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# GMAT Quantitative Paris Diderot - Paris 7 - 2018

Subject: ; Class: ; with 35 questions; test in 75 minutes; update 23/11/2017
 Time 75 minutes Time to take the test Start exam Click button start to test. Guide to the test Subjects Gmat test Update 23/11/2017 Class Level 3 Number of questions 35 View 1164 Tested 1

Question 1.

If X ≠e 2, then  $$3x ^2 (x- 2)- x+ 2 \over x-2$$ =

 (A) 3x 2 - x+2 (B) 3x 2 +1 (C) 3x 2 (D) 3x 2 -1 (E) 3x 2 -2

Question 2.

In the figure shown above, line segment QR has length 12, and rectangle MPQT is a square. If the area of rectangular region MPRS is 540, what is the area of rectangular region TQRS ?

 (A) 144 (B) 216 (C) 324 (D) 360 (E) 396

Question 3.

Atrain travels from New York City to Chicago, a distance of approximately 840 miles, at an average rate of 60 miles per hour and arrives in Chicago at 6:00 in the evening, Chicago time. At what hour in the morning, New York City time, did the train depart for Chicago? (Note: Chicago time is one hour earlier than New York City time.)

 (A) 4:00 (B) 5:00 (C) 6:00 (D) 7:00 (E) 8:00

Question 4.

Last year Manfred received 26 paychecks. Each of his first 6 paychecks was $750; each of his remaining paychecks was$30 more than each of his first 6 paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his paychecks for the year?

 (A) $752 (B)$755 (C) $765 (D)$773 (E) $775 Question 5. If 25 percent of p is equal to 10 percent of q, and pq ≠ 0, then p is what percent of q ?  (A) 2.5% (B) 15% (C) 20% (D) 35% (E) 40% Question 6. If the length of an edge of cube X is twice the length of an edge of cube Y, what is the ratio of the volume of cube Y to the volume of cube X?  (A) $$1\over 2$$ (B) $$1\over 4$$ (C) $$1\over 6$$ (D) $$1\over 8$$ (E) $$1\over 27$$ Question 7. Machines A and 8 always operate independently and at their respective constant rates. When working alone, Machine A can fill a production lot in 5 hours, and Machine 8 can fill the same lot in x hours. When the two machines operate simultaneously to fill the production lot, it takes them 2 hours to complete the job. What is the value of x ?  (A) 3$$1 \over 3$$ (B) 3 (C) 2$$1 \over 2$$ (D) 2$$1 \over 3$$ (E) 1$$1 \over 2$$ Question 8. An artist wishes to paint a circular region on a square poster that is 2 feet on a side. If the area of the circular region is to be $$1 \over 2$$ the area of the poster, what must be the radius of the circular region in feet?  (A) $$1 \over \pi$$ (B) $$\sqrt{2 \over \pi}$$ (C) 1 (D) $$2 \over \sqrt \pi$$ (E) $$\pi \over 2$$ Question 9. A driver completed the first 20 miles of a 40-mile trip at an average speed of 50 miles per hour. At what average speed must the driver complete the remaining 20 miles to achieve an average speed of 60 miles per hour for the entire 40-mile trip? (Assume that the driver did not make any stops during the 40-mile trip.)  (A) 65 mph (B) 68 mph (C) 70 mph (D) 75 mph (E) 80 mph Question 10. A$500 investment and a $1,500 investment have a combined yearly return of 8.5 percent of the total of the two investments. If the$500 investment has a yearly return of 7 percent, what percent yearly return does the $1,500 investment have?  (A) 9% (B) 10% (C) 10 $$5 \over 8$$ % (D) 11% (E) 12% Question 11. For any integer ngreater than 1, In denotes the product of all the integers from 1 to n, inclusive. How many prime numbers are there between !Q + 2 and !Q + 6, inclusive?  (A) None (B) 1 (C) 2 (D) 3 (E) 4 Question 12. The figure shown above consists of three identical circles that are tangent to each other. If the area of the shaded region is 64$$\sqrt{3}$$- 32π, what is the radius of each circle?  (A) 4 (B) 8 (C) 16 (D) 24 (E) 32 Question 13. On a certain transatlantic crossing, 20 percent of a ship's passengers held round-trip tickets and also took their cars aboard the ship. If 60 percent of the passengers with round-trip tickets did not take their cars aboard the ship, what percent of the ship's passengers held round-trip tickets?  (A) 33$$1 \over 3$$ % (B) 40% (C) 50% (D) 60% (E) 66$$2\over 3$$% Question 14. If the variables, X, Y, and Ztake on only the values 10, 20, 30, 40, 50, 60, or 70 with frequencies indicated by the shaded regions above, for which of the frequency distributions is the mean equal to the median?  (A) Xonly (B) Yonly (C) Zonly (D) XandY (E) Xand Z Question 15. For every even positive integer m, f(m) represents the product of all even integers from 2 to m, inclusive. For example, f(12) = 2 x 4 x 6 x 8 x 10 x 12. What is the greatest prime factor of f(24) ?  (A) 23 (B) 19 (C) 17 (D) 13 (E) 11 Question 16. Note: Not drawn to scale In pentagon PQRST, PQ = 3, QR = 2, RS = 4, and ST = 5. Which of the lengths 5, 10, and 15 could be the value of PT?  (A) 5 only (B) 15 only (C) 5 and 10 only (D) 10 and 15 only (E) 5, 10, and 15 Question 17. A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?  (A) 42 (B) 70 (C) 140 (D) 165 (E) 315 Question 18. 2x+ y = 12 IYI ≤ 12 For how many ordered pairs (x,y) that are solutions of the system above are x and y both integers?  (A) 7 (B) 10 (C) 12 (D) 13 (E) 14 Question 19. A survey of employers found that during 1993 employment costs rose 3.5 percent, where employment costs consist of salary costs and fringebenefit costs. If salary costs rose 3 percent and fringe-benefit costs rose 5.5 percent during 1993, then fringe-benefit costs represented what percent of employment costs at the beginning of 1993?  (A) 16.5% (B) 20% (C) 35% (D) 55% (E) 65% Question 20. A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales in 1997 were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996?  (A) 1:2 (B) 4:5 (C) 1:1 (D) 3:2 (E) 5:3 Question 21. A group of store managers must assemble 280 displays for an upcoming sale. If they assemble 25 percent of the displays during the first hour and 40 percent of the remaining displays during the second hour, how many of the displays will not have been assembled by the end of the second hour?  (A) 70 (B) 98 (C) 126 (D) 168 (E) 182 Question 22. A couple decides to have 4 children. If they succeed in having 4 children and each child is equally likely to be a boy or a girl, what is the probability that they will have exactly 2 girls and 2 boys?  (A) $$3 \over 8$$ (B) $$1 \over 4$$ (C) $$3 \over 16$$ (D) $$1 \over 8$$ (E) $$1 \over 16$$ Question 23. 3, k, 2, 8, m, 3 The arithmetic mean of the list of numbers above is 4. If k and m are integers and k ""' m, what is the median of the list?  (A) 2 (B) 2.5 (C) 3 (D) 3.5 (E) 4 Question 24. In the figure above, point 0 is the center of the circle and OC = AC = AB. What is the value of x ?  (A) 40 (B) 36 (C) 34 (D) 32 (E) 30 Question 25. $$(8^2)(3^3)(2^4) \over 96^2$$ =  (A) 3 (B) 6 (C) 9 (D) 12 (E) 18 Question 26. When 10 is divided by the positive integer n, the remainder is n- 4. Which of the following could be the value of n?  (A) 3 (B) 4 (C) 7 (D) 8 (E) 12 Question 27. If $$1 \over 2$$ of the money in a certain trust fund was invested in stocks, $$1 \over 4$$ in bonds,$$1 \over 5$$ in a mutual fund, and the remaining$10,000 in a government certificate, what
was the total amount of the trust fund?

 (A) $100,000 (B)$ 150,000 (C) $200,000 (D)$ 500,000 (E) \$ 2,000,000

Question 28.

If m is an integer such that (-2)2m = 29 - m, then m =

 (A) 1 (B) 2 (C) 3 (D) 4 (E) 6

Question 29.

In a mayoral election, Candidate X received $$1 \over 3$$ more votes than Candidate Y, and Candidate Yreceived$$1 \over 4$$ fewer votes than Candidate Z . If Candidate Z received 24,000 votes, how many votes did Candidate X receive?

 (A) 18,000 (B) 22,000 (C) 24,000 (D) 26,000 (E) 32,000

Question 30.

An airline passenger is planning a trip that involves three connecting flights that leave from Airports A, 8, and C, respectively. The first flight leaves Airport A every hour, beginning at 8:00 a.m., and arrives at Airport B 2$$1\over 2$$ hours later. The second flight leavesAirport 8 every 20 minutes, beginning at 8:00 a.m ; and arrives at Airport C  1$$1 \over 6$$ hours later. The third flight leaves Airport C every hour, beginning at 8:45 a.m. What is the least total amount of time the passenger must spend between flights if all flights keep to their schedules?

 (A) 25 min (B) 1 hr 5 min (C) 1 hr 15 min (D) 2 hr 20 min (E) 3 hr 40 min

Question 31.

If nis a positive integer and n2 is divisible by 72, then the largest positive integer that must divide nis

 (A) 6 (B) 12 (C) 24 (D) 36 (E) 48

Question 32.

If nis a positive integer and k + 2 = 3n, which of the following could NOT be a value of k ?

 (A) 1 (B) 4 (C) 7 (D) 25 (E) 79

Question 33.

A certain grocery purchased x pounds of produce for p dollars per pound. If y pounds of the produce had to be discarded due to spoilage and the grocery sold the rest for s dollars per pound, which of the following represents the gross profit on the sale of the produce?

 (A) (x-y)s-xp (B) (x-y)p-ys (C) (s-p)y-xp (D) xp- ys (E) (x-y)(s-p)

Question 34.

Running at their respective constant rates, Machine X takes 2 days longer to produce w widgets than Machine Y. At these rates, if the two machines together produce $$5 \over 4$$ w widgets in 3 days, how many days would it take Machine Xalone to produce 2w widgets?

 (A) 4 (B) 6 (C) 8 (D) 10 (E) 12

Question 35.

A square wooden plaque has a square brass inlay in the center, leaving a wooden strip of uniform width around the brass square. If the ratio of the brass area to the wooden area is 25 to 39, which of the following could be the width, in inches, of the wooden strip?

I. 1
II. 3
Ill. 4

 (A) I only (B) II only (C) I and II only (D) I and Ill only (E) I, II, and Ill

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