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- Tips and
CHAPTER
23 Strategies
for the
Quantitative
Section
The following bullets summarize some of the major points discussed in the lessons and highlight critical
things to remember while preparing for the Quantitative section. Use these tips to help focus your review as
you work through the practice questions.
When multiplying or dividing an even number of negatives, the result is positive, but if the number of
■
negatives is odd, the result is negative.
In questions that use a unit of measurement (such as meters, pounds, and so on), be sure that all neces-
■
sary conversions have taken place and that your answer also has the correct unit.
Memorize frequently used decimal, percent, and fractional equivalents so that you will recognize them
■
quickly on the test.
Any number multiplied by zero is equal to zero.
■
A number raised to the zero power is equal to one.
■
Remember that division by zero is undefined.
■
For complicated algebra questions, substitute or plug in numbers to try to find an answer choice that is
■
reasonable.
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- – TIPS AND STRATEGIES FOR THE QUANTITATIVE SECTION –
When given algebraic expressions in fraction form, try to cancel out any common factors in order to
■
simplify the fraction.
When multiplying like bases, add the exponents. When dividing like bases, subtract the exponents.
■
Know how to factor the difference between two squares: x 2 – y 2 = (x + y)(x – y).
■
Use FOIL to help multiply and factor polynomials. For example, (x + y)2 = (x + y)(x + y) = x 2 + xy +
■
xy + y 2 = x 2 + 2xy + y 2.
When squaring a number, two possible choices result in the same square (i.e., 22 = 4 and [–2]2 = 4).
■
Even though the total interior degree measure increases with the number of sides of a polygon, the sum
■
of the exterior angles is always 360 degrees.
Know the rule for 45—45—90 right triangles: The length of a leg multiplied by 2 is the length of the
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hypotenuse.
Know the rule for 30—60—90 right triangles: The shortest side doubled is the hypotenuse and the short-
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est side times 3 is the side across from the 60-degree angle.
The incorrect answer choices for problem solving questions will often be the result of making common
■
errors. Be aware of these traps.
To solve the data-sufficiency questions, try to solve the problem first using only statement (1). If that
■
works, the correct answer will be either a or d. If statement (1) is not sufficient, the correct answer will
be b, c, or e.
To save time on the test, memorize the directions and possible answer choices for the data-sufficiency
■
questions.
With the data-sufficiency questions, stop as soon as you know if you have enough information. You do
■
not actually have to complete the problem.
Although any figures used will be drawn to scale, be wary of any diagrams in data-sufficiency prob-
■
lems. The diagram may or may not conform with statements (1) and (2).
Familiarize yourself with the monitor screen and mouse of your test-taking station before beginning
■
the actual exam. Practice basic computer skills by taking the tutorial before the actual test begins.
Use the available scrap paper to work out problems. You can also use it as a ruler on the computer
■
screen, if necessary. Remember, no calculators are allowed.
The HELP feature will use up time if it is used during the exam.
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A time icon appears on the screen, so find this before the test starts and use it during the test to help
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pace yourself. Remember, you have on average about two minutes per question.
Since each question must be answered before you can advance to the next question, on problems you
■
are unsure about, try to eliminate impossible answer choices before making an educated guess from the
remaining selections.
Only confirm an answer selection when you are sure about it — you cannot go back to any previous
■
questions. Reread the question a final time before selecting your answer.
Spend a bit more time on the first few questions — by getting these questions correct, you will be given
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more difficult questions. More difficult questions score more points.
368
- CHAPTER
24 Quantitative
Practice Test
The following Quantitative section practice test contains 80 multiple-choice questions that are similar to the
questions you will encounter on the GMAT® exam. These questions are designed to give you a chance to prac-
tice the skills you have learned in a format that simulates the actual exam. Answer these practice questions
carefully. Use the results to assess your strengths and weaknesses and determine which areas, if any, you need
to study further.
With 80 questions, this practice section has more than twice the number of questions you will see on
the actual exam. To practice the timing of the GMAT exam, complete the entire practice section in 162 min-
utes (2 hours and 42 minutes).
Record your answers on the answer sheet provided. Make sure you mark your answer clearly in the cir-
cle that corresponds to the question.
Remember that the GMAT exam is a CAT, and you will not be able to write anywhere on the exam. To
mimic the exam environment, do not write on the test pages. Make any notes or calculations on a separate
sheet of paper.
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- – QUANTITATIVE PRACTICE TEST –
ANSWER SHEET
1. a b c d e 28. a b c d e 55. a b c d e
2. a b c d e 29. a b c d e 56. a b c d e
3. a b c d e 30. a b c d e 57. a b c d e
4. a b c d e 31. a b c d e 58 a b c d e
5. a b c d e 32. a b c d e 59. a b c d e
6. a b c d e 33. a b c d e 60. a b c d e
7. a b c d e 34. a b c d e 61. a b c d e
8. a b c d e 35. a b c d e 62. a b c d e
9. a b c d e 36. a b c d e 63. a b c d e
10. a b c d e 37. a b c d e 64 a b c d e
11. a b c d e 38. a b c d e 65. a b c d e
12. a b c d e 39. a b c d e 66. a b c d e
13. a b c d e 40. a b c d e 67. a b c d e
14. a b c d e 41. a b c d e 68. a b c d e
15. a b c d e 42. a b c d e 69. a b c d e
16. a b c d e 43. a b c d e 70. a b c d e
17. a b c d e 44. a b c d e 71. a b c d e
18. a b c d e 45. a b c d e 72. a b c d e
19. a b c d e 46. a b c d e 73. a b c d e
20. a b c d e 47. a b c d e 74. a b c d e
21. a b c d e 48. a b c d e 75. a b c d e
22. a b c d e 49. a b c d e 76. a b c d e
23. a b c d e 50. a b c d e 77. a b c d e
24. a b c d e 51. a b c d e 78. a b c d e
25. a b c d e 52. a b c d e 79. a b c d e
26. a b c d e 53. a b c d e 80. a b c d e
27. a b c d e 54. a b c d e
Directions: Solve the problem and choose the letter indicating the best answer choice. The numbers used in
this section are real numbers. The figures used are drawn to scale and lie in a plane unless otherwise noted.
1. If the least common multiple of two prime numbers x and y is 10, where x y, then the value of 2x +
y is
a. 7
b. 9
c. 11
d. 12
e. 21
2. What is the product of 6% and 14%?
a. 0.00084
b. 0.0084
c. 0.084
d. 0.84
e. 8.4
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- – QUANTITATIVE PRACTICE TEST –
1
3. A taxicab fare costs x dollars for the first quarter of a mile and dollars for each quarter of a mile
4x
1
after that. How much will the total cost be for a 22 mile ride?
a. 3x
13
b. 4x
c. 10x
5
d. 4x
e. 2.5x
4. Which of the following measures could form the sides of a triangle?
I. 3, 3, 5
II. 6, 6, 12
III. 1, 2, 3
a. I only
b. II only
c. III only
d. I and II only
e. II and III only
5. Scott’s average (arithmetic mean) golf score on his first four rounds was 78. What score does he need
on his fifth round to drop his average score by 2 points?
a. 68
b. 72
c. 78
d. 88
e. 312
6. Celeste worked for h hours each day for d consecutive days. If she earns $9.50 per hour, what is the
total amount she earned?
9.50
a. h
d
b. 9.50 + d + h
c. 9.50 + dh
d. 9.50h + d
e. 9.50dh
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- – QUANTITATIVE PRACTICE TEST –
7. A certain jacket was marked down 20% the first week and another 20% the next week. What percent of
the regular price was the final cost of the jacket after the two markdowns?
a. 30%
b. 36%
c. 40%
d. 60%
e. 64%
8. If 20 typists can type 48 letters in 20 minutes, then how many letters will 30 typists working at the
same rate complete in 1 hour?
a. 63
b. 72
c. 144
d. 216
e. 400
9. What is the final balance of a bank account after two years if the starting balance is $1,000 at an annual
rate of 5%, using simple interest? Assume no other money was withdrawn or deposited.
a. $50
b. $100
c. $1,050
d. $1,100
e. $1,150
10. Which of the following has the smallest numerical value?
a. 23 × 22
b. 26
c. 25 × 21
d. (22)3
e. 23 × 33
11. How many liters of a 40% iodine solution need to be mixed with 35 liters of a 20% iodine solution to
create a 35% iodine solution?
a. 35
b. 49
c. 100
d. 105
e. 140
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- – QUANTITATIVE PRACTICE TEST –
12. If it takes Steve 6 hours to tile a floor and Cheryl 4 hours to tile the same floor, how long would it take
both Steve and Cheryl to tile the floor if they worked together?
a. 2 hours 12 minutes
b. 2 hours 24 minutes
c. 3 hours
d. 3 hours 12 minutes
e. 10 hours
13. Given the area of the three squares, find the perimeter of ABC.
A
25
9
C
B
16
a. 12
b. 12.5
c. 19.5
d. 20
e. 25
14. During a sale, the price of a pair of shoes is marked down 10% from the regular price. After the sale
ends, the price goes back to the original price. What is the percent of increase to the nearest percent
from the sale price back to the regular price for the shoes?
a. 9%
b. 10%
c. 11%
d. 15%
e. 90%
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- – QUANTITATIVE PRACTICE TEST –
15. How many degrees is the smaller angle?
3x – 40
2x
NOTE: FIGURE NOT DRAWN TO SCALE
a. 44
b. 88
c. 92
d. 132
e. 180
16. If the average (arithmetic mean) of x, x + 2, and x + 4 is 33, what is the value of x?
a. 30
b. 31
c. 32
d. 32
e. 37
17. If it costs d dollars to make the first 100 copies of a poster and e dollars for each poster after that, what
is the total cost of 125 posters?
a. 25d + 100e
b. 100d + 25e
c. 125de
d. d + 25e
e. 125de
18. If the volume of a cube is x 3 cubic units, what is the number of square units in the surface area of the
cube?
a. x 2
b. x 3
c. x 6
d. 6x 2
e. 6x 3
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- – QUANTITATIVE PRACTICE TEST –
19. If x – 3 is a multiple of two, what is the next larger multiple of two?
a. 2x
b. x – 2
c. x – 1
d. x – 5
e. x + 2
20. If 3x + 1 = 81, then x – 1 =
a. 2
b. 3
c. 4
d. 9
e. 27
21. For dinner at a restaurant, there are x choices of appetizers, y + 1 main courses, and z choices of
dessert. How many total possible choices are there if you choose 1 appetizer, 1 main course, and 1
dessert for your meal?
a. x + y + z + 1
b. xyz + xz
c. xy + z + 1
d. xyz + 1
1
e. xyz + 2
22. If x $ y is defined as 2(x + y)2, then what is the value of 2 $ 3?
a. 25
b. 36
c. 50
d. 100
e. 144
23. If x, y, and z are real numbers, which is always true?
I. x(yz) = (xy)z
x y
II. y z
III. z (x + y) = zx + zy
a. I only
b. II only
c. I and II only
d. I and III only
e. I, II, and III
375
- – QUANTITATIVE PRACTICE TEST –
24. If y = 6x, then 6y equals
a. 6x
b. 6x+1
c. 6x + 6
d. 6x
e. 6 x – 1
25. What is the smallest of six consecutive odd integers whose average (arithmetic mean) is x + 2?
a. x – 5
b. x – 3
c. x – 1
d. x
e. x + 1
26. The product of a and b is equal to 11 more than twice the sum of a and b. If b = 7, what is the value of
b – a?
a. 2
b. 5
c. 7
d. 24
e. 35
3
27. c 23 12 x 2 d
2
a. x
b. 3 x
c. x
d. x 2
e. x 3
4 2
28. The instructions state that Cheryl needs square yards of one type of material and square yards of
9 3
another type of material for a project. She buys exactly that amount. After finishing the project, how-
8
ever, she has square yards left that she did not use. What is the total amount of square yards of
18
material Cheryl used?
1
a. 12
1
b. 9
2
c. 3
1
d. 19
21
e. 9
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- – QUANTITATIVE PRACTICE TEST –
29. Which of the following values of x would satisfy the inequality x 1?
13
12
I. x = 2
II. x = 1 4 2
–2
3
–2
–1
III. x = 1 3 2
a. I only
b. II only
c. II and III only
d. I and III only
e. I, II, and III
30. John is three times as old as Sam. If John will be twice as old as Sam in six years, how old was Sam two
years ago?
a. 2
b. 4
c. 6
d. 8
e. 16
31. Given a spinner with four sections of equal size labeled A, B, C, and D, what is the probability of NOT
getting an A after spinning the spinner two times?
9
a. 16
1
b. 8
1
c. 4
1
d. 2
15
e. 16
32. A case of 12 rolls of paper towels sells for $9. The cost of one roll sold individually is $1. What is the
percent of savings per roll for the 12-roll package over the cost of 12 rolls purchased individually?
a. 9%
b. 11%
c. 15%
d. 25%
e. 90%
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33. How many different committees can be formed from a group of two women and four men if three
people are on the committee and at least one member must be a woman?
a. 6
b. 8
c. 10
d. 12
e. 16
34. Susan spent one-third of her money on books and half of the remaining money on clothing. She then
spent three-fourths of what she had left on food. She had $5 left over. How much money did she start
with?
a. $60
b. $80
c. $120
d. $160
e. $180
35. A truck travels 20 miles due north, 30 miles due east, and then 20 miles due north. How many miles is
the truck from the starting point?
a. 20.3
b. 70
c. 44.7
d. 50
e. 120
1 2× 1 2
1 2
2 5
36.
.04
a. .20
b. .5
c. 2
d. 5
e. 20
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- – QUANTITATIVE PRACTICE TEST –
37. A rectangular swimming pool is 20 feet by 28 feet. A deck that has uniform width surrounds the pool.
The total area of the pool and deck is 884 square feet. What is the width of the deck?
a. 2 feet
b. 2.5 feet
c. 3 feet
d. 4 feet
e. 5 feet
38. If a person randomly guesses on each question of a test with n questions, what is the probability of
guessing half of the questions correctly if each question has five possible answer choices?
a. 5n
5
b. 1 2
2n
n
1
c. 1 2
5
n
12
d. 1 2
5
2n
1
e. 1 2
5
39. Two integers are in the ratio of 1 to 4. If 6 is added to the smaller number, the ratio becomes 1 to 2.
Find the larger integer.
a. 4
b. 6
c. 12
d. 24
e. 30
40. The measure of the side of a square is tripled. If x represents the perimeter of the original square, what
is the value of the new perimeter?
a. 3x
b. 4x
c. 9x
d. 12x
e. 27x
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- – QUANTITATIVE PRACTICE TEST –
D ata Sufficiency Questions
Directions: Each of the following problems contains a question that is followed by two statements. Select your
answer using the data in statement (1) and statement (2), and determine whether they provide enough infor-
mation to answer the initial question. If you are asked for the value of a quantity, the information is suffi-
cient when it is possible to determine only one value for the quantity. The five possible answer choices are as
follows:
a. Statement (1), BY ITSELF, will suffice to solve the problem, but NOT statement (2) by itself.
b. Statement (2), BY ITSELF, will suffice to solve the problem, but NOT statement (1) by itself.
c. The problem can be solved using statement (1) and statement (2) TOGETHER, but not ONLY
statement (1) or statement (2).
d. The problem can be solved using EITHER statement (1) only or statement (2) only.
e. The problem CANNOT be solved using statement (1) and statement (2) TOGETHER.
The numbers used are real numbers. If a figure accompanies a question, the figure will be drawn to scale
according to the original question or information, but will not necessarily be consistent with the informa-
tion given in statements (1) and (2).
41. What is the value of x + 2y?
(1) 2x + 4y = 20
(2) y = 5 – 1 x
2
42. Is r – 5 a real number?
(1) r is a rational number.
(2) 2 r is an irrational number.
43. Is rectangle ABCD a square?
(1) m ∠ABC = 90
(2) AC CD
44. What is the measure of an interior vertex angle of a pentagon?
(1) The measure of each adjacent exterior angle is 72.
(2) The pentagon is a regular polygon.
45. What is the value of x?
(1) x + y = 6
(2) 2x – y = 9
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- – QUANTITATIVE PRACTICE TEST –
46. What is the value of x?
A
X°
D
B C
NOTE: FIGURE NOT DRAWN TO SCALE
(1) m∠ACB = 30
(2) m∠A + ∠B = 150
47. It takes Joe and Ted four hours to paint a room when they work together. How long does it take Joe
working by himself to paint the same room?
(1) The dimensions of the room are 12' by 12' by 8'.
(2) It takes Ted seven hours to paint the room by himself.
48. Is xy 0?
(1) x 1
(2) y 0
49. Given that C is the center of the circle and DB passes through C, what is the area of the sector of the
circle?
A
C
D B
(1) The diameter of the circle is 12.
(2) m ∠C = 30°.
50. Points A, B, and C are located in the same plane. What is the distance between point A and point C?
(1) The distance between A and B is 100 cm.
(2) The distance between A and B is twice the distance between B and C.
381
- – QUANTITATIVE PRACTICE TEST –
51. In the following figure, p || n. Is x supplementary to y?
n
p
x
l
y
m
(1) l ⊥ p
(2) l || m
52. Which store has a greater discount, store A or store B?
(1) Store B has 20% off all items.
(2) Store A has $20 off all items.
53. Is x + 1 a factor of 12?
(1) x + 1 is even.
(2) x + 1 is a factor of both 2 and 3.
54. What is the value of x?
(1) 22 3x + 1 28
(2) x is an integer.
55. If x and y are consecutive even integers, what is the value of xy?
(1) x + y = 98
(2) y – x = 2
56. What is the numerical value of x 2 – 25?
(1) x – 5 = 3
(2) 4 – x = 5
57. A rectangular courtyard with whole-number dimensions has an area of 60 square meters. Find the
length of the courtyard.
(1) The width is two more than twice the length.
(2) The length of the diagonal of the courtyard is 13 meters.
382
- – QUANTITATIVE PRACTICE TEST –
58. Is x + y 2z ?
A
xy
z
B C
D
(1) ABC is equilateral.
(2) AD ⊥ BC
59. The circles in the diagram are concentric circles. What is the area of the shaded region?
(1) The area of the inner circle is 25 .
(2) The diameter of the larger circle is 20.
60. Find the value of x.
A
x
30°
C
B
(1) The length of BC is 2 3.
(2) The length of AC is 4.
383
- – QUANTITATIVE PRACTICE TEST –
61. What is the value of a + b?
(1) a 2 + b 2 = 13
12
(2) 2b a
62. Between what two numbers is the measure of the third side of the triangle?
(1) The sum of the two known sides is 10.
(2) The difference between the two known sides is 6.
63. What is the area of the circle?
(1) The radius is 6.
(2) The circumference is 12 .
64. What is the positive value of z ?
(1) 3y + z = 4
(2) z 2 – z = 12
65. Two cars leave the same city traveling on the same road in the same direction. The second car leaves
one hour after the first. How long will it take the second car to catch up with the first?
(1) The second car is traveling 10 miles per hour faster than the first car.
(2) The second car averages 60 miles per hour.
66. In right triangle XYZ, the m∠y = 90 . What is the length of XZ?
(1) The length of YZ = 6.
(2) m ∠z = 45
x y
7
67. Is ?
y x
(1) 3x = 6y
x
71
(2) y
68. What is the total cost of six pencils and four notebooks?
(1) Ten pencils and nine notebooks cost $11.50.
(2) Twelve pencils and eight notebooks cost $11.00.
69. What is the ratio of the corresponding sides of two similar triangles?
(1) The ratio of the perimeters of the two triangles is 3:1.
(2) The ratio of the areas of the two triangles is 9:1.
384
- – QUANTITATIVE PRACTICE TEST –
70. What percent of the class period is over?
(1) The time remaining is 1 of the time that has passed.
4
(2) The class period is 42 minutes long.
71. Daniel rides to school each day on a path that takes him first to a point directly east of his house and
then from there directly north to his school. How much shorter would his ride to school be if he could
walk on a straight-line path directly to school from his home, instead of east and then north?
(1) The direct straight-line distance from home to school is 17 miles.
(2) The distance he rides to the east is 7 miles less than the distance he rides going north.
72. What is the slope of line m?
(1) Line m intersects the x-axis at the point (4, 0).
(2) The equation of line m is 3y = x – 4.
73. Jacob is a salesperson. He earns a monthly salary plus a commission on all sales over $4,000. How
much did he earn this month?
(1) His monthly salary is $855 and his total sales over $4,000 were $4,532.30.
(2) His total sales for the month were $8,532.30.
74. Is ABC similar to ADE ?
A
D E
B C
(1) BC is parallel to DE
(2) AD = AE
75. The formula for compounded interest can be defined as A = p (1 + r)n, where A is the total value of the
investment, p is the principle invested, r is the interest rate per period, and n is the number of periods.
If a $1,000 principle is invested, which bank gives a better interest rate for a savings account, Bank A or
Bank B?
(1) The interest rate at Bank A is 4% compounded annually.
(2) The total amount of interest earned at Bank B over a period of five years is $276.28.
385
- – QUANTITATIVE PRACTICE TEST –
76. A fence has a square gate. What is the height of the gate?
(1) The width of the gate is 30 inches.
(2) The length of the diagonal brace of the gate is 30 2 inches.
77. Find the area of the shaded region.
D
A B
C
(1) m ∠A = 43°.
(2) AB = 10 cm.
78. A circle and a straight line are drawn on the same coordinate graph. In how many places do the two
graphs intersect?
(1) The equation of the circle is x 2 + y 2 = 25.
(2) The y-intercept of the straight line is 6.
79. Michael left a city in a car traveling directly west. Katie left the same city two hours later going directly
east traveling at the same rate as Michael. How long after Katie left will they be 350 miles apart?
(1) An hour and a half after Katie left they are 250 miles apart.
(2) Michael’s destination is 150 miles farther than Katie’s.
80. What is the area of the shaded region?
O
A B
C
(1) ABC is equilateral.
(2) The length of BC is 16 inches.
386
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