CAT Quantitative Aptitude Questions | CAT Number Systems - Remainders

The question is from CAT Number Theory - Remainders. Given the remainder when N² is divided by 'a', what is the remainder when N is divided by 'b'. A range of CAT questions can be asked based on Remainders. Sometimes the rigorous method works, sometimes trial and error works. In rare cases, the trial and error method is very instructive for future questions. Those questions are usually found in the 2IIM questionbank!!

Question 6: N² leaves a remainder of 1 when divided by 24. What are the possible remainders we can get if we divide N by 12?

1. 1, 5, 7 and 11
2. 1 and 5
3. 5, 9, and 11
4. 1 and 11

Explanatory Answer

Method of solving this CAT Question from Number Theory - Remainders: Sometimes the rigorous method works, sometimes trial and error works. In rare cases, the trial and error method is very instructive for future questions.

This again is a question that we need to solve by trial and error. Clearly, N is an odd number. So, the remainder when we divide N by 24 has to be odd.

If the remainder when we divide N by 24 = 1, then N² also has a remainder of 1. we can also see that if the remainder when we divide N by 24 is -1, then N² a remainder of 1.

When remainder when we divide N by 24 is ±3, then N² has a remainder of 9.
When remainder when we divide N by 24 is ±5, then N² has a remainder of 1.
When remainder when we divide N by 24 is ±7, then N² has a remainder of 1.
When remainder when we divide N by 24 is ±9, then N² has a remainder of 9.
When remainder when we divide N by 24 is ±11, then N² has a remainder of 1.

So, the remainder when we divide N by 24 could be ±1, ±5, ±7 or ±11.

Or, the possible remainders when we divide N by 24 are 1, 5, 7, 11, 13, 17, 19, 23.

Or, the possible remainders when we divide N by 12 are 1, 5, 7, 11.

The question is "What are the possible remainders we can get if we divide N by 12?"

Hence the answer is "1, 5, 7, 11".

Choice A is the correct answer.