B) 25 (C) 30
(D) 35 (E) 40

11
GMAT Math PROBLEM SOLVING
17. If 2x + 5y =8 and 3x = 2y, what is the SECTION 5
value of 2x + y? 30 Minutes (20 Questions)
(A) 4
1. What is the average (arithmetic mean) of
70 the numbers 15, 16, 17, 17, 18, and 19?
(B)
19
(A) 14.2
64
(C) (B) 16.5
19 (C) 17
56 (D) 17.5
(D)
19 (E) 18
40
(E) 2. Kathy bought 4 times as many shares in
19 Company X as Carl, and Carl bought 3
times as many shares in the same
18. A ladder 25 feet long is leaning against a company as Tom. Which of the following
wall that is perpendicular to level is the ratio of the number of shares
ground. The bottom of the ladder is 7 bought by Kathy to the number of shares
feet from the base of the wall. If the top bought by Tom?
of the ladder slips down 4 feet, how
many feet will the bottom of the ladder 3
slip? (A)
4
(A) 4 (B) 5 (C) 8 4
(D) 9 (E) 15 (B)
3
19. What is the least possible product of 4 3
(C)
different integers, each of which has a 1
value between 5 and 10, inclusive? 4
(D)
(A) 5040 (B) 3600 1
(C) 720 (D) 600 12
(E) 120 (E)
1
20. If a motorist had driven 1 hour longer
3. Of the following, which if closest to
on a certain day and at an average rate
of 5 miles per hour faster, he would 0.15 495
?
have covered 70 more miles than he 9.97
actually did. How many more miles (A) 7.5
would he have covered than he actually (B) 15
did if he had driven 2 hours longer and (C) 75
at an average rate of 10 miles per hour (D) 150
faster on that day? (E) 750
(A) 100 (B) 120 (C) 140
(D) 150 (E) 160 4. A manager has $6,000 budgeted for raises
for 4 full-time and 2 part-time
employees. Each of the full-time
employees receives the same raise, which
is twice the raise that each of the part-
time employees receives. What is the
amount of the raise that each full-time
employee receives?
(A) $750

12
 1
-
2

GMAT Math PROBLEM SOLVING

(B) $1,000 (E) 11
(C) $1,200
(D) $1,500 x x-y
(E) $3,000 9. If 2, then
y x

x (A) 1
5. x 2 ( ) 2 1
2 (B)
2
(A) x2 - x
1
x2 (C)
(B) 2
4 (D) 1
x2 (E) 2
(C)
2
10. If each photocopy of a manuscript costs
3x 2 4 cents per page, what is the cost, in
(D)
4 cents, to reproduce x copies of an x-page
3x 2 manuscript?
(E)
2 (A) 4x
(B) 16x
6. A hospital pharmacy charges $0.40 per (C) x2
fluidram of a certain medicine but allows (D) 4x2
a discount of 15 percent to Medicare (E) 16x2
patients. How much should the pharmacy
charge a Medicare patient for 3 11. Ken left a job paying $75,000 per year
fluidounces of the medicine?(128 to accept a sales job paying $45,000 per
fluidrams = 16 fluidounces) year plus 15 percent commission. If
(A) $9.60 each of his sales is for $750, what is the
(B) $8.16 least number of sales he must make per
(C) $3.20 year if he is not to lose money because
(D) $2.72 of the change?
(E) $1.02 (A) 40
(B) 200
7. (-1)2 - (-1)3= (C) 266
(D) 267
(A) 2
(E) 600
(B) 1
(C) 0
(D) 1
(E) 2

8. At a certain bowling alley, it costs $0.50

to rent bowling shoes for the day and
$1.25 to bowl 1 game. If a person has
$12.80 and must rent shoes, what is the
greatest number of complete games that
person can bowl in one day?
(A) 7
(B) 8
(C) 9
(D) 10

13
GMAT Math PROBLEM SOLVING
MONTHLY KILOWATT-HOURS 15
500 1,000 1,500 2,000 0.025 48
Present $24.0 $41.00 $57.00 $73.00 2
16.
0 3
Propos $26.0 $45.00 $62.00 $79.00 5 0.0024
ed 0 4
(A) 0.1
12. The table above shows present rates and (B) 0.2
proposed rates for electricity for (C) 100
residential customers. For which of the (D) 200
monthly kilowatt-hours shown would (E) 1,000
the proposed rate be the greatest percent
increase over the present rate? 17. A student responded to all of the 22
questions on a test and received a score
(A) 500 of 63.5. If the scores were derived by
(B) 1,000 adding 3.5 points for each correct
(C) 1,500 answer and deducting 1 point for each
(D) 2,000 incorrect answer, how many questions
(E) Each of the percent increases is the did the student answer incorrectly?
same.
(A) 3
13. If a, b, and c are three consecutive odd (B) 4
integers such that 10<a<b<c<20 and if (C) 15
b and c are prime numbers, what is the (D) 18
value of a + b? (E) 20
(A) 24 (B) 28 (C) 30
(D) 32 (E) 36

14. Of a group of people surveyed in a

political poll, 60 percent said that they
would vote for candidate R. Of those
who said they would vote for R. 90
percent actually voted for R. and of 18. The figure above represents a
those who did not say that they would rectangular parking lot that is 30 meters
vote for R. 5 percent actually voted for by 40 meters and an attached
R. What percent of the group voted for semicircular driveway that has an outer
R? radius of 20 meters and an inner radius
of 10 meters. If the shaded region is not
(A) 56% (B) 59% (C) 62% included, what is the area, in square
(D) 65% (E) 74% meters, of the lot and driveway?
1 1 1 1 (A) 1,350
15. If r 1 and s 1 r , (B) 1,200 + 400
3 9 27 3
(C) 1,200 + 300
then s exceeds r by
(D) 1,200 + 200
1 1 1 (E) 1,200 + 150
(A) (B) (C)
3 6 9
19. One-fifth of the light switches produced
1 1 by a certain factory are defective. Four-
(D) (E)
27 81 fifths of the defective switches are
1
rejected and of the nondefective
20
switches are rejected by mistake. If all

14
GMAT Math PROBLEM SOLVING
the switches not rejected are sold, what SECTION 6
percent of the switches sold by the 30 Minutes (20 Questions)
factory are defective?
1. If x is an even integer, which of the
(A) 4%
following is an odd integer?
(B) 5%
(C) 6.25% (A) 3x + 2
(D) 11% (B) 7x
(E) 16% (C) 8x +5
(D) x2
(E) x3

2. On a purchase of $120, a store offered a

payment plan consisting of a $20 down
payment and 12 monthly payments of
$10 each. What percent of the purchase
price, to the nearest tenth of a percent,
did the customer pay in interest by using
this plan?
20. In PQS above, if PQ =3 and PS = 4, (A) 16.7%
then PR (B) 30%
(C) 75.8%
9 (D) 106.7%
(A)
4 (E) 107.5%
12
(B) 5 3
5 3. ( 42 )
16 4 16
(C) (A) 6.3
5
(B) 9.8
15 (C) 179.2
(D)
4 (D) 224
20 (E) 280
(E)
3
4. When magnified 1,000 times by an
electron microscope, the image of a
certain circular piece of tissue has a
diameter of 0.5 centimeter. The actual
diameter of the tissue, in centimeters, is
(A) 0.005
(B) 0.002
(C) 0.001
(D) 0.0005
(E) 0.0002

5. In 1970 there were 8,902 women

stockbrokers in the United States. By
1978 the number had increased to
19,947. Approximately what was the
percent increase?
(A) 45%

15
GMAT Math PROBLEM SOLVING
(B) 125% x
(C) 145% (B)
24n
(D) 150%
(E) 225% xn
(C)
24
(D) 12xn
(E) 24xn

10. For a positive integer n, the number n!

is defined to be n(n - 1)(n - 2)(1). For
example, 4!=4(3)(2)(1). What is the
value of 5!-3!?

6. In the figure above, two rectangles with (A) 120 (B) 114 (C) 20
the same dimensions overlap to form the (D) 15 (E) 2
shaded region. If each rectangle has
perimeter 12 and the shaded region has 11. A man who died left an estate valued at
perimeter 3, what is the total length of $111,000. His will stipulated that his
the heavy line segments? estate was to be distributed so that each
of his three children received from the
(A) 15 (B) 18 (C) 21 estate and his previous gifts, combined,
(D) 22 (E) 23 the same total amount. If he had
previously given his oldest child
7. If one root of the equation 2x2 + 3x k = $15,000, his middle child $10,000, and
0 is 6, what is the value of k? his youngest $2,000, how much did the
(A) 90 youngest child receive from the estate?
(B) 42 (A) $50,000
(C) 18 (B) $48,000
(D) 10 (C) $46,000
(E) 10 (D) $44,000
(E) $39,000
8. Bottle R contains 250 capsules and costs
$6.25. Bottle T contains 130 capsules and 12. If y > 0, which of the following is equal
costs $2.99. What is the difference to 48 y 3
between the cost per capsule for bottle R
and the cost per capsule for bottle T? (A) 4 y 3 y
(A) $0.25 (B) 3 y 4 y
(B) $0.12 (C) 2 12 y
(C) $0.05 (D) 3 8 y
(D) $0.03
(E) 16 y 3 y
(E) $0.002

9. Trucking transportation rates are x dollars

per metric ton per kilometer. How much
does it cost, in dollars, to transport one 13. The volume of a box with a square base
dozen cars, which weigh two metric tons is 54 cubic centimeters. If the height of
each, n kilometers by truck? the box is twice the width of the base,
what is the height, in centimeters?
x
(A) (A) 2
12n
(B) 3
(C) 4

16
GMAT Math PROBLEM SOLVING
(D) 6 (D) 15% (E) 18%
(E) 9
18. When the integer n is divided by 6, the
q3 3
remainder is 3, Which of the following
r 1 2 3 is NOT a multiple of 6?
s 3 3
(A) n 3
(B) n + 3
14. If q, r and s are the numbers shown
(C) 2n
above, which of the following shows
(D) 3n
their order from greatest to least?
(E) 4n
(A) q, r, s
(B) q, s, r 19. How many liters of pure alcohol must
(C) r, q, s be added to a 100-liter solution that is
(D) s, q, r 20 percent alcohol in order to produce a
(E) s, r, q solution that is 25 percent alcohol?

15. The sum of the interior angles of any 7

(A)
polygon with n sides is 180(n 2) 2
degrees. If the sum of the interior angles (B) 5
of polygon P is three times the sum of 20
the interior angles of quadrilateral Q, (C)
3
how many sides does P have? (D) 8
(A) 6 (B) 8 (C) 10 39
(D) 12 (E) 14 (E)
4
16. In Company X, 30 percent of the 20. If 10 persons meet at a reunion and each
employees live over ten miles from person shakes hands exactly once with
work and 60 percent of the employees each of the others, what is the total
who live over ten miles from work are number of handshakes?
in car pools. If 40 percent of the
employees of Company X are in car (A) 10987654321
pools, what percent of the employees of (B) 1010
Company X live ten miles or less from (C) 109
work and are in car pools? (D) 45
(E) 36
(A) 12%
(B) 20%
(C) 22%
(D) 28%
(E) 32%

17. If an organization were to sell n tickets

for a theater production, the total
revenue from ticket sales would be 20
percent greater than the total costs of the
production. If the organization actually
sold all but 5 percent of the n tickets, the
total revenue from ticket sales was what
percent greater than the total costs of the
production?
(A) 4% (B) 10% (C) 14%

17
GMAT Math PROBLEM SOLVING
SECTION 7 (E) 0.0410
30 Minutes (20 Questions)
6. Mr. Jones drove from Town A to Town B
1. At the rate of $7.50 per hour, how many in x hours. On the return trip over the
hours must a person work to earn same route, his average speed was twice
$232.50? as fast. Which of the following expresses
the total number of driving hours for the
(A) 25
round trip?
(B) 27
(C) 29 2
(D) 30 (A) x
3
(E) 31
3
(B) x
2. Each month for 6 months the amount of 2
money in a benefit fund is doubled. At 5
(C) x
the end of the 6 months there is a total of 3
$640 in the fund. How much money was (D) 2x
in the fund at the end of 3 months? (E) 3x
(A) $80
(B) $100 7. If 3 is the greatest common divisor of
(C) $120 positive integers r and s, what is the
(D) $160 greatest common divisor of 2r and 2s?
(E) $320 (A) 2
(B) 3
3. 6[-2(6-9)+11-23]= (C) 4
(A) 224 (D) 6
(B) 108 (E) 12
(C) 36
(D) 24 1 1
8. If x +y = 5 and xy=6, then
(E) 79 x y

2 3 5 8 2 1
4. If , then n (A)
3 5 8 n 10 6
1
1 (B)
(A) 5
10 5
1 (C)
(B) 6
5 6
(C) 5 (D)
(D) 10 5
(E) 100 (E) 5

9. After 5 games, a rugby team had an

5. If d= 3.0641 and d is the number
average of 28 points per game. In order
obtained by rounding d to the nearest
to increase the average by n points, how
hundredth, then d d many points must be scored in a 6th
(A) 0.0001 game?
(B) 0.0041 (A) n
(C) 0.0059 (B) 6n
(D) 0.0141 (C) 28n

18
GMAT Math PROBLEM SOLVING
(D) 28 + n 9 months of operation. During the final
(E) 28 + 6n quarter the number of publicly listed
shares was increased to 10,000,000
10. On July 1, 1982, Ms. Fox deposited shares, and fourth quarter earnings were
$10,000 in a new account at the annual reported as $1.25 per share. What are
interest rate of 12 percent compounded the average annual earnings per share
monthly. If no additional deposits or based on the number of shares at the end
withdrawals were made and if interest of the year?
was credited on the last day of each
(A) $1.83
month, what was the amount of money
(B) $2.43
in the account on September 1, 1982?
(C) $4.85
(A) $10,200 (D) $8.45
(B) $10,201 (E) $9.70
(C) $11,100
(D) $12,100 15. In 1980 the government spent $12
(E) $12,544 billion for direct cash payments to
single parents with dependent children.
11. How many prime numbers are less than If this was 2,000 percent of the amount
25 and greater than 10? spent in 1956, what was the amount
spent in 1956? (1 billion =
(A) Three
1,000,000,000)
(B) Four
(C) Five (A) $6 million
(D) Six (B) $24 million
(E) Seven (C) $60 million
(D) $240 million
12. Erica has $460 in 5-and 10-dollar bills (E) $600 million
only. If she has fewer 10-than 5-dollar
bills, what is the least possible number
of 5-dollar bills she could have?
(A) 32
(B) 30
(C) 29
(D) 28
(E) 27
16. The triangles in the figure above are
equilateral and the ratio of the length of
13. Which of the following is equivalent to a side of the larger triangle to the length
2 2
the statement that 0.5 is between
n of a side of the smaller triangle is . If
1
3 the area of the larger triangular region is
and
n K, what is the area of the shaded region
in terms of K?
(A) 1<n<6
(B) 2<n<3 3
(C) 2<n<5 (A) K
4
(D) 4<n<6
(E) n>10 2
(B) K
3
14. A corporation with 5,000,000 shares of 1
publicly listed stock reported total (C) K
2
earnings of $7.20 per share for the first

19
GMAT Math PROBLEM SOLVING
1 (B) 10,200
(D) K (C) 15,050
3
(D) 20,050
1 (E) 20,100
(E) K
4
20. A merchant purchased a jacket for $60
17. Four cups of milk are to be poured into and then determined a selling price that
a 2-cup bottle and a 4-cup bottle. If each equalled the purchase price of the jacket
bottle is to be filled to the same fraction plus a markup that was 25 percent of the
of its capacity, how many cups of milk selling price. During a sale, the
should be poured into the 4-cup bottle? merchant discounted the selling price by
20 percent and sold the jacket. What
2
(A) was the merchants gross profit on this
3 sale?
7
(B) (A) $0
3 (B) $3
5 (C) $4
(C)
2 (D) $12
8 (E) $15
(D)
3
(E) 3

18. The outline of a sign for an ice-cream

3
store is made by placing of the
4
circumference of a circle with radius 2
feet on top of an isosceles triangle with
height 5 feet, as shown above. What is
the perimeter, in feet, of the sign?
(A) 3 3 3
(B) 3 6 3
(C) 3 2 33
(D) 4 3 3
(E) 4 6 3

19. The sum of the first 100 positive

integers is 5,050. What is the sum of the
first 200 positive integers?
(A) 10,100

20
GMAT Math PROBLEM SOLVING
SECTION 8 2
30 Minutes (20 Questions) (A)
3
1. A certain club has 237 local branches, 2
(B)
one national office, and one social 2
service office. If each local branch has 2
officers, and each of the two other offices
has 4 officers, how many officers does (C) ( 3)2
the club have altogether?
(A) 482 (B) 476 (C) 474
4
(D) 239 (E) 235 7 3
(D) ( )
2. An employee is paid a salary of $300 per
month and earns a 6 percent commission 8
on all her sales. What must her annual
sales be in order for her to have a gross
annual salary of exactly $21,600?
3
(E) 2( )
(A) $22,896
(B) $26,712
7
(C) $300,000
(D) $330,000 m2 m 3
6. If 1 then m could equal
(E) $360,000 3
(A) 1
3. Of the 1,000 students who entered (B) 0
College X as freshmen in September (C) 1
1979,112 did not graduate in May 1983. (D) 2
If 962 students graduated in May 1983, (E) 3
how many of the graduates did not enter
College X as freshmen in September
1979?
(A) 38 (B) 74 (C) 112
(D) 150 (E) 188

4. On the number line above, what is the

length of segment AB?
(A) 13
(B) 1.4 7. The figure above represents a rectangular
(C) 1.3 desk blotter in a holder with dimensions
(D) 0.13 shown. If x = 8 centimeters, what is the
(E) 0.013 area, in square centimeters, of the shaded
portion of the blotter?
(A) 4,200
(B) 4,184
5. Which of the following has a value (C) 4,124
greater than 1? (D) 4,072
(E) 3,944

21
GMAT Math PROBLEM SOLVING
8. The number 25 is 2.5 percent of which of 19
the following? (C)
31
(A) 10 117
(B) 62.5 (D)
196
(C) 100
107
(D) 625 (E)
(E) 1,000 186

9. Cottages at a resort are rented for half the 12. On a certain airline, the price of a ticket
summer price in each of the 3 spring is directly proportional to the number of
months and one-third the summer price miles to be traveled. If the ticket for a
in each of the 6 fall and winter months. If 900-mile trip on this airline costs $120,
each cottage brings in a total of $3,861 which of the following gives the number
when rented for each of the 12 months of of dollars charged for a k-mile trip on
the year, what is the monthly rent for this airline?
each of the 3 summer months? 2k
(A)
(A) $297 15
(B) $594 2
(C) $702 (B)
(D) $858 15k
(E) $1,782 15
(C)
2k
15k
(D)
2
40k
(E)
3
10. In 1980 Johns salary was $15,000 a
year and Dons salary was $20,000 a n m
13. If is 1 more than , then n =
year. If every year thereafter. John 41 41
receives a raise of $2,450 and Don
receives a raise of $2,000, the first year (A) m 41
in which Johns salary will be more than (B) m + 1
Dons salary is (C) m + 41
(D) m + 42
(A) 1987 (E) 41m
(B) 1988
(C) 1991 14. A discount of 20 percent on an order of
(D) 1992 goods followed by a discount of 10
(E) 2000 percent amounts to
11. Which of the following is equal to (A) less than one 15 percent discount
351 (B) the same as one 15 percent discount
? (C) the same as one 30 percent discount
558 (D) less than a discount of 10 percent
7 followed by a discount of 20 percent
(A) (E) the same as a discount of 10 percent
11 followed by a discount of 20 percent
39
(B)
62 15. If k is an even integer and p and r are
odd integers, which of the following

22
GMAT Math PROBLEM SOLVING
CANNOT be an integer? triangle have areas of A, B, C, and X as
shown. If A = 144, B=81, and C=225,
r then X =
(A)
k
(A) 150
k
(B) (B) 144
p (C) 80
p (D) 54
(C) (E) 36
r
kp
(D) 19. Three types of pencils, J,K, and L, cost
r $0.05, $0.10, and $0.25 each,
kr respectively. If a box of 32 of these
(E)
p pencils costs a total of $3.40 and if there
are twice as many K pencils as L pencils
16. Today Al is 3 times as old as Pat, In 13 in the box, how many J pencils are in
years, Al will be one year less than the box?
twice as old as Pat will be then. How (A) 6
many years old is Al today? (B) 12
(A) 12 (C) 14
(B) 33 (D) 18
(C) 36 (E) 20
(D) 42
(E) 49 20. Forty percent of the rats included in an
experiment were male rats. If some of
17. When the integer n is divided by 17, the the rats died during the experiment and
quotient is x and the remainder is 5. 30 percent of the rats that died were
When n is divided by 23, the quotient is male rats, what was the ratio of the
y and the remainder is 14. Which of the death rate among the male rats to the
following is true? death rate among the female rats?
(A) 23x + 17y =19 9 3 9
(B) 17x 23y = 9 (A) (B) (C)
14 4 11
(C) 17x +23y =19 6 7
(D) 14x + 5y = 6 (D) (E)
(E) 5x 14y = -6 7 8

18. In the figure above, three squares and a

23