# CAT Quantitative Aptitude Questions | CAT Number Theory - Digits questions

###### CAT Questions | Number Theory | Divisibility of powers CAT Questions

The question is about Divisibility of higher powers of a number. A term is divisible by x and we need to find out another term which is also divisible by x . Dealing with digits and base system of a number is a vital component in CAT Number Systems. A range of CAT questions can be asked based on this simple concept in the CAT Exam.

Question 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

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##### Method of solving this CAT Question from Number Theory - Digits: Application of an algebraic expansion would be helpful!

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

The question is "Which among the following is also divisible by x?"

##### Hence the answer is 448 + 1

Choice D is the correct answer.

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