Baten80 wrote:
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
(1) x = 5
(2) y = 2
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
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