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# If x and y are integers, is x-y an even number? 1) x+3y is even 2) (

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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If x and y are integers, is x-y an even number? 1) x+3y is even 2) (  [#permalink]

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04 Nov 2017, 18:18
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45% (medium)

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57% (01:24) correct 43% (00:58) wrong based on 61 sessions

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[GMAT math practice question]

If x and y are integers, is x-y an even number?

1) x+3y is even
2) (x-1)^2(y+1)^2 is even

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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 $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" PS Forum Moderator Joined: 25 Feb 2013 Posts: 1201 Location: India GPA: 3.82 If x and y are integers, is x-y an even number? 1) x+3y is even 2) ( [#permalink] ### Show Tags Updated on: 04 Nov 2017, 22:07 MathRevolution wrote: [GMAT math practice question] If x and y are integers, is x-y an even number? 1) x+3y is even 2) (x-1)^2(y+1)^2 is even For $$x-y$$ to be even both $$x$$ & $$y$$ has to be ODD or Even Statement 1: $$x+3y=Even => x=Even-3y$$ Case 1: $$y=Odd$$, then $$x=Odd$$, hence $$x-y=Even$$ Case 2: $$y=even$$, then $$x=even$$, hence $$x-y=Even$$ So in all possible scenarios we have $$x-y=Even$$. Sufficient Statement 2: $$[(x-1)(y+1)]^2=Even$$ Case 1: $$y=Odd$$, then $$x=Even$$ / $$Odd$$, hence $$x-y=Even$$ / $$Odd$$ Hence there can be both the scenarios . So insufficient there is no need to test other scenarios here. Option A Originally posted by niks18 on 04 Nov 2017, 21:34. Last edited by niks18 on 04 Nov 2017, 22:07, edited 1 time in total. Math Expert Joined: 02 Aug 2009 Posts: 6523 Re: If x and y are integers, is x-y an even number? 1) x+3y is even 2) ( [#permalink] ### Show Tags 04 Nov 2017, 22:02 MathRevolution wrote: [GMAT math practice question] If x and y are integers, is x-y an even number? 1) x+3y is even 2) (x-1)^2(y+1)^2 is even x-y will be EVEN when BOTH x and y are odd or BOTH are even + or - requires both to be SAME * requires just ONE to be EVEN lets see the statements 1) x+3y is even as 3 is ODD, x+3y will be EVEN when BOTH x and y are of same type - both even or both odd so x-y is EVEN suff 2) $$(x-1)^2(y+1)^2$$ is even so this is multiplication.. here either both x-1 and y+1 are EVEN or just ONE of the two can be even.. if both are EVEN, x and y will be ODD and x-y will be EVEN if only one is even, one of x and y will be odd and other even so x-y will be ODD insuff A _________________ 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: 6013 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If x and y are integers, is x-y an even number? 1) x+3y is even 2) ( [#permalink] ### Show Tags 05 Nov 2017, 18:22 => 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 that equal number of variables and independent equations ensures a solution Condition 1) x – y = ( x + 3y ) - 4y is a difference of even integers, since x + 3y is even and 4y is even. This is sufficient. Condition 2) x = 3, y = 1 ➔ x – y = 2 is even. x = 3, y = 2 ➔ x – y = 1 is odd. This is not sufficient. Therefore, the answer is A. Normally for cases where we need 2 more equations, such as original conditions with 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore, C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer, hence using 1) and 2) together. (It saves us time). Obviously, there may be cases where the answer is A, B, D or E. Answer: A _________________ 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$99 for 3 month Online Course"
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Re: If x and y are integers, is x-y an even number? 1) x+3y is even 2) ( &nbs [#permalink] 05 Nov 2017, 18:22
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