# CAT Practice : Number System - Remainders

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Remainders are consistent for addition, subtraction and multiplication. As long as the divisor is same, you can add two numbers and take the remainder or add the two remainders.

## Remainders - basics

Q.9: Three numbers leave remainders of 43, 47 and 49 on division by N. The sum of the three numbers leaves a remainder 9 on division by N. What are the values N can take?
1. 65
2. 96
3. 125
4. More than one value is possible

Choice D. More than one value is possible

## Detailed Solution

In this question, the sum of the three numbers should leave a remainder 43 + 47 + 49 = 139. Or, it should be of the form N * k + 139, where K is an integer.

However, it leaves a remainder 9, or it is of the form N * m + 9.

N * k + 139 = N * m + 9
N * (m - k) = 130

Or, N should be a factor of 130. Since the remainders left on division by N are 43, 47 and 49, N should be greater than 49.

The only factors of 130 that are greater than 49 are 65 and 130. So, N can take 2 values – 65 or 130.

Correct Answer: More than one value is possible

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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.