# CAT Practice : Number System - Remainders

You are here: Home  CAT Questionbank   CAT Quant  Number System: Remainders  Question 14
What divides a3 + b3?

## Remainder - Large number

Q.14: If N = (243 + 253 + 263 + 273), then N divided by 102 leaves a remainder of?
1. 18
2. 12
3. 1
4. 0

Choice D. 0

## Detailed Solution

N = 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

Correct Answer: Choice D

## Our Online Course, Now on Google Playstore!

### 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!

## More questions from Number Theory - 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.