inderjeetdhillon wrote:
If x and y are integers, is xy even?
(1) x = y + 1.
(2) x/y is an even integer.
Target question:
Is xy even?Aside: For xy to be even, we need x to be even, or y to be even (or both even).
Statement 1: x = y+1This tells us that x is 1 greater than y.
This means that x and y are consecutive integers.
If x and y are consecutive integers, then one must be odd and the other must be even.
As such, the product
xy must be even.
So, statement 1 is SUFFICIENT
Statement 2: x/y is an even integer.If x/y is an even integer, then we can write x/y = 2k (where k is an integer)
Now take the equation and multiply both sides by y to get: x = 2ky
If k and y are both integers, we can see that 2ky (also known as x) must be even.
If x is even, then the product
xy must be even.
So, statement 2 is SUFFICIENT
Answer =
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