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When x and y are integers, is x+y an even?

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When x and y are integers, is x+y an even? [#permalink]

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When x and y are integers, is x+y an even?
1) x^2+y^2 is an even
2) (x+1)^2+(y+1)^2 is an even

*An answer will be posted in 2 days.
[Reveal] Spoiler: OA

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Re: When x and y are integers, is x+y an even? [#permalink]

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New post 22 May 2016, 19:09
MathRevolution wrote:
When x and y are integers, is x+y an even?
1) x^2+y^2 is an even
2) (x+1)^2+(y+1)^2 is an even

*An answer will be posted in 2 days.


X and Y are integers and we have to find if x+y is integers...
If BOTH x and y are same type of numbers that is both odd or both even , ans is YES, otherwise No..

lets test the statements-
1) x^2+y^2 is an even
clearly x and y are either both odd or both even..
ans is YES..
Suff

2) (x+1)^2+(y+1)^2 is an even
clearly x and y are either both odd or both even..
ans is YES..
Suff

D
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Re: When x and y are integers, is x+y an even? [#permalink]

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New post 25 May 2016, 02:41
X and y in the conditions 1) and 2) can end up being both odd or both even.
The answer to both conditions are ‘yes’, which make the conditions sufficient.
The correct answer, hence, is D.
- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
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When x and y are integers, is x+y an even? [#permalink]

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New post 20 Nov 2016, 06:55
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This is a great Question which is testing our fundamental knowledge of evens and odds.
There is one very important property that we must know when we are dealing with even and odd numbers on the GMAT.

POWER/EXPONENTS Do not affect the even/odd nature of any integer.

Now in this question we are told that both x and y are integers(Very important info)
We need to get if x+y is even or not
For x+y to be even => both x and y must have the same even odd nature.

Lets look at statement
Statement 1
x^2+y^2 = even
hmm
as power doesn't not affect the even/odd nature
x+y must be even too

Hence Sufficient
Statement 2
(x+1)^2 +(y+1)^2 is even
Okay
again we can say that
x+1+y+1 is even
hence x+y+2 is even
so x+y must be even too
hence Sufficient

Hence D
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Re: When x and y are integers, is x+y an even? [#permalink]

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New post 20 Nov 2016, 07:07
MathRevolution wrote:
When x and y are integers, is x+y an even?
1) x^2+y^2 is an even
2) (x+1)^2+(y+1)^2 is an even

*An answer will be posted in 2 days.


FROM STATEMENT - I ( SUFFICIENT )

\(x^2+y^2 = Even\)

Either x = y = Even
Or, x = y = Even

In either case x + y will be even

FROM STATEMENT - II ( SUFFICIENT )

\((x+1)^2+(y+1)^2 = Even\)

\(x = y = Odd\)

Thus , \(x + y = Even\)

So , EACH statement ALONE is sufficient to answer the question asked answer will be (D)...

PS : Really love stonecold's explanation, wonderfully explained, Kudos is the least I can add..

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Re: When x and y are integers, is x+y an even? [#permalink]

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New post 25 Feb 2017, 05:17
As the question does not mention that x and y are positive integers,shouldn't we include the cases where both are negative as well?
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Re: When x and y are integers, is x+y an even? [#permalink]

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New post 25 Feb 2017, 11:15
Environo0792 wrote:
As the question does not mention that x and y are positive integers,shouldn't we include the cases where both are negative as well?


Yes, you should, but it doesn't change the solution or the answer. The rules for odds and evens are the same for negative numbers as they are for positive numbers. For instance, -2 and -4 are both even, and their sum is even; -3 and -7 are both odd and their sum is also even.
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Re: When x and y are integers, is x+y an even?   [#permalink] 25 Feb 2017, 11:15
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