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GMAT Quantitative Paris-Sud 2018

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; Subject: ; Class: ; with 37 questions; test in 75 minutes; update 15/11/2017
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Subjects Update 15/11/2017
Class Number of questions 37
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Question 1.

The two circles above have centers at A and B, and their circumferences are x and y respectively. If the two circles touch at one point, what is the distance between A and B?

(A)

\(2 \pi x + 2 \pi y\)

(B)

\(x+y \over 2\pi\)

(C)

\(\pi \over x+y\)

(D)

\( \pi x + \pi y\)

(E)

\(x+y \over \pi\)

Question 2.

For all numbers x , the operation ( ) is defined by (x) = x - x:5 

If ((w))=32 , then what is the value of w ?

(A)

15

(B)

25

(C)

35

(D)

50

(E)

60

Question 3.

If the average (arithmetic mean) of 3, 6, 10, m and n is 9, then what is the average of m + 4 and n – 2 ?

(A)

9

(B)

13

(C)

14

(D)

18

(E)

26

Question 4.

If the average (arithmetic mean) of a and b is 45, and the average (arithmetic mean) of b and c is 35, then a – c =

(A)

5

(B)

10

(C)

20

(D)

30

(E)

40

Question 5.

If d is the average (arithmetic mean) of a, b and c, then c =

(A)

3d - a -b

(B)

3d -a +b

(C)

d -3 a -3 b

(D)

d -3 a + 3 b

(E)

\(a+b \over 3d\)

Question 6.

If there are 16 people to choose from, what is the ratio of the number of possible 7-person  committees to the number of possible 8-person committees?

(A)

7:8

(B)

8:7

(C)

7:9

(D)

8:9

(E)

9:8

Question 7.

In how many ways can Ann, Bea, Cam, Don, Ella and Fey be seated if Ann and Bea cannot be seated next to each other?

(A)

240

(B)

360

(C)

480

(D)

600

(E)

720

Question 8.

If p and q are prime numbers, how many divisors does the product p3q6bhave?

(A)

9

(B)

12

(C)

18

(D)

28

(E)

36

Question 9.

How many positive integers less than 10,000 are there in which the sum of the digits equals 5?
 

(A)

31

(B)

51

(C)

56

(D)

62

(E)

93

Question 10.

In the xy-coordinate plane, the points (a , b ) and (a + k , b – 3) are on the line defined by y = 2x – 5. What is the value of k ?

(A)

-5/2

(B)

-5/3

(C)

-3/2

(D)

-2/3

(E)

-2/5

Question 11.

Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into a hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10?

(A)

3

(B)

4

(C)

5

(D)

6

(E)

7

Question 12.

Two missiles are launched simultaneously. Missile 1 launches at a speed of x miles per hour, increasing its speed by a factor of \( \sqrt{x}\)every 10 minutes (so that after 10 minutes its speed is x(\( \sqrt{x}\)), after 20 minutes its speed is x(\( \sqrt{x}\))(\( \sqrt{x}\) ) , and so forth. Missile 2 launches at a speed of y miles per hour, doubling its speed every 10 minutes. After 1 hour, is the speed of Missile 1 greater than that of Missile 2?

1) x =\( \sqrt{y}\)
2) x >8

(A)

Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.

(B)

Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.

(C)

Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.

(D)

EACH statement ALONE is sufficient to answer the question.

(E)

Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question.

Question 13.

If \({(13!)^{16}- (13!)^{8}}\over {(13!)^{8}+ (13!)^{4}}\)   = \(\alpha\) what is the unit’s digit of \(\alpha \over (13!)^4\)

(A)

0

(B)

1

(C)

3

(D)

5

(E)

9

Question 14.

The dimensions of a rectangular floor are 16 feet by 20 feet. When a rectangular rug is placed on the floor, a strip of floor 3 feet wide is exposed on all sides. What are the dimensions of the rug, in feet?

(A)

10 by 14

(B)

10 by 17

(C)

13 by 14

(D)

13 by 17

(E)

14 by 16

Question 15.

How many different subsets of the set {10,14,17,24} are there that contain an odd number of elements?

(A)

3

(B)

6

(C)

8

(D)

10

(E)

12

Question 16.

Seven men and seven women have to sit around a circular table so that no 2 women are together. In how many different ways can this be done? 

(A)

24

(B)

6

(C)

4

(D)

12

(E)

3

Question 17.

If the sum of five consecutive positive integers is A, then the sum of the next five consecutive integers in terms of A is:

(A)

A+1

(B)

A+5

(C)

A+25

(D)

2A

(E)

5A

Question 18.

If P represents the product of the first 15 positive integers, then P is not a multiple of:

(A)

99

(B)

84

(C)

72

(D)

65

(E)

57

Question 19.

5 girls and 3 boys are arranged randomly in a row. Find the probability that:

A) there is one boy on each end.

B) There is one girl on each end.

(A)

5/14

(B)

3/4

(C)

5/3

(D)

2/5

(E)

3/7

Question 20.

If Bob and Jen are two of 5 participants in a race, how many different ways can the race finish where Jen always finishes in front of Bob?

(A)

20

(B)

30

(C)

40

(D)

50

(E)

60

Question 21.

A set of numbers has the property that for any number t in the set, t + 2 is in the set. If –1 is in the set, which of the following must also be in the set?

I. –3 II. 1 III. 5

(A)

I only

(B)

II only

(C)

I and II only

(D)

II and III only

(E)

I, II, and III

Question 22.

A number is selected at random from first 30 natural numbers. What is the probability that the number is a multiple of either 3 or 13?

(A)

17/30

(B)

2/5

(C)

7/15

(D)

4/15

(E)

11/30

Question 23.

Two numbers are less than a third number by 30% and 37 % respectively. How much percent is the second number less than the first?

(A)

10%

(B)

7%

(C)

4%

(D)

3%

(E)

5%

Question 24.

If y ≠ 3 and 2x/y is a prime integer greater than 2, which of the following must be true?
I. x = y
II
. y = 1
III. x and y are prime integers.
 

(A)

None

(B)

I only

(C)

II only

(D)

III only

(E)

I and II

Question 25.

Someone passed a certain bridge, which needs fee. There are 2 ways for him to choice. A : $13/month+$0.2/time , B: $0.75/time . He passes the bridge twice a day. How many days at least he passes the bridge in a month, it is economic by A way?
 

(A)

11

(B)

12

(C)

13

(D)

14

(E)

15

Question 26.

Every student of a certain school must take one and only one elective course. In last year, 1/2 of the students took biology as an elective, 1/3 of the students took chemistry as an elective, and all of the other students took physics. In this year, 1/3 of the students who took biology and 1/4 of the students who took chemistry left school, other students did not leave, and no fresh student come in. What fraction of all students took biology and took chemistry?
 

(A)

7/9

(B)

6/7

(C)

5/7

(D)

4/9

(E)

2/5

Question 27.

There are 8 students. 4 of them are men and 4 of them are women. If 4 students are selected from the 8 students. What is the probability that the number of men is equal to that of women?

(A)

18/35

(B)

16/35

(C)

14/35

(D)

13/35

(E)

12/35

Question 28.

The area of an equilateral triangle is 9.what is the area of it circumcircle

(A)

10PI

(B)

12PI

(C)

14PI

(D)

16PI

(E)

18PI

Question 29.

A group of people participate in some curriculums, 20 of them practice Yoga, 10 study cooking, 12 study weaving, 3 of them study cooking only, 4 of them study both the cooking and yoga, 2 of them participate all curriculums. How many people study both cooking and weaving?

(A)

1

(B)

2

(C)

3

(D)

4

(E)

5

Question 30.

There 3 kinds of books in the library fiction, non-fiction and biology. Ratio of fiction to non-fiction is 3 to 2; ratio of non-fiction to biology is 4 to 3, and the total of the books is more than 1000?which one of following can be the total of the book?

(A)

1001

(B)

1009

(C)

1008

(D)

1007

(E)

1006

Question 31.

In a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 5% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?

(A)

5

(B)

10

(C)

15

(D)

20

(E)

25

Question 32.

For a certain company, operating costs and commissions totaled $550 million in 1990, representing an increase of 10 percent from the previous year. The sum of operating costs and commissions for both years was

(A)

$1,000 million

(B)

$1,050 million

(C)

$1,100 million

(D)

$1,150 million

(E)

$1,155 million

Question 33.

Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $9 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discounts rates is 22 percent, what is the discount rate on Pony jeans?

(A)

9 %

(B)

10 %

(C)

11%

(D)

12%

(E)

15%

Question 34.

There are 2 kinds of staff members in a certain company, PART TIME AND FULL TIME. 25 percent of the total members are PART TIME members others are FULL TIME members. The work time of part time members is 3/5 of the full time members. Wage per hour is same. What is the ratio of total wage of part time members to total wage of all members.

(A)

1/4

(B)

1/5

(C)

1/6

(D)

1/7

(E)

1/8

Question 35.

If 75% of a class answered the 1st question on a certain test correctly, 55% answered the 2nd question on the test correctly and 20% answered neither of the questions correctly, what percent answered both correctly?

(A)

10%

(B)

20%

(C)

30%

(D)

50%

(E)

65%

Question 36.

A set of data consists of the following 5 numbers: 0,2,4,6, and 8. Which two numbers, if added to create a set of 7 numbers, will result in a new standard deviation that is close to the standard deviation for the original 5 numbers?

(A)

-1 and 9

(B)

4 and 4

(C)

3 and 5

(D)

2 and 6

(E)

0 and 8

Question 37.

How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3?

(A)

14

(B)

15

(C)

16

(D)

17

(E)

18

Question 1    Question 2    Question 3    Question 4    Question 5    Question 6    Question 7    Question 8    Question 9    Question 10    Question 11    Question 12    Question 13    Question 14    Question 15    Question 16    Question 17    Question 18    Question 19    Question 20    Question 21    Question 22    Question 23    Question 24    Question 25    Question 26    Question 27    Question 28    Question 29    Question 30    Question 31    Question 32    Question 33    Question 34    Question 35    Question 36    Question 37   
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