# CAT Quantitative Aptitude Questions | CAT Number Systems - Remainders

###### CAT Questions | Number Theory | Possible Remainders
CAT Questions

The question is from CAT Number Theory Remainders.How many possible remainders are there when A is divided by B, especially when we know that A by C leaves a specific remainder. A range of CAT questions can be asked based on 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.

Question 4: N leaves a remainder of 4 when divided by 33, what are the possible remainders when N is divided by 55?

1. 3
2. 5
3. 4
4. 2

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

The LCM of 33 and 55 is 165. This is the starting point. If a number leaves a remainder of 4 when divided by 33, it can leave remainders 4, 37, 70, 103, and 136.

Or the number can be of the form 165n +4, or 165n + 37 or 165n + 70, 103 or 136

When divided by 55, the possible remainders are 4, 37, 15, 48 and 26

The question is "N leaves a remainder of 4 when divided by 33, what are the possible remainders when N is divided by 55?"

##### Hence the answer is "5 possible remainders".

Choice B is the correct answer.

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