# Problem Solving Select Many GRE Sample Questions 5

## GRE Problem Solving Select Many Sample Questions

1. Question:

Which of the following are the 10th and 12th terms of the geometric series 5, 25, 125,...? Indicate all correct choices.

• A. 125
• B. 5^2
• C. 5^10
• D. 5^12
• E. 5^24

[5^2=5*5]

Explanation:

The series is 5, 25, 125,...

The first term, a, is 5 and the common ratio, r, is 5

The 10th term is given by T10= a*r^(10-1)

= 5*5^(10-1)

= 5*5^9 = 5^(9+1)

= 5^10

The 12th term is given by T12=a*r^(12-1)

= 5*5^(12-1)

= 5*5^11

= 5^(11+1)

= 5^12

The correct options are C and D

2. Question:

Four horses are tied to the corners of a square field of 14m length. Each horse can just touch its adjacent horses. They were able to graze in the area accessible to them for 11 days. Which of the following statements is true? Indicate all such statements.

• A. They can graze in the remaining area for 3 days
• B. One horse can graze in the whole field for 50 days
• C. They can graze in the remaining area for 12 days
• D. They can graze in the remaining area for 10 days
• E. One horse can graze in the whole field for 56 days

Explanation:

Area of field = side^2=14*14

= 196 sq.m.

Area accessible to the four horses = pi*r^2, where r is the length of their rope

r = 14/2 = 7

Area accessible to each horse = 49pi

Area grazed by the 4 horses in one day = 49pi/11

Remaining area = total area - 49pi

= 196-49pi

Days for which the remaining area will be available = (196-49pi)/49pi/11

= (196-49pi)*11/49pi

= 3 days

Option A is true and C and D are false.

One horse can graze in the whole field for 4*11+4*3

= 4*14 = 56 days

Option B is false and E is true.

[pi=22/7, r^2=r*r]

3. Question:

Which of the following are the next two numbers in the series 2, 5, 9, 19, 37,___? Indicate all correct options.

• A. 74
• B. 75
• C. 76
• D. 140
• E. 149

Explanation:

The series is 2, 5, 9, 19, 37,___

5 = 2*2+1

9 = 2*5 - 1

19 = 2*9 + 1

37 = 2 *19 -1

The next number will be 2*37+1 = 75

The next number will be 2*75 -1 = 149

Options B and E are true.