# CAT Practice : Number System - Remainders

You are here: Home  CAT Questionbank   CAT Quant  Number System: Remainders  Question 2
How did Binomial theorem get into Number Theory? More importantly, why did it? Why did the chicken cross the road?

## Number Theory - Binomial Theorem

Q.2: What is the remainder when (13100 + 17100) is divided by 25?
1. 0
2. 2
3. 4
4. 11

Choice B. 2

## Detailed Solution

(13100 + 17100) = (15 – 2)100 + (15 + 2)100

Now 52 = 25, So, any term that has 52 or any higher power of 5 will be a multiple of 25. So, for the above question, for computing remainder, we need to think about only the terms with 150 or 151.

(15 – 2)100 + (15 + 2)100
Coefficient of 150 = (-2)100 + 2100
Coefficient of 151 = 100C1 * 151* (-2)99 + 100C1 * 151* (-2)99. These two terms cancel each other.So, the sum is 0.
Remainder is nothing but (-2)100 + 2100 = (2)100 + 2100

2101
Remainder of dividing 21 by 25 = 2
Remainder of dividing 22 by 25 = 4
Remainder of dividing 23 by 25 = 8
Remainder of dividing 24 by 25 = 16
Remainder of dividing 25 by 25 = 32 = 7
Remainder of dividing 210 by 25 = 72 = 49 = -1
Remainder of dividing 220 by 25 = (-1)2 = 1
Remainder of dividing 2101 by 25 = Remainder of dividing 2100 by 25 * Remainder of dividing 21 by 25 = 1 * 2 = 2

## 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.