# Problem Solving Select Many GRE Sample Questions 10

## GRE Problem Solving Select Many Sample Questions

1. Question:

C(n,8) = C(n,6). Which of the following is true? Indicate all correct choices.

• A. n = 14
• B. n = 1
• C. n< 8
• D. C(n,2) = 91
• E. C(n, 2) = 12

Explanation:

C(n,8) = C(n,6)

n!/[8!(n-8)!] = n!/[6!(n-6)!]

6!(n-6)! = 8!(n-8)!

6!(n-6)(n-7)(n-8)!=8*7*6!(n-8)!

(n-8)(n-7)=7*8

n^2-13n+42=56

n^2-13n-14=0

n^2-14n+n-14=0

n(n-14)+1(n-14)=0

n=-1, 14

Since n cannot be nagative, n = 14

Option A is true and B and C are false.

C(n,2) = C(14,2)

= 14!/[2!(14-2)!]

= 14!/(2!12!)

= 14*13/2 = 7*13 = 91

Option D is true and E is false.

2. Question:

There are 5 letters to be put into 5 envelops. Each letter and each envelop bears the name of the receipent. Which of the following is true? Indicate all correct options.

• A. There is only one way of putting the letters in the correct envelops
• B. There are total 120 ways of putting the letters in the envelops
• C. There are 119 wrong ways of putting the letters in the envelops
• D. There are 25 ways of putting the letters in the envelops
• E. There are 24 wrong ways of putting the letters in the envelops
Correct Answer: A, B and C

Explanation:

The first letter can be put in the envelops in 5 ways

The second letter canbe put in the envelops in 4 ways

The third letter can be put in the envelops in 3 ways

and so on

Total number of ways = 5*4*3*2*1

= 120

There is only 1 correct way of putting the letters in the envelops

There are 120-1 = 119 incorrect ways.

Options A, B and C are true.

3. Question:

Two dice are tossed together. Which of the following is true? Indicate all correct choices.

• A. The probability that the sum of the two numbers is divisible by 3 is 1/12
• B. The probability that the sum of the two numbers is divisible by 4 is 1/12
• C. The probability that the sum of the two numbers is divisible by 3 is 1/3
• D. The probability that the sum of the two numbers is divisible by 4 is 1/4
• E. The probability that the sum of the two numbers is divisible by 3 or 4 is 5/9
Correct Answer: C, D and E

Explanation:

Let the event of divisibility by 3 be A and that of divisibility by 4 be B.

Total possible outcomes are 6*6=36

Elements in the sample space for which sum of numbers is 3: (1,2),(2,1),(1,5),(5,1),(2,4), (4,2), (4,5)

(5,4),(3,6)(6,3)(6,6)

P(A) = 12/36 = 1/3

Elements in the sample space for which sum of numbers is 4: (2,2),(1,3),(3,1),(3,5), (5,3), (4,4)

(2,6)(6,2)(6,6)

P(B) = 9/36 = 1/4

Options A and B are false and C and D are true.

Number of events nwhich the sum of numebrs is divisible by 3 and 4 both= 1 (6,6)

P(sum of numbers is divisible by 3 or 4) = P(A)+P(B) - P(sum is divisible by 3 and 4)

= 1/3+1/4-1/36 = 5/9

Option E is true.