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102
Subject
Mathematics
Date
Jan 9, 2024
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8
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·t -~ r GMAT™ Official Gulde 2021 D5
04
536 320. Every object in a box is either a sphere or a cube
, and every object in the box ls either' red or green. How many objects are in the box? ( 1) There are six cubes and five green objects in the box. 0 (2) There are two red spheres in the box. 0S01425 321. If x and y are positive integers, is xy even? (1) x
2 + y
2 -
1 is divisible by 4. (2) x + y is odd. 0S1
4502 322. If a and b are integers, is a+ b + 3 an odd integer? (1) ab is an odd integer. (2) a -
b is an even integer
. 0S08308 323. If x and y are positive integers, what is the value of Jx+Jy? (1) x+ Y= 15 (2) Jxy =6 0S05312 l . 324. A certain truck uses 12 + kv
2 gallons of fuel per mile when its speed is v miles per hour, where k is a constant. At what speed should the truck travel so that it uses _i_ gallon of fuel per mile? 12 (1) The value of k is IO,~OO. (2) When the truck travels at 30 miles per hour, it uses _!_ gallon of fuel per mile. 6 m 0S48710.02 32
5_ In the figure shown, is f 1 II f2 ? (1) r=S (2) t= u 210 0S51531.02 326. What is the volume of the right circular cyr lnder X? (1) The height of Xis 20
. (2) The base of X has area 25n. 0S76502.
01 327. If rand s are positive integers, is r +seven? (I) r is even. (2) s is even. 0S27502.
01 Q y" 58° P'-------~R 328. In the figure above, .t1PQR has angle measures as shown. ls x<y? (1) PQ= QR (2) PR> QR DS!0602.
0I 329. If Sis a set of odd integers and 3 and-I are in S, is -15 in S? (1) 5 is in S. (2) Whenever two numbers are in S, their product is · in S. DS0J602.0l 330. Is the integer x a 3-digit integer? (I) xis the square of an integer. (2) 90 < X < 150 DS
JJ602
.
0l is 331
. If the 1st term of a sequence is 0 and the 2nd term 332. 1, is the 5th term 2? (1) Each odd-numbered term is either O or 2
· (2) The 3rd term is 2. DS21602.0J ? Is the sum of four particular integers even. d tw are even. (1) Two of the integers are odd an ° (2) The average (ar
i
thmetic mean) of th
e four integers is an integer.
OS
7
06
02.0I 333
_ If a school district paid a total of $35 per desk for x desks and a total of $30 per table for y tables, what was the total amount that the district paid for these desks and tables? (1) The total amount the district paid for the y tables was $900. (2) x = 90, and the total amount the district paid for the x desks was 3.5 times the total amount the district paid for the y tables. 0
S9060
2.
01 334. Three children inherited a total of X dollars. If the oldest child inherited $7,000 more than the youngest child, and the youngest child inherited $9,000 less than the middle child, what is the value of X? (1) The middle child inherited $27,000. (2) The youngest child and the middle child together inherited a total of $45,000. 0S41602.01 x4z2 335. If xyz * 0, what is the value of 22 ? z y (1) y2 = x4 (2) x = 2 and y = 4 0S81602.01 336. If a and b are integers, and b > O does a -
l = ? ' b+l b. (1) a=b-4 (2) a=-b DS12602.0l 337. In a sequence of numbers in which each term is 2 more than the preceding term, what is the fourth term? (1) The last term is 90. (2) The first term is 2. 0S32602.01 3
38. Is the integer p divisible by 5 ? (1) Pis divisible by 10. (2) Pis not divisible by 15. 5.3 Data Sufficiency Practice Questions 0S5260
2.
0I 339. The 9 squares above are to be filled with xs and o's, with only one symbol in each square. How many of the squares will contain an x ? (1) More than ½
of the number of squares will contain an o. (2) Each of the 4 corner squares will contain an x. 0S72602
.
01 340. Is the sum of two integers divisible by 10 ? (1) One of the integers is even. (2) One of the integers is a multiple of 5. 0S22602.0l 341. Is x an integer? (1) x
3
=8 (2) X= .J4 0S42602.0l 342. If a building has 6,000 square meters of floor space, how many offices are in the building? (1) 1 Exactly 4 of the floor space is not used for offices. (2) There are exactly 20 executive offices and each of these occupies 3 times as much floor space as the average for all of the remaining offices. DS43602.0l 343. If p, r, and s are consecutive integers in ascending order and x is the average (arithmetic mean) of the three integers, what is the value of x ? (1) Twice x is equal to the sum of p, r, and s. (2) The sum of p, r, and s is zero. DS53602.0l 344. If m and n are integers, what is the value of m + n ? (1) (x+m)(x+n)=x
2
+5x+mnandx::t0
. (2) mn=4 211
f J GMAT™ Official Gulde 2021 s X
0 I
t' p R Q D
S6
360
2.
01 345. In the figure above, RST is a triangle with angle measures as shown and PRTQ is a line segment. What is the value of x + y? (1) 5=40 (2) r= 70 D$04602.0 346. If R, S, and Tare points on a line, and if R is 5 meters from T and 2 meters from S, how far is S from T ? (I) R is between S and T. (2) S is to the left of R, and T is to the right of R. DS65602.0I 347. Is n equal to zero? (1) The product of n and some nonzero number is 0. (2) The sum of n and O is 0. DS45602.01 348. On a map,
½
inch represents 100 miles. According to this map, how many miles is City X from City Y ? (I~
: City X is 3 inches from City Yon the map. (21 Cities X and Y are each 300 miles from City Z. DS07502.01 349. What is the remainder when the positive integer n is divided by 5 ? (1) When n is divided by 3, the quotient is 4 and the remainder is I . (2) When n is divided by 4, the remainder is 1. DS37502
.0! 350. If rand s are positive numbers and () is one of the operations, +, - , x, or+, which operation is () ? (1) If r = s, then re s = o. (2) If r * s, then r e s * s 0 r. 212 ' 0S5
75
02.01 351. In any sequence of n nonzero numbers, a Pair of consecutive terms with oppos
i
te signs represents a sign change. For example
, the sequence -2, 3, --4 5 has three sign changes. Does the sequence of non.zero numbers s
1, s
2, s
3, . . . , Sn have an even number of sign changes? (1) (2) sk = (-1 )k for all positive integers k from I to n. n is odd. D
S86
50
2.
01 352. Jack picked 76 apples
. Of these, he sold 4y apples to Juanita and 3t apples to Sylvia. If he kept the remaining apples, how many apples did he keep? (t and y are positive integers.) (1) y 15 and t = 2 (2) Y= 17 0S47502
.
01 353
. What number is 6 more than x + y? (1) y is 3 less than x. (2) y is twice x. 0S0850
2.
01 354. The total price of 5 pounds of regular coffee and 3 pounds of decaffeinated coffee was $21.50. What was the price of the 5 pounds of regular coffee? (1) (2) If the price of the 5 pounds of regula
r coffee had been reduced IO percent and the price of the 3 pounds of decaffeinated coffee had been reduced 20 percent, the total price would have been $18
.
45. The price of the 5 pounds of regular coffee was $3. 50 more than the price of the 3 pounds of decaffeinated coffee
. DS
3850
2.
01 355. If a and b are integers
, is a
5 < 4b ? (1) a
3 = -27 (2) b
2
=16 DS28
502.01 j .
5 356
. If each side of parallelogram P has length 1. wha 1 the area of P ? ( (1) One angle of P measures 45 degrees. (2) The altitude of Pis f. ~-A
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2.
0I 35
7_ If xis an integer greater than 0, what Is the remainder when x is divided by 4 ? ( 1) The remainder is 3 when x + 1 is divided by 4. (2) The remainder is O when 2x is divided by 4. DS0060
2.0
I 358. A certain painting job requires a mixture of yellow, green, and white paint. If 12 quarts of paint are needed for the job, how many quarts of green paint are needed? (ll The ratio of the amount of green paint to the amount of yellow and white paint combined needs to be 1 to 3. (2) The ratio of the amount of yellow paint to the amount of green paint needs to be 3 to 2. DS69502.0l 359. Is the average (arithmetic mean) of the numbers x, y, and z greater than z ? (1) Z-X<y-z (2) X<Z<Y DS30602.01 360. Is the point Q on the circle wi
th center C ? (1) R is a point on the circle and the distance from Q to R is equal to the distance from Q to C. (2) S is a point on the circle and the distance from Q to Sis equal to the distance
1
from S to C. A C DS59502.01 361. In the figure above, if A, B, and Care the areas, respectively, of the three nonoverlapping regions formed by the intersection of two circles of equal area, what is the value of 8 + C ? (1) A+2B+C=24 (2) A+ C= 18 and 8 = 3 5.3 Data Suff
ici
e
ncy Practice Questions DS6
1
602
.0J 362. A company produces a certain toy in only 2 sizes, small or large, and in only 2 colors, red or green. If, for each size, there are equal numbers of red and green toys in a certain production lot, what fraction of the total number of green toys is large? (1) In the production lot, 400 of the small toys are green. (2) In the production lot, of the toys produced are small. DS51602.0l 363. Is quadrilateral PQRS a parallelogram? (1) Adjacent sides PQ and QR have the same length. (2) Adjacent sides RS and SP have the same length. y p (a,3) R (b
,
3) -
-
S X (d,O) DS71602
.0l 364. In the figure above, the vertices of .6.OPQ and .6.QRS have coordinates as indicated. Do .6.OPQ and .6.QRS have equal areas? (1) b=2a (2) d= 2c DS92602
.0l 365. After the first two terms in a sequence of numbers, each term in the sequence is formed by adding all of the preceding terms. Is 12 the fifth term in the sequence? (1) The sum of the first 3 terms in the sequence is 6. (2) The fourth term in the sequence is 6. DS13602.01 366
. Jones has worked at Firm X twice as many years as Green
, and Green has worked at Firm X four years longer than Smith. How many years has Green worked at Firm X? (1) Jones has worked at Firm X 9 years longer than Smith. (2) Green has worked at Firm X 5 years less than Jones
. 213
GMAT™ Official Guide 2021 K 60
° 30
° J.
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L DS8
360
2.
0I 367. In tiJKL shown above, what is the length of segment JL? (1) JK = IO (2) KL= 5 DS
24602.
01 368. A six-sided mosaic contains 24 triangular pieces of tile of the same size and shape, as shown in the figure above. If the sections of tile fit together perfectly, how many square centimeters of tile are in the mosaic? 369. 214 (1) Each side of each triangular piece of tile is 9 centimeters long. (2) The mosaic can be put inside a rectangular frame that is 40 centimeters wide. A E B D C 0S34602.
0l If, in the figure above, ABCD is a rectangular region, . area of llEDA what is the value of the ratio f EBC ? area o fl (1) AD=4 (2) AE = 2 and EB = 4 0S64602.0! 370. A noncompressible ball in the h b s ape of a h e passed through a square ope . . sp ere is t . th . ning in a b o
Is e perimeter of the opening? 0
ard
. Wha
t
(1) The radius of the ball is equal t 2 . o inches (2) The square opening is the small t · opening through which the ball ;;~ fi~~uare Q ---r7---
-
--
R 6 p 10 s 0S74602.01 371. In the figure above, what is the area of region PQRST? (1) PQ=RS (2) PT= QT Q R ,,.. __ _
____ _..,... --
--
--
--
T p s 0S8460
2.
0l 372. The figure above represents a box that has the shape of a cube
. What is the volume of the box? (1) PR=lOcm (2) QT= 5'16 cm 373. 0S94602.01 I If x and Y are the lengths of the legs of a right triang e, what is the value of xy ? (1) The hypotenuse of the triangle is 10./2. (2) The area of the triangular region is 50
.
R DS
75602.
0I . I Wh . h h figu
re above PQRT Is a rectang e. at Is t e ?4 Int e ' 3 · length of segment PQ ? (1) The area of region PQRS is 39 and TS= 6. (
2
) The area of region PQRT is 30 and QR= 10. 0S
0
8420 375 on June 1, Mary paid Omar $360 for rent and utilities · for the month of June. Mary moved out early, and Omar refunded the money she paid for utilities, but not for rent, for the days in June after she moved out. How many dollars did Omar refund to Mary? (1) Mary moved out on June 24. (2) The amount Mary paid for utilities was less than ! the amount Mary paid for rent. 5 DSD4057 t 376. If x = 2t and y = 3
, what is the value of x
2 -
y2 ? (1) 12-3=6 (2) t3=-27 0S02939 377. The 1 O students in a history class recently took an examination. What was the maximum score on the examination? (1) The mean of the scores was 75. (2) The standard deviation of the scores was 5. DS0!34! 378
. Last school year, each of the 200 students at a certain high school attended the school for the entire year. If there were 8 cultural performances at the school during the last school year, what was the average (arithmetic mean) number of students attending each cultural performance? (1) Last school year, each student attended at least one cultural performance. (2) Last school year, the average number of cultural performances attended per student was 4. 5.3 Da
ta Sufficiency Practice Questions D814
56
9 379
. A cloth
i
ng manufacturer makes jacket
s that are wool or cotton or a combination of wool and cotton. The manufacturer has 3,000 pounds of wool and 2,000 pounds of cotton on hand. Is this enough wool and cotton to make at least 1,000 jackets? (1) Each wool jacket requires 4 pounds of wool, and no cotton. (2) Each cotton jacket requires 6 pounds of cotton, and no wool. DS05377 380. If n is an integer, what is the greatest common divisor of 12 and n? (1) The product of 12 and n is 432. (2) The greatest common divisor of 24 and n is 12. DS11287 381. Each month, Jim receives a base salary plus a 10 percent commission on the price of each car he sells that month. If Jim sold 15 cars last month, what was the total amount of base salary and commissions that Jim received that month? (1) Last month, Jim's base salary was $3,000. (2) Last month, Jim sold 3 cars whose prices totaled $60,000 and 5 cars whose prices totaled $120,000. DSI 7615 382
. If x is a positive integer greater than 1, what is the value of x? (1) 2x is a common factor of 18 and 24. (2) x is a factor of 6. DSl3408 383. By what percentage was the price of a certain television set discounted for a sale? (1) The price of the television set before it was discounted for the sale was 25 percent greater than the discounted price. (2) The price of the television set was discounted by $60 for the sale. 215
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1\ / (' GMAT™ Offlclal Gu
lde 2021 PS05
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9 384. Jack wa
nts to use a circul
ar rug on his rectangular office floor to cover two small circular stains, each less than _!!_ square feet in area and each more than 100 3 feet from the nearest wall
. Can the rug be placed to cover both stains? (1 J Jack's rug covers an area of 91t square feet. (2) The centers of the stains are less than 4 feet apart. DS
2475
1.
0l 385. A paint mixture was formed by mixing exactly 3 colors of paint. By volume, the mixture was x% blue paint, y% green paint, and z% red paint. If exactly 1 gallon of blue paint and 3 gallons of red paint were used, how many gallons of green paint were used? (1) X = y (2) Z= 60 -~-J a f bj c a d e f b e g h C f h 1 D$05772 386. In the multiplication table above, each letter represents an integer. What is the value of c ? (1) C = f (2) h ac 0 D509379 387. If n is an integer, is (O
.
lln greater than (lO)n? (1) n>-10 (2) n<lO D519!99 388. For a basic monthly fee of F yen (¥Fl, Naoko's first cell phone plan allowed him to use a maximum of 216 420 minutes on calls during the month. Then, for each of x additional minutes he used on calls, he was charged ¥M, making his total charge for the month ¥T, where T = F + xM
. What is the value of F? (1) Naoko used 450 minutes on calls the first month and the total charge for the month was ¥13,755. (2) Naoko used 400 minutes on calls the second month and the total charge for the month was ¥13,125. DSI 39
~9 389
. Is the sum of the prices of the 3 book
s that S
han bought les
s than $48 ? a (1 J The price of the mo
st expensive of the 3 book
s that Shana bought Is less than $17
. (2) The price of the least expens
i
ve of the 3 book
s that Shana bought is exactly $3 less than the price of the second most expensive book. D$1
2943 390
. If rand tare three-digit positive integers, is r greater than t? ( 1) The tens digit of r is greater than each of the three digits of t. (2) The tens digit of r is less than either of the other two digits of r. D5
!
4788 391. Is the product of two positive integers x and y divisib
le by the sum of x and y ? (1) X=Y (2) X=2 DS2
457J.01 X + b 392
. If a and bare constants, is the expression Jx+a defined for x = -2 ? (1) a= 5 (2) b=6 D$
0
5330 393. A company makes and sells two products, P and Q. The costs per unit of making and selling P and Q are $8.00 and $9
.
50, respectively, and the selling prices per unit of P and Qare $10.00 and $13.00, respectively. In one month ttie company sold a total of 834 units of these products. Was the total profit on these items more than $2,000.00? (1) During the month, more units of P than units of Q were sold. (2) During the month, at least 100 units of Q were sold. D50
304
5 394. Jill has applied for a job with each of two different companies. What is the probability that she will get job offers from both companies? (1 J The probability that she will get a job offer tram neither company is 0.3. (2) The probability that she will get a job offer tram exactly one of the two companies is 0.5
. --~~
i
Js
ioi
2
0~
2 m uter company produces two different 95 A ce
rt
a
in co Pd Q In 2010 what was the net profit 3 · . p
an · ' monitors
, le of the two monitors? fro
m the sa h ompany's expenses in 2010, rent and 1l ottec ( utilities totaled $500,000. 2010 the company sold 50,000 units of 1
2
) In nitor 1
p at $300 per unit and 30,000 units of mo ·t monitor Q at $650 per urn . 0
s0
1257 A conveyor belt moves bottles at a constant 396
· eed of 120 centimeters per second. If the 5
~nveyor belt moves a bottle from a loading dock ~o an unloading dock, is the distance that the conveyor belt moves the bottle less than 90 meters? (1 meter= 100 centimeters) (1) It takes the conveyor belt less than 1.2 minutes to· move the bottle from the loading dock to the unloading dock. (2) It takes the conveyor belt more than 1.1 minutes to move the bottle from the loading dock to the unloading dock. DS02706 397. If x, y, and z are positive numbers, what is the value of the average (arithmetic mean) of x and z ? (1) x
:
....
y=y-z (2) x
2
-y2=z D DS04428 398. The rectangular rug shown in the figure above has an accent border. What is the area of the portion of the rug that excludes the border? ll) The perimeter of the rug is 44 feet. (2) The width of the border on all sides is 1 foot. DS06537 399
· 11 h 2xz, what is the value of 2
xz + yz ? 2xz-y (1) 2x+y,:3 (2) l,: 2 ----,.,...,,.___ 5.3 Data Sufficiency Practice Questions y" DS04852 400. In the parallelogram shown, what is the value of x ? (1) Y= 2x (2) X+ Z= 120 DS06096 401. In a product test of a common cold remedy, x percent of the patients tested experienced side effects from the use of the drug and y percent experienced relief of cold symptoms. What percent of the patients tested experienced both side effects and relief of cold symptoms? (1) Of the 1,000 patients tested, 15 percent experienced neither side effects nor relief of cold symptoms. (2) Of the patients tested, 30 percent experienced relief of cold symptoms without side effects. DS13588 402. Is x < 5? (1) x
2 > 5 (2) x
2 +x < 5 DS72951.0l 403. Three roommates-Bela, Gyorgy, and Janos-together saved money for a trip. The amount that Bela saved was equal to 8% of his monthly income. The amount 1 that Gyorgy saved was exactly 3 of the total amount saved by all 3 roommates. What was the total amount saved for the trip by all 3 roommates? (1) Bela had a monthly income of $2,000. (2) Janos saved 1.5 times as much for the trip as Bela. DS11257 404. Is zp negative? (1) pz
4 < 0 (2) p+z
4
=14 217 r