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Is x+y divisible by 2? 1) There are 25 integers between x and y 2) x

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Joined: 08 Jul 2010
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Is x+y divisible by 2? 1) There are 25 integers between x and y 2) x [#permalink]

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New post 14 Nov 2017, 01:36
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

50% (00:43) correct 50% (01:02) wrong based on 42 sessions

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Is x+y divisible by 2?

1) There are 25 integers between x and y
2) x and y are Integers


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[Reveal] Spoiler: OA

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Re: Is x+y divisible by 2? 1) There are 25 integers between x and y 2) x [#permalink]

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New post 14 Nov 2017, 01:44
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You might pick A for this one.

1. If both are integers, they both are odd or both are even.
But we don't know if they are integers.
Insufficient.

2. x+y could be odd or even.
Insufficient.

Both.
Sufficient.

C.
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Re: Is x+y divisible by 2? 1) There are 25 integers between x and y 2) x [#permalink]

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New post 14 Nov 2017, 07:48
(1) x and y can be both integers, in which case, y = x+26 or x = y+26 (since there are 25 integers between them). So, in this case, either both will be even or both will be odd. And thus, their sum will be even in either case, and thus divisible by 2.

But its also possible that both x/y are not integers, and still have 25 integers between them. Eg, we can have x=1.7 and y = 27. Still there are 25 integers between them (2 to 26) but sum of x and y is not an integer, hence not divisible by 2.
So insufficient.

(2) x and y are both integers, but we dont know which is even and which is odd so we cant say about their sum. Insufficient.

Combining, since both are integers having 25 integers between them, either both will be even or both will be odd. So sum will be divisible by 2. Sufficient.

Hence C answer

Kudos [?]: 185 [0], given: 289

Re: Is x+y divisible by 2? 1) There are 25 integers between x and y 2) x   [#permalink] 14 Nov 2017, 07:48
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