CAT Quantitative Aptitude Questions | CAT Number Systems - Remainders

CAT Questions | Number Theory | Remainders - Large number

The question is from CAT Number Theory - Remainders. A large number is given and we need to find out the remainder when the number is divided by 102. A range of CAT questions can be asked based on this simple concept. 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 14: If N = (243 + 253 + 263 + 273), then N divided by 102 leaves a remainder of?

  1. 18
  2. 12
  3. 1
  4. 0

Best CAT Online Coaching
Try upto 40 hours for free
Learn from the best!


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: What divides a3 + b3?

= (243 + 253 + 263 + 273)
Unit digits of N = 4 + 5 + 6 + 3 = 18
N is divisible by 2

We know that, a3 + b3 = (a + b)(a2 – ab + b2)
=> (a + b) always divides a3 + b3
Therefore, 243 + 273 is divisible by 51 (24 + 27)

Also, 253 + 263 is divisible by 51 (25 + 26)
The given divisor 102 can be expressed as 51 * 2
Hence, N is completely divisible by 102
Remainder = 0

The question is "If N = (243 + 253 + 263 + 273), then N divided by 102 leaves a remainder of?"

Hence the answer is 0.

Choice D 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