CAT Practice : Number System - Remainders

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Another in the genre of possible remainders.

Remainders

    Q.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

 

  • Correct Answer
    Choice B. 5

Detailed Solution

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

Correct Answer: 5 possible remainders

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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.