Brent@GMATPrepNow wrote: ↑

Wed Feb 03, 2021 10:25 am

If x and y are positive integers, what is the remainder when (10^x) + y is divided by y?

(1) x = 5
(2) y = 2

Answer: B
Source: official guide

Given: x and y are positive integers

Target question: What is the remainder when (10^x) + y is divided by y?

Statement 1: x = 5
Since we have no information about y, we cannot answer the target question with certainty
Statement 1 is NOT SUFFICIENT

Statement 2: y = 2
Important: When we divide an integer by 2, the remainder will be EITHER 1 OR 0, depending on whether the integer is odd or even.
If the number is ODD, then we get a remainder of 1 after dividing by 2
If the number is EVEN, then we get a remainder of 0 after dividing by 2

Now that we know the value of y, our target question becomes, "What is the remainder when 10^x + 2 is divided by 2?"
Since 10^x is EVEN for all positive integer values of x, we know that 10^x + 2 must be EVEN

So, our target question becomes, "What is the remainder when SOME EVEN NUMBER is divided by 2?"
The answer to this new target question is the remainder will be 0
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent