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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6826
GMAT 1: 760 Q51 V42
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When x and y are integers, is x+y an even?  [#permalink]

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22 May 2016, 16:55
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Difficulty:

25% (medium)

Question Stats:

77% (01:36) correct 23% (01:47) wrong based on 116 sessions

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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.

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 7212 Re: When x and y are integers, is x+y an even? [#permalink] ### Show Tags 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 _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html GMAT online Tutor Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6826 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: When x and y are integers, is x+y an even? [#permalink] ### Show Tags 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. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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When x and y are integers, is x+y an even?  [#permalink]

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20 Nov 2016, 06:55
2
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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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 , $$x + y = Even$$

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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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?
Manhattan Prep Instructor
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GMAT 1: 790 Q51 V49
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Re: When x and y are integers, is x+y an even?  [#permalink]

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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? &nbs [#permalink] 25 Feb 2017, 11:15
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# When x and y are integers, is x+y an even?

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