Quantitative Questions

1.  Which of the following is equivalent to  ycube < y?

a. 0 < y < 1

b. -1 < y < 1

c. -1 <y < 0 or y > 1

d. y < -1 or y > 1

e. y < -1 or 0 < y < 1

2. If xsquared – 7 = z what is the value of  2xsquared – 2x – 2z ?

3. In the graph for 1997, for which of the retail sources shown is the percent of books sold by that source represented by a  sector with a central angle measuring 72 degrees?

a. Book clubs

b. Small bookstores

c. Discount stores

4. In 1991, if 40% of the books sold by retail sources in the “others” category were sold by supermarkets, what percent of all books sold by retail sources in country T were sold by supermarkets?

a. 3.0%

b. 3.6%

c. 4.8%

d. 5.2%

e. 5.6%

5.  In 1997, the ratio of the number of books sold by large chain bookstores to the number of books by mail-order companies was closest to which of the following?

a. 11 to 1

b.  8 to 1

c 7 to 1

d. 6 to 1

e. 4 to 1

6. For the cars parked in the parking lot, the range of their odometer readings is 52,000 kilometers.  Two of the odometer readings are 66,000 kilometers and 84,000 kilometers.  Which of the following  values could be the odometer reading in kilometers , of one of the cars in the parking lot?

Indicate all such values.

a, 10,000

b. 30,000

c. 60,000

d. 90,000

e. 120,000

f. 140,000

7.  Joe remembers the first 8 digits of a 10-digit telephone number.  If he uses the digits he remembers, what is the maximum number of telephone numbers that he may have to enter in order to reach the correct telephone number ?

a. 20

b. 81

c. 90

d 100

e. 1024

8. If x is an odd integer, which of the following numbers must be the square of an odd integer?   Indicate all such numbers

a. xsquared  + 1

b. xsquared + 2squared

c. xsquared +4x + 4

9 A certain train will travel from City A to City B, and then back to City A.  along the same route.  The train is scheduled to spend a total of T hours traveling time for the round trip.  The train travels from City A to City B in 13 hours, traveling at an average speed of 25 miles per hour.  If the train is to arrive exactly on schedule, at what average speed must the train travel from City B to City A?

a. T-13

(25)(130)

b. (T-13) (130)

25

c. (25)(13)

T-13

d. 25

(23)(7-13)

10.  List A:  -2, 0, 2

List B: 3, 4, 5

List C: 9, 9.5, 10

Let a, b, c, be the standard deviations of the numbers in List A, B, and C, respectively.  Which of the following shows the order of a, b, , and c?

a.   a < b < c

b. a < c < b

c. b < a < c

d. c < a < b

e. c < b < a

11. The greatest prime divisor of 1,935 is

a. 5,

b 7

c. 13

d. 43

e. 45

12. The diameter of wheel A is half the diameter of wheel B, wheel rolls along a flat surface without slippage

Quantity A – The number of revolutions that wheel A makes in travelling 5,000 feet

Quantity B – the number of revolutions that wheel B makes in traveling 2,500 feet

a. Quantity A is greater

b. Quantity B is greater

c. The two quantities are equal

d. The relationship cannot be determined from the information given

13. n is a positive integer

Quantity A =  n/10

Quantity B = n+10/n+20

a. Quantity A is greater

b. Quantity B is greater

c. The two quantities are equal

d. The relationship cannot be determined from the information given

14. The sum of at least 3 integers of 6 consecutive integers is 150

Quantity A = The value of the greatest of the 6 consecutive integers

Quantity B = 54

a. Quantity A is greater

b. Quantity B is greater

c. The two quantities are equal

d. The relationship cannot be determined from the information given

15. The function f is definted for all nonzero numbers m by f(m)=1/m

Quantity A  –    f(f(3))  

Quantity  B –  3

a. Quantity A is greater

b. Quantity B is greater

c. The two quantities are equal

d. The relationship cannot be determined from the information given

16.  0 < x < 1 < y < 2

Quantity A  – 2x

Quantity B –  y

a. Quantity A is greater

b. Quantity B is greater

c. The two quantities are equal

d. The relationship cannot be determined from the information given

17 On the number line, the lengths of line segments SU, UV, and VT are 4, y, and 3, respectively, and the lengths of line segment ST is z.

Quantity A –  2z

Quantity B –   2y + 14

a. Quantity A is greater

b. Quantity B is greater

c. The two quantities are equal

d. The relationship cannot be determined from the information given

18. The average (arithmetic mean) of 4 measurements was 60.  After one measurement was discarded, the average of the remaining measures was 50

Quantity A – The discarded measurement

Quantity B – 50

a. Quantity A is greater

b. Quantity B is greater

c. The two quantities are equal

d. The relationship cannot be determined from the information given