CAT Quantitative Aptitude Questions | CAT Number Theory - Digits 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

Explanatory Answer

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.