CAT Practice : Number System - Remainders

You are here: Home  CAT Questionbank   CAT Quant  Number System: Remainders  Question 6
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!!

Remainders - Squares

    Q.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

 

  • Correct Answer
    Choice A. 1, 5, 7 and 11

Detailed Solution

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.

Correct Answer: 1, 5, 7, 11

Our Online Course, Now on Google Playstore!

2IIM's App

Fully Functional Course on Mobile

All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.


Cache Content for Offline Viewing

Download videos onto your mobile so you can learn on the fly, even when the network gets choppy!

Get it on Google Play

More questions from Number Theory - Remainders

  1. Remainders - Sum of digits
  2. Number Theory - Binomial Theorem
  3. Remainders
  4. Remainders
  5. Remainders - factorization properties
  6. Remainders - Squares
  7. Remainders, coprime numbers
  8. Remainders and LCM
  9. Remainders - basics
  10. 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.