# CAT Practice : Number System - Remainders

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Try expressing the given number in terms of multiples of the divisors

## Divisibility - Large Number

Q.12: Given a number, N = 555 + 175 – 725, then which of the following is true?
1. N is divisible by both 7 and 13
2. N is divisible by both 3 and 17
3. N is divisible by 17 but not 3
4. N is divisible by 11 but not 17

Choice B. N is divisible by both 3 and 17

## Detailed Solution

N = 555 + 175 – 725

N = (54 + 1)5 + (18 - 1)5 – 725
The above is divisible by 3

N = (51 + 4)5 + 175 – (68 + 4)5
The above is divisible by 17

N = 555 + (11 + 6)5 – (66 + 6)5
The above is divisible by 11

N cannot be expressed in favourable of 7 and 13 and hence is not divisible by 7 and 13

From the above the best answer choice is (B) – N is divisible by both 3 and 17

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## 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.