# CAT Practice : Number System - Remainders

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When does an even number become an odd number? When it is divided by 2 (but not always). Think about this.

## Remainders

Q.5: What is the remainder when we divide 390 + 590 by 34?
1. 0
2. 17
3. 33
4. 1

Choice A. 0

## Detailed Solution

390 + 590 can be written as (32)45 + (52)45
= (9)45 + (25)45

Any number of the form an + bn is a multiple of (a + b) whenever n is odd.

So (9)45 + (25)45 is a multiple of 9 + 25 = 34

So, the remainder when we divide (32)45 + (52)45 by 34 is equal to 0.

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## More questions from Number Theory - Remainders

When we divide 24 pigeons into 5 groups, 4 are left out or remain. This is the remainder. When there is a question based on this idea in the exam, we have a CAT among the pigeons.