a cả, , Letina fruit should ensune % In these questions, you are to classify each problem according to the five fixed answer choices, rather than find a solution to the problem -Each
Trang 2a cả, , Letina fruit should ensune
%
In these questions, you are to classify each problem according to
the five fixed answer choices, rather than find a solution to the problem
-Each problem consists of a question and two statements You are to decide
whether the information 1n each statement alone 38 sufficient to answer the
question.or, 1f neither 1s, whether the information in the two statements
together as sufficient
The following pages include test-taking strategies, sample questions,
‘ and a detailed explanation of every problem These‘explanations present
possible problem-solving strategies for the examples
4
1 Do not wasté valuable time solving a problem; you are 3 When geometric figures are involved, be very careful only to determine whether sufficient information ts given not to make unwarranted,assumptions based on the ‘
to solve the problem First consider statement (1) and figures Figures are not necessarily drawn to scale,
statement (2) separately and determine whether each they are generalized figures showing little more than alone gives sufficient information to solve the problem infersecting line segments and the betweenness of
Be sure to disregard the information given in statement (1) points, angles, and regions So, for example, if a figure , When you evaluate the information given in statement (2) described as a rectangle looks like a square you may ‘not
If either, or both, of the statements give sufficient infor- conclude that it 1s, in fact, a square just by looking at mation to solve the problem, click on the oval corresponding the figure
to the description of which statement(s) give sufficient ,
information to solve the problem If not, consider the
information in both statement (1) and statement (2)
Then click on the oval corresponding to the description ' `
of whether the statements TOGETHER give sufficient *
2 Remember that when you are determining whether there
1s sufficient information@Ovanswer a question of the
* form, “What 1s the value of 3?” the information given
must be sufficient to find one and only one value for y
Being able to determine minimum or maximum Values
or an answer of the form y = x + 2 1s not sufficient,
because such answers constitute a range of values rather
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Trang 3GMAT Test = Section 3: Quantitative
This data sufficiency problem consists of a question and two state-
ments, labeled (1) and (2), in which certain data are given You have
to decide whether the data given in the statements are sufficrent for
answering the question Using the data given in the statements plus
your knowledge of mathematics and everyday facts (such as the
number of days in July or the meaning of counterclockwise), you
the hands o clocle — rn TẾ `
@b To rermoye the lit, a+ Mp amtercloclews €
« statement (1) ALONE ts sufficient, but statement (2) alone is not
sufficient to answer the question asked; *
« statement (2) ALONE is sufficient, but statement (1) alone is not
sufficient to answer the question asked,
« BOTH statements (1) and (2) TOGETHER are sufficient to answer
the question asked; but NEITHER statement ALONE sufficient
e EACH statement ALONE is sufficient to answer the question asked,
« statements (1) and (2) TOGETHER are NOT sufficient to answer the
question asked, and additional data specific to the problem are
needed
i
Figures A figure accompanying a data sufficiency problem will conform
to the information given in the question, but will not necessarily —
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Help ‡ Confii
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Trang 4“ey
More TT conform to the additional information given in statements
(1) and (2)
Lines shown as straight can be assumed to be straight and
‘ lines that appear Jagged can also be assumed to be straight
Aaoviry o aengh | cư-ex^9^ Cy or You may assume that the positions of points, angles, regions,
etc , exist in the order shown and that angle measures are,
greater than zero
All figures lie in a plane unless otherwise indicated
are aft, level, suvfrte
In data sufficiency problems that ask for the value ofa quantity the data given in the statements are sufficient only when tt Is possible to determine exactly one numerical value for the quantity
Trang 5GMAT Test — Section 3: Quantitative Directions
Explanation: According to statement (1), PQ = PR, therefore, APQR 1s
isosceles and y= z Since x+ y+ z= 180, it follows that x + 2y= 180
Since statement (1) does not give a value for y, you cannot answer the
question using statement (1) alone According to statement (2), y = 40,
therefore, x+ z= 140 Since statement (2) does not give a value for Z,
you cannot answer the question using statement (2) alone Using both
statements together, since x + 2y = 180 and the value of y is given,
you can find the value of x Therefore, BOTH statements (1) and (2)
TOGETHER are sufficient to answer the question, but NEITHER
statement ALONE is sufficient
To review these directions for subsequent questions of this type, click on
HELP
Il TU
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Trang 6Ị
EACH statement ALONE 1s sufficient
At a certain picnic, each of the guests was served
either a single scoop or a double scoop of ice cream
How many of the guests were served a double scoop
of ice cream?
[
(1) At the picnic, 60 percent of the guests were
served a double scoop of ice cream
(2) A total of 120 scoops of ice cream were
served to all the guests at the picnic
A circular tub has a band painted around its circum-
ference, as shown above What is the surface area of
this painted band? -
(i) x=05
(2) The height of the tub 1s 1 meter
Is 1t true that a> b?
DATA SUFFICIENCY SAMPLE QUESTIONS
Statement (1) ALONE 1s sufficient, but statement (2) alone is not sufficient
Statement (2) ALONE 1s sufficient, but statement (1) alone 1s not sufficient `
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE 1s sufficient
Statements (1) and (2) TOGETHER are NOT sufficient
(1) Exactly 9 9 grams of flour are contained in
10 grams of the mix (2) Exactly 0 3 gram of baking powder 1s contained
in 30 grams ofthe mix
If a real estate agent recerved a commission of
6 pereent of the selling price of a certain house, what was the selling price of the house?
(1) The selling price minus the real estate agent’s commission was $84;600
(2) The selling price was 250 percent of the original purchase price of $36,000
@ What ts the value of lx| ?
Trang 7A Statement (1) ALONE 1s sufficient, but statement (2) alone 1s not sufficient
B_ Statement (2) ALONE 1s sufficient, but statement (1) alone 1s not sufficient
C BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE ts sufficient
D_ EACH statement ALONE 1s sufficient
E Statements (1) and (2) TOGETHER are NOT sufficient
9 A certain bakery sells rye bread in 16-ounce loaves 32.HA6
đu {op the sa loaves, and all loaves of the same size ~
sell fop the same price per loaf-regardless of the ˆ
number of loavés pũfchasedx What 1s the price of a 14 le — an a oa ere mane
(1) When the decimal is rounded to the nearest (1) The total price of a 16-ounce loaf and a tenth, 3 2 18 the result
24-ounce loaf of this bread is $2 40
- (2) When the decimal 1s rounded to the nearest (2) The total price of two 16-ounce loaves and ¬ hundredth, 3 24 1s the resuÌt,
one 24-ounce loaf of this bread 1s $3 40
15/ A certain company currently has how many employees?
(1) If 3 additional employees are hired by the
Ax
10 If y =n, what 1s the value of x ?
(1) yn = 10
the company
11 If m and n are consecutive positive integers, 1s (2) If no additional employees are hired by the
m greater than n ? company and 3 of the present employees
A resign, there will be fewer than 15 employees (1) m-—1land n+ 1 areconsecutive positive _ vy we in the company
(2) m 1s an even ese yaw ? on 2 II on 16 If x 1s equal to one of the numbers + —,OT —,
- - \Âm VÀ B _ è Na what 1s the value of x ? 4 8 3 ( 12 tam and Sand dụ ve mồng those people who sold re *
and Sandy sold a total of 100 of the tickets, how 4 2
many of the tickets did Paula sell? 3
(2) <x<z
2 (1) Sandy sold 3 as many of the raffle tickets as
Paula did vf a, b, and c are integers, is a—b+c greater
t
(2) Sandy sold 8 percent of all the raffle tickets sold hẳn at+b-c?
for Club X (1) Db 1s negative (2) ¢ 18 positive
13 Is the integer n odd?
Trang 8A Statement (1) ALONE 1s sufficient, but statement (2) alone 1s not sufficient
B_ Statement (2) ALONE 1s sufficient; but statement (1) alone 1s not sufficient
C BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE 1s sufficient
D EACH statement ALONE 1s sufficient
E Statements (1) and (2) TOGETHER are NOT sufficient
If n 1s an integer, then n 1s divisible by how many
positive integers?
t
(1) 2 1s the product of two different prime `
numbers
(2) n and 2° are each divisible by the same
number of positive integers
Ị
How many miles long is the route from Houghton
to Callahan?
(1) It will take 1 hour less time to travel the entire
route at an average rate of 55 miles per hour
than at an average rate of 50 miles per hour
(2) It will take 11 hours to travel the first half of
the route at an average rate of 25 miles per
hour
If x and y are positive, what is the value of x?
(1) x=3927y
(2) y=2279
John and David each received a salary increase
Which one received the greater dollar increase?
(1) John’s salary mcreased 8 percent
(2) David’s salary increased 5 percent
Carlotta can drive from her home to her office by
one of two possible routes If she must also return
by one of these routes, what 1s the distance of the
(1) When she drives from her home to her office
by the shorter route and returns by the
longer route, she drives a total of 42
kilometers ,
2) When she drives ‘both ways, from her home to
her office and back; by the longer route, she
drives a total of 46 kilometers
26 What is the number of 360-degree rotations that
a bicycle wheel made while rolling 100 meters in a straight {ine without slipping?
(1) The diameter of the bicycle wheel, including the
tire, was05 meter | (2) The wheel made twenty 360-degree rotations per minute
Vhat 1s the value of the sum of a list of n odd integers?
(1) n=8 (2) The square of the number of integers on the list >
(1) The cartoon runs without mterruption at the rate of 24 frames per second
(2) It takes 6 times as long to run the cartoon as it takes to rewind the film, and 1t takes a total
of 14 minutes to do both
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Trang 9What was the average number of miles per gallon
of gasoline for a car during a certain trip?
(1) The total cost of the gasoline used by the car
for the 180-mile trip was $12 00
(2) The cost of the gasoline used by the car for the
trip was $1 20 per gallon
PR = y, which of the three an f APQR _
has the.greatest degree measure? ee ee
The only contents of a parcel are 25 photographs
and 30 negatives What ts the total weight, in
ounces, of the parcel’s contents?
(1) The weight of each photograph 1s 3 times the
weight of each negative
(2) The total weight of 1 of the photographs and 2
of the negatives is = ounce ⁄
Statement (1) ALONE 18 sufficient, but statement (2) alone 1s not sufficient
Statement (2) ALONE 1s sufficient, but statement (1) alone is not sufficient › BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE 15 sufficient
Statements (1) and (2) TOGETHER are NOT sufficient
(2) trw=25
What is the ratio of x to y?
(1) x1s 4 more than twice y (2) The ratio of 0 5x to 2y 1s 3 to 5
If x, y, and z are three integers, are they consecu- tive integers?
(1) z-x=2 (2) x<y<z
What 1s the value of x?
(1) -@+y)=x-y
(2) x+y=2
A sum bf $200,000 from a certain estate was divided among a spouse and three children How much of the estate did the youngest child recéive?
"°
1 (1) The spouse received 2 of the sum from the estate, and the oldest child received of the remainder
(2) Each of the two younger children received
$12,500 more than the oldest child and
$62,500 less than the spouse
1
Trang 10If the Lincoln Library’s total expenditure for books,
periodicals, and newspapers last year was $35,000,
how much of the expenditure was for books?
(1) The expenditure for newspapers was 40 percent
greater than the expenditure for’ periodicals
(2) The total of the expenditure for periodicals and
newspapers was 25 percent less than the
expenditure for books
The symbol V represents one of the following
operations’ addition, subtraction, multiplication,
or division What is the value of 3 V 2 ?
(1) 0V1=l
(2) 1V0=1
”
The regular price for canned soup was reduced
during a sale How much money could one have
saved by purchasing a dozen 7-ounce cans of soup
at the reduced price rather than at the regular price?
(1) The regular price for the 7-ounce cans was 3 for
a dollar
(2) The reduced price for the 7-ounce cans was 4
for a dollar
If on a fishing trip Jim and Tom each caught some
fish, which one caught more fish?
(1) Jim caught 3 as many fish as Tom
(2) After Tom stopped fishing, Jim continued
fishing until he had caught 12 fish
If 5x + 3y = 17, what 1s the value of x ?
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
Statement (2) ALONE is sufficient, but statement (1) alone 1s not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient ⁄
Yesterday Nan parked her car at a certain parking garage that charges more for the first hour than for each additional hour If Nan’s total parking charge
at the garage yesterday was $3 75, for how many hours of parking was she charged?
(1) Parking charges at the garage are $0 75 for the first hour and $0 50 for each additional hour
or fraction of an hour (2) If the charge for the first hour had been $1 00, Nan’s total parking charge would have been
Trang 1148
49
A Statement (1) ALONE 1s sufficient, but statement (2) alone 1s not sufficient
B Statement (2) ALONE 1s sufficient, but statement (1) alone 1s not sufficient
C BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE 1s sufficient
D EACH statement ALONE 1s sufficient
E Statements (1) and (2) TOGETHER are NOT suffictent
(1) ~2x>0 54 If x+0, whats the value of (=) ?
(2) x=3
Of the 230 singie-family homes built in City X last
year, how many were occupied at the end of the
year? 55 From May 1, 1960, to May 1, 1975, the closing price
of a share of stock X doubled What was the (1) Of all single-family homes in City X, closing price of a share of stock X on May 1, 1960?
90 percent were occupied at the end of last
year
(2) A total of 7,200 single-family homes in City X
were occupied at the end of last year
(1) From May 1, 1975, to May 1, 1984, the closing price of a share of stock X doubled
(2) From May 1, 1975, to May 1, 1984, the closing price of a share of stock X mcreased by
50 Does the product ykmn equal 1 ?
jk 56 If d 1s a positive integer, 1s vd an integer?
(2) J= : and m= ; (2) Vd’ 1s the square of an integer
51 How many of the boys in a group of 100 children 57 If Q@ isan integer between 10 and 100, what 1s the
(1) One of Q’s digits 1s 3 more than the other, and (1) v the | ưng in the group, 60 percent have the sum of its digits 1s 9
(2) Of the children in the group, 40 are boys (2) 0<50
58 If digit A 1s the hundredths’ digit in the decimal
53 If p and gq are positive integers and pg = 24, 59 What 1s the value of x’ - y??
(lI) x-y=y+2
Q *-YFTS (2) 5 1s an integer
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Trang 12EACH statement ALONE 1s sufficient
MOO
wp
\
t
60 If represents one of the operations +, —,
and x,1s ke (2+ m)=(ke Q) + (ko m) for all
numbers k, 2, and m?
(1) ko 11s not equal to 1°k for some
numbers k
(2) » represents subtraction
61 Committee member W wants to schedule a one-
hour meeting on Thursday for himself and three
other committee members, X, Y, and Z Is there
a one-hour period on Thursday that 1s open for all
four members?
(1) On Thursday W and X‘ have an open period
from 9 00 am to 12 00 noon
(2) On Thursday Y has an‘open period from
10 00am to1 00 p.m, and Z has an open
period from 8 00am to 11 00 am
Y
62 If Jack’s and Kate’s annual salaries in 1985 were
each 10 percent higher than their respective annual
salaries in 1984, what was Jack’s annual salary in
(1) A total of 100 newspapers were sold at the
newsstand yesterday, 10 fewer than twace the
number sold today
(2) The number of newspapers sold at the news-
stand yesterday was 45 more than the
number sold today
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67 Twocars, S and T, each traveled a distance of
Statement (1) ALONE 1s.sufficient, but statement (2) alone 1s not sufficient
Statement (2) ALONE 1s sufficient, but statement (1) alone ts not sufficient
BOTH statements TOGETHER are sufficient; but NEITHER statement ALONE 1s sufficient
Statements (1) and (2) TOGETHER are NOT sufficient t
65 How much did a certain telephone call cost?
(1) The call lasted 53 minutes (2) The cost for the first 3 minutes was 5 times the cost for each additional minute
N68
66 A certain expressway has exits J, K, L, and M, 1n that order What is the road distance from exit K toexit L?
() The road distance from exit J to exit L 1s
21 kilometers (2) The road distance-from exit K to exit M is
(2) For the entire distance, car S traveled 20 miles per gallon of gasoline and car T traveled
25 miles per gallon of gasoline
68 If 1 1s a positive integer, 1s n odd?
⁄
(1) 3m 1s odd (2) m + 31s even
69 Does 2m—3n=0?
(1) m#0 (2) 6m = 9n
70 If xy <.3,is x<1?
(1) y>3 (2) x<3
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Trang 13Each of the eggs 1n a bowl 1s dyed red, or green, or
blue If one egg 1s to be removed at random, what 1s
the probability that the egg will be green?
(1) There are 5 red eggs 1n the bowl
(2) The probability that the egg wall be blue 1s
(1) The bucket currently contains 9 liters of water
(2) If3 liters of water are added to the bucket when
it 1s half full of water, the amount of water in the bucket will increase by
If ab # 0, in what quadrant of the coordinate system above does point (a, b) lie?
(1) (b, a) lies in quadrant IV
(2) (a, —b) hes in quadrant IIT
From 1984 to 1987, the value of foreign goods consumed annually in the United States increased by what percent?
(1) In 1984 the value of foreign goods consumed
constituted 19 8 percent of the total value of goods consumed 1n the United States that year
(2) In 1987 the value of foreign goods consumed constituted 22 7 percent of the total value of | goods consumed 1n the United States that year
If x, y, and z are positive, 1s x=S ?
Trang 14A Statement (1) ALONE is sufficient, but statement (2) alone 1s not sùfficrent
B Statement (2) ALONE 1s sufficient, but statement (1) alone is not sufficient
C BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE 1s sufficient
_- “Statements (1) and (2) TOGETHER are NOT sufficient
If k and n are integers, 1s n divisible by 7 ? 86 A total of 9 women and 12 men reside 1n the
- 21 apartments that are in a certain apartment
(1) n+3=2k building, one person to each apartment, If a poll
(2) 2k — 41s divisible by 7 ; taker 1s to select one of the apartments at random,
what 1s the probability that the resident of the apart- ment selected will be a woman who 1s a student?
If x and y are integers and
(2) Of the women, 5 are not students * (1) x <4
(2) d+005>2 ` 88 Hoses X and Y simultaneously fill an empty
swimming pool that has a capacity of 50,000 liters
` ⁄ If the flow in each hose 1s independent of the flow in
The participants 1n a race consisted of 3 teams with the other hose, how many hours will it take to fill
3 runners on each team A team was awarded 6 —n the pool?
points sf one of its runners finished in nth place,
race and if there were no ties, was each team pool
awarded at least one point?
; ` (2) Hose Y alone would take 36 hours to fill the
(1) No team was awarded more than a total of pool
6 points
(2) No pair of teammates finished in consecutive „⁄ k
(2) r and s are not integers
90 If x and y are integers, what 1s the value of y ?
Trang 1591
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE 1s sufficient
96 If P and Q are each circular regions, what is the radius of the larger of these regions?
(1) The area of P plus the area of @ 1s equal
(2) The larger circular region has a radius that 1s
3 times the radius of the smaller circular
A Statement (1) ALONE 15s sufficient, but statement (2) alone 1s not sufficient
B Statement (2) ALONE 1s sufficient, but statement (1) alone 1s not sufficient
C
D EACH statement ALONE 1s sufficient
E —_ Statements (1) and (2) TOGETHER are NOT sufficient
In the figure above, segments PR and QR are
each parallel to one of the rectangular coordinate
axes Is the ratio of the length of QR to the length
In a school election, 1f each of the 900 voters voted
for either Edith or José (but not both), what percent
of the female voters 1n this election voted for José?
(1) E:ghty percent of the female voters voted for
Edith
(2) Sixty percent of the male voters voted for José
During week W, how much did it cost, per mile,
for the gasoline used by car X?
(1) During week W, car X used gasoline that
cost $1 24 per gallon-
(2) Durmg week W, car X was driven 270 miles
If r and s are integers, 1s r divisible by 7 ?
(1) The product rs 1s divisible by 7
If the total price of n equally priced shares of a certain stock was $12,000, what was the price per share of the stock?
(1) If the price per share of the stock had been $1 more, the total price of the n shares would have been $300 more
(2) If the price per share of the stock had been $2 less, the total price of the n shares would have been 5 percent less
99 Whatis the ratioofx y z2 (1) z=1 and xy = 32
Is xy >5?
(1) 1sxs3and2<ys4 (2) x+y=5
Trang 16A Statement (1) ALONE 1s sufficient, but statement (2) alone 1s not sufficient
B Statement (2) ALONE ts sufficient, but statement (1) alone 1s not suffictent
”C BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE 1s sufficient
D EACH statement ALONE 1s sufficient
E Statements (1) and (2) TOGETHER are NOT sufficient
102 In year X, 8 7 percent of the men in the labor force 107 Can the positive integer n be written as the sum of were unemployed in June compared with 8 4 percent two different positive prime numbers?
in May If the number of men 1n the labor force was ` -
the same for both months, how many men were (1) n 1s greater than 3
unemployed in June of that year? (2) n 1s odd
(1) In May of year X, the number of unemployed
`_ men in the labor force was 3 36 million
(2) In year X, 120,000 more menn the labor
force were unemployed 1n June than m May
103 If the average (arithmetic mean) of 4 numbers ts 50,
how many of the numbers are greater than 50 ?
(1) None of the four numbers 1s equal to 50
(2) Two of the numbers are equal to 25
104 On Monday morning a certain machine ran continu-
ously at a uniform rate to fill 4 production order At* 108 In the figure above, segments RS and TU repre- what time did 1t completely fill the order that sent two positions of the same ladder leaning against
“ much greater than the length of RV?
(1) The machine began filling the order at 9 30 am \ ,
1 (1) The length of TU is 10 meters (2) The machine had filled 2 of the order by (2) The length of RV 1s 5 meters
10,30 am and > of the order by 1110am
6 109 Ifboth x and y are nonzero numbers, what is the
105 If n+k=m, whats the value of & ? Tố x
(2) m+10=n - (2) yrex
106 Town T has 20,000 residents, 60 percent of whom 110, If x =O rstu, where r, s, t, and u each repre-
(1) r=3s=2t=6u (1) The number of female residents who were (2) The product of r and u 1s equal to the
born in Town T 18 twice the number of male _ produet of s and ứ
residents who were not born in Town T
(2) The number of female residents who were not
born in Town T 1s twice the number of
female residents who were boin in Town T
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