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# Is x+y odd?

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Joined: 12 Aug 2015
Posts: 2571
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Is x+y odd?  [#permalink]

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21 Nov 2016, 02:22
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15% (low)

Question Stats:

79% (01:09) correct 21% (01:10) wrong based on 103 sessions

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Is x+y odd?

(1) 2y + x is even
(2) 2x + y is even

Give me an algebraic Solution

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Joined: 12 Sep 2015
Posts: 4000
Re: Is x+y odd?  [#permalink]

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21 Nov 2016, 09:58
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Top Contributor
stonecold wrote:
Is x+y odd?

(1) 2y + x is even
(2) 2x + y is even

Target question: Is x+y odd?

Statement 1: 2y + x is even
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 2 and y = 1. So, 2y + x = (2)(1) + 2 = 4, which is even. In this case x + y = 2 + 1 = 3, and 3 is ODD
Case b: x = 2 and y = 2. So, 2y + x = (2)(2) + 2 = 6, which is even. In this case x + y = 2 + 2 = 4, and 4 is EVEN
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: http://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: 2x + y is even
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 1 and y = 2. So, 2x + y = (2)(1) + 2 = 4, which is even. In this case x + y = 1 + 2 = 3, and 3 is ODD
Case b: x = 2 and y = 2. So, 2x + y = (2)(2) + 2 = 6, which is even. In this case x + y = 2 + 2 = 4, and 4 is EVEN
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that 2y + x = even
Statement 2 tells us that 2x + y = even
ADD the equations to get: (2y+x) + (2x+y) = even + even
Simplify: 3x + 3y = EVEN
Factor: 3(x + y) = EVEN
Since we know that (ODD)(EVEN) = EVEN, and since 3 is ODD, we can conclude that x+y must be EVEN
In other words, x+y is NOT odd
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

RELATED VIDEO

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Current Student
Joined: 12 Aug 2015
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GRE 1: Q169 V154
Re: Is x+y odd?  [#permalink]

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21 Nov 2016, 10:24
GMATPrepNow wrote:
stonecold wrote:
Is x+y odd?

(1) 2y + x is even
(2) 2x + y is even

Target question: Is x+y odd?

Statement 1: 2y + x is even
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 2 and y = 1. So, 2y + x = (2)(1) + 2 = 4, which is even. In this case x + y = 2 + 1 = 3, and 3 is ODD
Case b: x = 2 and y = 2. So, 2y + x = (2)(2) + 2 = 6, which is even. In this case x + y = 2 + 2 = 4, and 4 is EVEN
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: http://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: 2x + y is even
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 1 and y = 2. So, 2x + y = (2)(1) + 2 = 4, which is even. In this case x + y = 1 + 2 = 3, and 3 is ODD
Case b: x = 2 and y = 2. So, 2x + y = (2)(2) + 2 = 6, which is even. In this case x + y = 2 + 2 = 4, and 4 is EVEN
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that 2y + x = even
Statement 2 tells us that 2x + y = even
ADD the equations to get: (2y+x) + (2x+y) = even + even
Simplify: 3x + 3y = EVEN
Factor: 3(x + y) = EVEN
Since we know that (ODD)(EVEN) = EVEN, and since 3 is ODD, we can conclude that x+y must be EVEN
In other words, x+y is NOT odd
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

RELATED VIDEO

Great Explanation Brent
One Quick Query

What if x+y=2/3?

3*2/3 = even

Regards
Stone Cold
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Re: Is x+y odd?  [#permalink]

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21 Nov 2016, 10:50
stonecold wrote:
Is x+y odd?

(1) 2y + x is even
(2) 2x + y is even

FROM STATEMENT - I ( INSUFFICIENT )

2y = Even

Since, 2y + x = Even

x = Even ( Because Even + Even = Even & Odd + Odd =Even )

But what about y ? It can be Odd/Even

FROM STATEMENT - II ( INSUFFICIENT )

2x = Even

Since, 2x + y = Even

y = Even ( Because Even + Even = Even & Odd + Odd =Even )

But what about x ? It can be Odd/Even

FROM STATEMENT I & II ( SUFFICIENT )

From I - x = Even
From II - y = Even

Thus, x + y = Even..

Hence, BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked, answer will be (C)

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Thanks and Regards

Abhishek....

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Re: Is x+y odd?   [#permalink] 21 Nov 2016, 10:50
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# Is x+y odd?

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