CAT Quantitative Aptitude Questions | CAT Number Systems - Remainders

CAT Questions | Number Theory | Possible 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

🏏 CAT 2021 could be your Gabba Victory!
Fabulous 5,000 off on online courses.


2IIM : Best Online CAT Coaching.


Best CAT Coaching in Chennai


CAT Coaching in Chennai - CAT 2021
Online Batches Available Now!


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.

 


CAT Online Coaching | CAT Number Systems questions Videos On YouTube


Other useful sources for Number System Questions | Number Theory Remainders Sample Questions


CAT Questions | CAT Quantitative Aptitude

CAT Questions | CAT DILR

CAT Questions | Verbal Ability for CAT


Where is 2IIM located?

2IIM Online CAT Coaching
A Fermat Education Initiative,
58/16, Indira Gandhi Street,
Kaveri Rangan Nagar, Saligramam, Chennai 600 093

How to reach 2IIM?

Phone: (91) 44 4505 8484
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now
Email: prep@2iim.com