For integers x and y, is x + y even?

Question

(1) x^2 − y^2 is even

(2) x − y is even

Amolpi · Answer

Answer is D.
There are only two situations when Addition/Subtraction of two integers yields an Even Output.
1) Odd+/-Odd=Even
2) Even+/-Even=Even

As per this logic, Statement (1) is an Even and hence X+Y has to be even. This is sufficient to answer the question.

Statement (2) is also an Even hence X+Y has to be even.This is sufficient to answer the question.

0akshay0 · Answer

St I x^2 − y^2 is even => (x-y)(x+y) is even; If (x + y) or (x - y) is even then x and y are both even or odd. So, (x + y) has to be even. ---------Sufficient St II. x-y is even; If you take any 2 Integers whose difference is even their sum will always be even, Hence (x+y) is even -------Sufficient eg; 9-5=4 even and 9+5=14 even 10-2=8 even and 10+2=12 even Hence Option D is correct. Hit Kudos if you liked it 8-)

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Kurtosis · Answer

If (x + y) or (x - y) is even then x and y are both even or odd. So, (x + y) has to be even.

Answer: D

0akshay0 · Answer

guess I need some coffee now. Thanks Vyshak , have edited my reply to the Question

Cez005 · Answer

1) Tells us that x and y both have to have the same sign. SUFF

2) Tells us that x and y both have to have the same sign. SUFF

D

JeffTargetTestPrep · Answer

We need to determine whether x + y is even. Before jumping into the statements, there are two important rules to consider.

Rule #1:

When an odd integer is raised to a positive integer exponent, the result will still be odd, and when an even number is raised to a positive integer exponent, the result will still be even.

Rule #2:

Addition rules for even and odd numbers are the same as subtraction rules for even and odd numbers.

Statement One Alone:

x^2 - y^2 is even.

Since x^2 - y^2 is even, following rules one and two, we see that x + y will also be even. Statement one alone is sufficient to answer the question.

Statement Two Alone:

x - y is even.

Following rule two, we see that if x - y is even, then x + y will also be even. Statement two alone is also sufficient to answer the question.

Answer: D

BillyZ · Answer

Official solution from Veritas Prep.

D. This question is a good example of the GMAT's classic "C trap", in which the statements are written to bait you toward selecting C. Yes, you can deconstruct statement 1 into:

(x + y)(x - y)  is even

But at this point you don't need to use statement 2 along with it. Your options now with statement 1 alone are:

(Even + Even)(Even - Even) = Even

and

(Odd + Odd)(Odd - Odd) = Even

It   cannot   be  (Even + Odd)(Even - Odd)  because then the two parentheticals would both be odd, making the product odd. So statement 1 guarantees that each of  (x + y)  and  (x - y)  are even.

Similarly, statement 2 guarantees that  x + y  is even. For  x - y  to be even, it's either Odd - Odd or Even - Even. Change that minus to a plus in either case and the result will still be even, so statement 2 is sufficient, also. The correct answer is D.

CapnSal · Answer

Statement 1 analysis: 
if we deconstruct statement 1: (x-y)(x+y) = even. Product of 2 terms can be even if: 
1) one of them is even or 
2) both of them are even

Using point 2) above we are able to get (x+y) is even, however, if we use point 1) then (x+Y) may or may not be even thus giving us not sufficient. Where am I going wrong for statement 1 analysis?

For integers x and y, is x + y even?

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For integers x and y, is x + y even?

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