# CAT Practice : Number System

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How does one find the 44th digit of an 80-digit number?

## 44th digit of a number

Q.8:N is an 80-digit positive integer (in the decimal scale). All digits except the 44th digit (from the left) are 2. If N is divisible by 13, find the 26th digit?
1. 5
2. 6
3. 1
4. 2

Choice B. 6

## Detailed Solution

To begin with, the question should read "find the 44th digit".

Any number of the form abcabc is a multiple of 1001. 1001 is 7 * 11 * 13. So, any number of the form abcabc is a multiple of 13.

So, a number comprising 42 2's would be a multiple of 13, so would a number comprising 36 2's. So, in effect, we are left with a two digit number 2a, where a is the 44th digit. 26 is a multiple of 13, so the 44th digit should be 6.

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