## Solution
If x = 2 then f(x) = 8/31 and f(1/x) = -8/31 which is equal to -f(x)
## What the question and answer could be
If f(x) = x^3/(x^5 - 1), what is f(1/x) in terms of f(x)?
Options:
(A) -f(x)
(B) 1/f(x)
(C) 2/f(x)
(D) 3/f(x)
(E) f(x)
(A)

## Solution
Since the coin is a fair coin, every toss is independent of any other toss. Hence, the probability of appearance of tail on the fifth toss is = 1/2
## What the question and answer could be
A fair coin is tossed repeatedly. If head appears on the first four tosses, then the probability of appearance of tail on the fifth toss is.
Options:
(A) 1/7
(B) 1/2
(C) 3/7
(D) 2/3
(E) 1/3
(B)

## Solution
12
12 4 + 2 = 50
50 4 + 2 = 202
202 4 + 2 = 810
810 4 + 2 = 3242
3242 4 + 2 = 12970
## What the question and answer could be
What number comes next in the following number series? 12, 50, 202, 810, 3242, _____
Options:
(A) 12400
(B) 12800
(C) 12970
(D) 13015
(E) 16000
(C)

## Solution
1 to 9 = 9 * 9 = 81
1 to 5 = 5 * 10 = 50
5 to 9 = 5 * 8 = 40
5th = 50 + 40 = 90 81 = 9
## What the question and answer could be
The average of 9 observations was 9, that of the 1st of 5 being 10 and that of the last 5 being 8. What was the 5th observation?
Options:
(A) 9
(B) 8
(C) 5
(D) 5
(E) 4
(A)