Quantitative Comparison Questions 295 Quantitative Comparison Exercise B Directions: Each of the Questions 1-50 consists of two quantities, one in Column A and one in Column B.. The 15
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It takes x men to complete a Job in l2 days, but x — '4 men require A days
to do the same job
45 Weight of Mark and Lori Weight of Philip and Lori
46 The distance covered going at the The distance covered in 3 hours going
average rate of 40 miles per hour for at 50 miles per hour for the first hour
30 miles per hour for the next 2 hours
Martin is 5 times as old as Sara
Michael’s age is : of Martin’s age
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Quantitative Comparison Exercise B
Directions: Each of the Questions 1-50 consists of two quantities, one in Column A and one in Column B You are to compare the two quantities and choose
A if the quantity in Column A is greater;
B if the quantity in Column B 1s greater;
C if the two quantities are equal;
D if the relationship cannot be determined from the information given
Note: Since there are only four choices, NEVER MARK (E)
Common
Information: Ina question, information concerning one or both of the quantities to be compared is centered above the
two columns A symbol that appears in both columns represents the same thing in Column A as it does in
8 Area of square with perimeter of 32 Area of isosceles right triangle with
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10 The length of side AB of square The length of side KL of square
ABCD with a perimeter of 8 units KLMN with an area of 4 units
12 The volume of a cube is 27 The volume of a cube in which the
length of a diagonal of one face is
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27 Martin’s average speed if he walks 8 Michael’s average speed if he walks 5
miles in 2 hours miles in an hour and 30 minutes
32 2 hours, 40 minutes The elapsed time from 8:55 p.m to
10:15 the same evening
The distance from Mark’s house to the Waban school is 3 miles: the distance
from Sara’s house to this school is 4 miles
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Trang 9300 Quantitative Comparison Questions
Trang 10The discrete quantitative questions are like the standard
multiple-choice questions you have encountered in math
classes and on other standardized tests They cover
basic arithmetic operations, elementary algebra, and
plane geometry They test your knowledge of basic
mathematical concepts and also, in some cases, your
ability to apply that knowledge, as in questions that ask
you to solve a problem involving an actual or an abstract
situation The arithmetic questions deal with operations on
numbers and finding powers, roots of powers, percents,
and averages The algebra questions include linear equa-
tions, factorization, inequalities, exponents, and radicals
Also, some questions test the ability to set up an equation
TESTING TACTICS
You have 30 minutes for 30 questions The 15 quantitative
comparison questions should be done in 10 minutes That
leaves 20 minutes to do 5 data interpretation questions
and 10 discrete quantitative questions Thus, it is logical to
expect to allow a minute or a minute and a half for each
question If you find that you are spending as much as two
minutes on a question, you must come to some decision
about your answer right then and there However, mark the
question in some way so that you can return to it when you
have completed the section At that time the question may
read differently or perhaps some item that came up since
you left the question will help you answer it In any event
do not leave it blank There is no penalty for guessing on
orem, and coordinate geometry
There are 10 discrete quantitative questions in each quantitative section of the test—usually questions 16—20
and 26-30, with a set of 5 data interpretation questions in
between Generally, the first 5 discrete quantitative ques-
tions are easier than the last 5 The tactics and practice
exercises that follow will help you answer these
questions
Expect to encounter relatively easy questions in the early
part of the test Don’t be surprised to find a beginning
question such as the following:
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The example that follows was question 30 on a recent test,
and only 22% of the people who took the test chose the
correct answer The solution uses a time-saving strategy
of representing variable quantities by convenient
numbers of your own choice
If the length of each of the sides of three square gar-
den plots is increased by 50 percent, by what percent
is the sum of the areas of the three plots increased?
Time saved on a question permits more time for the chal-
lenging questions Remember that all questions carry the
same weight In general, GRE questions do not involve
lengthy, time-consuming computation Therefore, if you
come to a question that seems to require straightforward
but complex computation, look for a shortcut; there
almost always is one Consider this question Can you
arrive at the answer in less than 30 seconds, including
time to read the question?
1.116963 is exactly equal to 0.369 yeq
(A) 3.023 (B) 3.024 (C) 3.025 (D) 3.026
n a question such as this one, your ability to do compli-
cated division is not being tested Since the question indi-
cates that the quotient is exactly one of the answers, the
correct answer must obviously have, as its last digit, 7,
which when multiplied by 9 (the last digit of the de-
nominator) will yield 3 (the last digit of the numerator)
Choose (E)
Let the sides of the original three squares be 4, 6, and 8, respectively The enlarged squares would have sides 6, 9, and 12, respectively The sum of the areas of the original
squares would be 16 + 36 + 64 for a total of 116 square
units The sum of the areas of the three enlarged
squares would be 36 + 81 + 144 for a total of 261 square units, which is an increase of 145 square units:
Amount of increase Percent Increase = Original amount — x 100%
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Read the Questions Carefully
A dresser drawer contains 15 garments If 40 percent
of those garments are blouses, how many are NOT
blouses?
Read each question carefully to make sure you answer (A) 6
the question that was asked and not the one you (B) 8
expected to be asked Also, make sure you take all rele- (C) 9
vant information into consideration and that you work with (D) 10
This is a relatively easy question but the 82% that did not
choose (C) carelessly overlooked the word NOT
Visualize the Situation Presented;
make a pictorial representation of the facts situation
The length of a rectangular floor is 16 feet and its Point B is on line segment AC, and point E is on
width is 12 feet If each dimension were reduced by line segment DF If AB > DE and BC = EF, then
s feet to make the ratio of length to width 3 to 2,
what would be the value of s? (A) AC< DF (B)AC =DF (C)AC > DF
(D) DF >AC (E) EF > DF (A) 0
(B) 2
(C) 4
(D) 6
(E) 8
To obtain the correct answer quickly, use the following
Caution: The sketches you make need not be works of art Solution and sketch:
Don't spend time showing off; your test booklet will not be
quantities, the sums are unequal in the same
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Since ABCF is an isosceles trapezoid;
its area = (average of bases) x height
Be Prepared to Apply Basic Rules,
Formulas, and Concepts
Examinees are expected to have basic mathematical lem discussed under Tactic 5 the Pythagorean theorem
knowledge of arithmetic, algebra, and geometry, andtobe — was applied, as well as the formula for the area of an isos-
able to apply that knowledge in some cases In the prob- celes trapezoid
Look at the Answer Choices Before
Attempting to Answer Complex Problems
This tactic is important for several reasons you do not This should alert you to several possibili-
ties: you may be able to save time by estimating, there
is agood chance that a shortcut is involved, and you may be able to get the correct answer by eliminating
choices that just are not reasonable
1 Looking at the answer choices may show you a quick
way of solving the problem, as in the first example for
Tactic 1
3 The answer choices show you the form that is required
2 The answer choices give you an idea of how exact This information will Keep you from wasting time putting
your figuring has to be For example, if the choices are your answer in a form that is not-given For example, if
3, 4, 5, 6, 7, you Know you have to get a pretty exact the answers are all decimals, you do not want to com-
answer, whereas if the choices are 9, 18, 40, 80, 90, pute your answer in terms of fractions.
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If You Can’t Answer a Question, Try to
Work Back from the Answer Choices
sometimes this is easier and faster than trying to solve the Choice (A) is not correct because, when R = 2, S does
problem through other means For example, in the not = 5 Choice (B) is not correct because, when R = 3,
following question the best way to do this is to start with S does not = 8 Choice (C) is not correct because, when
answer choice (A) and substitute the values of the table in R= 1,S doesnot = 2 Choice (D), S = 3R — 1, is
each of the possible answers satisfied by all values in the table: (3 x 1) — (1) = 2,
(3 x 2) -1=5,(3 x 3) -1=8,(4 x 3) -1=11
(5 x 3) — 1 = 14, and (6 x 3) — 17 Choice (E) is
not correct because, when R = 7, S doesnot = 2
Which of the following equations gives the
relationship between R and S in the table above?
(A) S = 2R (B) S=KR +]
(CC) S=K&'-]
(D) S=3R— 1 (E) S=2R+s
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In 1970, it cost $12 to purchase 100 pounds of fer-
tilizer In 1990, it cost $34 to purchase 100 pounds
of fertilizer The price of 100 pounds of fertilizer
increased how many dollars between 1970 and
A house cost Ms Jones C dollars in 1989 Three
years later she sold the house for 25% more than she
paid for it She has to pay a tax of 50% of the gain
(The gain is the selling price minus the cost.) How
much tax must Ms Jones pay?
If the length of a rectangle is increased by 20%, and
the width of the same rectangle is decreased by
20%, then the area of the rectangle
Eight percent of the people eligible to vote are
between 18 and 21 In an election, 85% of those eli- gible to vote who were between 18 and 21 actually
voted In that election, people between 18 and 21
who actually voted were what percent of those peo- ple eligible to vote?
(A) 4.2 (B) 6.4 (C) 6.8 (D) 8 (E) 8.5
5
Directions: Each of the Questions 1|—25 has five answer choices For each of these questions, select the best of the
If n and p are both odd numbers, which of the fol-
lowing numbers must be an even number?
In the figure above, what is the length of the line segment that connects A to B?
Acab driver’s income consists of his salary and tips His salary is $50 a week During one week his tips were Ề of his salary What fraction of his income for
the week came from tips?
AZ By OZ (Đã (Bà
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10 Eggs cost 90¢ a dozen Peppers cost 20¢ each An °
omelet consists of 3 eggs and 2 of a pepper How
much will the ingredients for 8 omelets cost?
11 Itis 185 miles from Binghamton to New York
City If a bus takes 2 hours to travel the first 85
miles, how many minutes must the bus take to trav-
el the final 100 miles in order to average 50 miles
an hour for the entire trip?
|2 What is the area of the figure above, if ABDC is a
rectangle and BDE is an isosceles right triangle?
(E) none of these
4 In 1967, a new boat cost $2,500; in 1992, the same
type of boat cost $4,800 The cost of that type of
boat increased by what percent between 1967 and
Ifx + y = 6and 3x — y = 4, thenx — y=
In the figure above, BD is perpendicular to AC BA
and BC have length a What is the area of the trian-
gle ABC?
(B) xV⁄4 - x?
(C) aVa — x2 (D) 2aV⁄2 — a2 (E) xV»? - a
If two places are one inch apart on a map, then they are actually 160 miles apart (The scale on the map
is one inch equals 160 miles) If Seton is 2— inches
from Monroe on the map, how many miles is it from
Seton to Monroe?
(A) 3 (B) 27 (C) 300 (D) 360 (E) 460
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20 In the figure above, ABCD 1s a rectangle The area
of isosceles right triangle ABE = 7, EC = 3(BE)
(A) 21 (B) 28 ()42 (D) 56 (E) 84
21 An automobile tire has two punctures The first
puncture by itself would make the tire flat in 9 min-
utes The second puncture by itself would make the
tire flat in 6 minutes How long will it take for both
punctures together to make the tire flat? (Assume the
air leaks out at a constant rate )
22 For the integer n, if n’ is odd, which of the following
Statements is (are) true?
Discrete Quantitative Exercise B
Directions: Each of the Questions 1—25 has five answer choices
answer choices given
a —— —_—
1 A bus uses one gallon of gasoline to travel 15 miles 3
After a tune-up, the bus travels 15% farther on one
gallon How many gallons of gasoline (to the nearest
tenth) will it take for the bus to travel 150 miles after
a tune-up?
(A) 8.5 (B) 8.7 (C) 8.9 (D) 9.0 (E) 10.0
2 Ifx + 2y = 4 and} = 2, thenx =
(A)0 (B)3 (CO 1 (D3 (E)2
There are 50 students enrolled in Business 100 Of the enrolled students, 90% took the final exam Two-
thirds of the students who took the final exam passed
the final exam How many students passed the final
exam?
(A) 30 (B) 33) (C) 34 (D35 (E) 45
If a is less than b, which of the following numbers is
greater than a and less than b?
(A)
In the figure above, OR and PR are radii of circles
PR is tangent to the circle with center O The
length of OP is 4 If OR = 2 what is the length of
For each of these questions, select the best of the
It costs $1,000 to make the first thousand copies of a book and x dollars to make each subsequent copy If
it costs a total of $7,230 to make the first 8,000 cop-
ies of a book, what is x?
(A) 0.89 (B) 0.90375 (C) 1.00
(D) 89 (E) 90.375