# CAT Quantitative Aptitude Questions | CAT Number Systems - Remainders

###### CAT Questions | Number Theory | Remainders - basics CAT Questions

The question is from CAT Number Theory - Remainders. We need to find out the divisor,N, with the given details. 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.

Question 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

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##### Method of solving this CAT Question from Number Theory - Remainders: 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.

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.

The question is "What are the values N can take?"

##### Hence the answer is "More than one value is possible".

Choice D is the correct answer.

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