# GRE Questions

0%

#### 1. What is the remainder when (53)^35 is divided by 13?

Correct! Wrong!

"Consider two positive integers a1 & b1, which leave a remainder r1 & r2 when divided by a number q. The product of the two numbers a1 & b1 when divided by q will leave the same remainder as the product of r1 & r2 when divided by q. For example, the numbers 23 and 13 when divided by the number 8 leave a remainder 7 and 5 respectively. 23x13 = 299 when divided by 8 leaves a remainder 3 7x5 = 35 also leaves a remainder 3 when divided by 3. Using the above logic and using the fact that 53 when divided by 13 will leave a remainder 1, we can say that 53^2 when divided by 13 will also leave a remainder 1. 53^3 will also leave the same remainder because 53^3 = 53 x 53^2. Similarly, 53^35 will also leave a remainder 1. For the more mathematically minded readers, we can arrive at the above result using Binomial Theorem. 53^35 = (52 + 1)^35 = 52^35 + (34 terms which all contain a power of 52) + 1 In the above expansion, since 52 is divisible by 13, all the terms are divisible by 13 except the last term which is the number 1."

Correct! Wrong!

Correct! Wrong!

Correct! Wrong!

### Galvanize Test Prep

+91 95000 20740
[email protected]
Call Me Back