CAT Quantitative Aptitude Questions | CAT Number Systems - Remainders

The question is from CAT Number Theory Remainders. A number is given in the form of(x^a + y^a). We need to find out the remainder when it is divided by b.When does an even number become an odd number? When it is divided by 2 (but not always). Think about this.

Question 5: What is the remainder when we divide 3⁹⁰ + 5⁹⁰ by 34?

1. 0
2. 17
3. 33
4. 1

Explanatory Answer

Method of solving this CAT Question from Number Theory - Remainders: When does an even number become an odd number? When it is divided by 2 (but not always). Think about this.

3⁹⁰ + 5⁹⁰ can be written as (3²)⁴⁵ + (5²)⁴⁵
= (9)⁴⁵ + (25)⁴⁵

Any number of the form aⁿ + bⁿ is a multiple of (a + b) whenever n is odd.

So (9)⁴⁵ + (25)⁴⁵ is a multiple of 9 + 25 = 34

So, the remainder when we divide (3²)⁴⁵ + (5²)⁴⁵ by 34 is equal to 0.

The question is "What is the remainder when we divide 3⁹⁰ + 5⁹⁰ by 34?"

Hence the answer is "0".

Choice A is the correct answer.