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Joined: 28 Jul 2018
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If x and y are integers, is x + y even?
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28 Jul 2018, 20:33
Question Stats:
78% (00:53) correct 22% (01:05) wrong based on 159 sessions
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If x and y are integers, is x + y even? (1) x + 2y is odd. (2) xy is odd.
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Intern
Joined: 28 Jul 2018
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Re: If x and y are integers, is x + y even?
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28 Jul 2018, 20:38
This one (from GMATPrep Exam 5) has me pulling my hair out. According to the OA, only (2) is sufficient. I think (1) is sufficient alone too, however.
My logic for (1):  x + 2y > O  2y must be even (any integer times 2 is even)  thus x must be odd  "x + y" is only odd if either x or y is odd  thus (1) indicates that "x + y" is odd



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Re: If x and y are integers, is x + y even?
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28 Jul 2018, 20:53
To determine whether x + y is even or odd Statement 1x + 2y is odd => 2y is always even irrespective of even/odd nature of y (any integer multiplied by even results in an even integer) => x + 2y = odd => x = odd  2y = odd  even = odd So, x is odd and y can either be odd or even if x is odd and y is odd => x + y = odd + odd = even if x is odd and y is even => x + y = odd + even = odd As we have two possible cases, statement 1 is insufficient Statement 2xy is odd => xy is odd if and only if x is odd and y is odd => x + y = odd + odd = even Statement 2 is sufficientHence option B
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Re: If x and y are integers, is x + y even?
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28 Jul 2018, 20:54
emanresu1 wrote: This one (from GMATPrep Exam 5) has me pulling my hair out. According to the OA, only (2) is sufficient. I think (1) is sufficient alone too, however.
My logic for (1):  x + 2y > O  2y must be even (any integer times 2 is even)  thus x must be odd  "x + y" is only odd if either x or y is odd  thus (1) indicates that "x + y" is odd emanresu1, 'y' could be even OR odd for 'x' + '2y' to result in an odd integer. Therefore, statement (a) does not give us sufficient information as to whether integer 'y' is indeed an odd integer. Therefore, plugging it into the question stem (x+y) may result in an even OR an odd expression, hence insufficient. Hope that helps



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Re: If x and y are integers, is x + y even?
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28 Jul 2018, 20:56
emanresu1 wrote: This one (from GMATPrep Exam 5) has me pulling my hair out. According to the OA, only (2) is sufficient. I think (1) is sufficient alone too, however.
My logic for (1):  x + 2y > O  2y must be even (any integer times 2 is even)  thus x must be odd  "x + y" is only odd if either x or y is odd  thus (1) indicates that "x + y" is odd If both x and y are odd then x + y becomes even. You only know the even/odd nature of x and y can be either even or odd. Hence statement 1 is insufficient Example x = 3 and y = 6 => x + y = 3 + 6 = 9 odd x = 3 and y = 7 => x + y = 3 + 7 = 10 even
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Re: If x and y are integers, is x + y even?
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28 Jul 2018, 21:03
workout wrote: To determine whether x + y is even or odd
Statement 1
x + 2y is odd
=> 2y is always even irrespective of even/odd nature of y (any integer multiplied by even results in an even integer)
=> x + 2y = odd
=> x = odd  2y = odd  even = odd
So, x is odd and y can either be odd or even
if x is odd and y is odd => x + y = odd + odd = even
if x is odd and y is even => x + y = odd + even = odd
As we have two possible cases, statement 1 is insufficient
Statement 2
xy is odd
=> xy is odd if and only if x is odd and y is odd
=> x + y = odd + odd = even
Statement 2 is sufficient
Hence option B THANK YOU! This Quant pressure has me flubbing even simple things like thinking 7+7 is odd (yes, I really thought that during my practice exam, and thus the ridiculous confusion)



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Joined: 18 Dec 2018
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Re: If x and y are integers, is x + y even?
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18 Dec 2018, 21:16
x + y will be even only if either both of them are even or both of them are odd. Statement 1: x + 2y is odd. 2y is a multiple of 2 therefore it can’t be odd. So, x is odd. But we don’t know if ‘y’ is odd or even. Hence, Insufficient. Statement 2: ‘xy’ is odd. This is only possible if ‘x’ and ‘y’ both are odd. Since, ‘x’ and ‘y’ are odd, x + y is even. Hence, Sufficient.



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Re: If x and y are integers, is x + y even?
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12 Jan 2019, 21:28
x + y will be even only if either both of them are even or both of them are odd. Statement 1: x + 2y is odd. 2y is a multiple of 2 therefore it can’t be odd. So, x is odd. But we don’t know if ‘y’ is odd or even. Hence, Insufficient. Statement 2: ‘xy’ is odd. This is only possible if ‘x’ and ‘y’ both are odd. Since, ‘x’ and ‘y’ are odd, x + y is even. Hence, Sufficient.




Re: If x and y are integers, is x + y even?
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12 Jan 2019, 21:28






