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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
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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, 17:18
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Difficulty:

45% (medium)

Question Stats:

55% (01:22) correct 45% (00:58) wrong based on 53 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
[Reveal] Spoiler: OA

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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, 20:34
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

Last edited by niks18 on 04 Nov 2017, 21:07, edited 1 time in total.

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Math Expert
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Posts: 5341

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Re: 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, 21:02
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
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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

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05 Nov 2017, 17:22
=>

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.

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.
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Re: If x and y are integers, is x-y an even number? 1) x+3y is even 2) (   [#permalink] 05 Nov 2017, 17:22
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