# CAT Practice : Number System - Remainders

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Remember! The difference between the numbers too leave the same remainder!

## Same remainder

Q.13: The integers 573921 and 575713 when divided by a 3 digit number leave the same remainder. What is that 3 digit number?
1. 206
2. 256
3. 274
4. 189

Choice B. 256

## Detailed Solution

Let N be the 3 digit number.
Let R be the remainder.
So 573921 – R and 575713 – R will be divisible by N
This means the difference between them is also divisible by N.

Difference = (575713 – R – 573921 + R) is divisible by N
Or 1792 divisible by N

N can be 256 from the answer choices!

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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.