# CAT Practice : Number System

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## Divisibility of powers

Q.9: A number 416 + 1 is divisible by x. Which among the following is also divisible by x?
1. 496 + 1
2. 432 + 1
3. 48 + 1
4. 448 + 1

Choice D. 448 + 1

## Detailed Solution

We know a3 + b3 = (a + b)3 – 3ab(a + b)
If (a + b) is divisible by x, then a3 + b3 is also divisible by x.
If 416 + 1 is divisible by x, then (416)3 + 13 is also divisible by x
Or 448 + 1 is divisible by x

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