bestofbala wrote:For integers x and y is x+y Even?
(1) x*x - y*y is even
(2) x-y is even
Knowing the various rules (as Anju has demonstrated) is the best approach to these kinds of questions. However, if you don't know how to proceed in that manner, you can always test possible cases. This is more time-consuming, but still manageable within a 2-minute time frame.
For each statement, we'll examine the 4 different cases involving x and y. They are:
case a) x is even and y is even
case b) x is even and y is odd
case c) x is odd and y is even
case d) x is odd and y is odd
Target question:
Is x+y even?
Statement 1: x^2 - y^2 is even
Let's examine x^2 - y^2 via the 4 cases. To do this, we'll plug in a 2 for an even number and a 1 for an odd number
case a) x is even and y is even: x^2 - y^2 = 2^2 - 2^2 = 0 (EVEN)
case b) x is even and y is odd: x^2 - y^2 = 2^2 - 1^2 = 3 (ODD)
case c) x is odd and y is even: x^2 - y^2 = 1^2 - 2^2 = -3 (ODD)
case d) x is odd and y is odd: x^2 - y^2 = 1^2 - 1^2 = 0 (EVEN)
Statement 1 tells us that x^2 - y^2 is EVEN. So, that means either case a is true or case d is true.
If case a is true, then x and y are both even, which means
x+y is even.
If case d is true, then x and y are both odd, which means
x+y is even.
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: x-y is even
Let's examine x-y via the 4 cases. To do this, we'll plug in a 2 for an even number and a 1 for an odd number
case a) x is even and y is even: x-y = 2-2 = 0 (EVEN)
case b) x is even and y is odd: x-y = 2-1 = 1 (ODD)
case c) x is odd and y is even: x-y = 1-2 = -1 (ODD)
case d) x is odd and y is odd: x-y = 1-1 = 0 (EVEN))
Statement 2 tells us that x-y is EVEN. So, that means either case a is true or case d is true.
If case a is true, then x and y are both even, which means
x+y is even.
If case d is true, then x and y are both odd, which means
x+y is even.
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer =
D
If you're interested, we have a free video that further explains this technique of testing cases:
https://www.gmatprepnow.com/module/gmat- ... ies?id=839
Cheers,
Brent
