# GRE Problem Solving Select Many SAMPLE QUESTIONS-6

## GRE Problem Solving Select Many Sample Questions

1. Question:

Ritu goes to college by bus at 16 km/hr speed. She returns at 9 km/hr by a bicycle. Which of the following is true? Indicate all such choices.

A. Her average speed for the journey cannot be determined

B. Her average speed for the journey is (16+9)/2 km/hr

C. Her average speed would remain the same if she went to college by a bicycle and returned by a bus at the same speeds respectively.

D. Her average speed does not depend on the distance travelled

E. Her average speed is 11.52 km/hr

Correct Answer: C and E

Explanation:

Let the distance covered be x km and t1 and t2 be the time taken for the onward and return journeys

Speed = distance/time

16 = x/t1 and 9 = x/t2

x = 16*t1 and x = 9*t2

Average speed = total distance/total time

= (x+x)/(t1+t2)

= 2x/(x/16+x/9)

= 2x/ (9x+16x)/(9*16)

= 2/25*9*16

= 11.52 km/hr

Options A and B are false and E is true.

Option C is true.

Option D is false.

2. Question:

Which of the following is equal to C(6,4)? Indicate all such choices.

A. 6!/4!

B. (6+4)!

C. 4!/(6!2!)

D. 6!(4!2!)

E. 15

Correct Answer: D and E

Explanation:

C(6,4) = 6!/[4!(4-2)!]

= 6!/(4!2!)

= 6*5/2 = 3*5 = 15

Options D and E are true.

3. Question:

A and B invested a total of \$7514 at 10% rate of compound interest. A received the same amount in 7 years as B did in 9 years.

Which of the following is true? Indicate all correct statements.

A. A invested \$4114

B. B invested \$4114

C. A invested \$2057

D. B invested \$3400

E. A invested \$3400

Correct Answer: A and D

Explanation:

Let the share of A be \$x

B's share will be (7514-x)

The amount after t years at r% rate of interest for a sum P is given by

A=P(1+r/100)^t

According to the conditions,

x(1+10/100)^7 = (7514-x)(1+10/100)^9

x=(7514-x)(1+10/100)^(9-7)

x=(7514-x)(11/10)^2

x=(7514-x)(121/100)

x=7514*121/100-121x/100

x+121x/100 = 7514*121/100

221x/100=7514*121/100

x=7514*121/221

x= 4114

A invested \$4114

B invested \$(7514-4114) = \$3400

Options A and D are true.

[100^t=100*100*....t times]