# Q. How many integers are there between 1 and 100 which have 4 as a digit but are not divisible by 4?

(a) 5

(b) 11

(c) 12

(d) 13

Correct Answer: (c) 12

#### Question from UPSC Prelims 2020 CSAT Paper

**Explanation : **

## Largest Number

Let’s solve this problem step by step. A negative exponent means that the base is inverted and the exponent becomes positive. For example, (1/2)^-6 can be written as (2/1)^6.

Using this logic, we can rewrite all the options as follows:

(a) (1/2)^-6 = (2/1)^6 = 64

(b) (1/4)^-3 = (4/1)^3 = 64

(c) (1/3)^-4 = (3/1)^4 = 81

(d) (1/6)^-2 = (6/1)^2 = 36

So among these options, the largest number is 81.

So (c) (1/3)^-4 is indeed the correct answer.