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
