# CAT Quantitative Aptitude Questions | CAT Number Systems - Remainders

###### CAT Questions | Number Theory | Remainders - Sum of Digits
CAT Questions

The question is from CAT Number Theory Remainders. A number is given in the form of(xa + ya). 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

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##### 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.

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