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If x + y is an integer, is y an integer? (1) x y is an

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If x + y is an integer, is y an integer? (1) x y is an [#permalink]

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New post 17 Mar 2009, 21:18
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If x + y is an integer, is y an integer?
(1) x – y is an integer.
(2) x + 2y is an integer.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

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Re: DS + Algebra [#permalink]

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New post 17 Mar 2009, 23:36
Can you please elobarate on your answer ?

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Re: DS + Algebra [#permalink]

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New post 18 Mar 2009, 00:07
I will go for B

ques says ... x+y = integer1
from option (2), x + 2y = integer2
hence x+y+y = integer2
hence... integer1 + y = integer2
y= integer2 - integer1 = integer3

hence (2) alone is sufficient
what is OA ?
@priyankur_saha@ml.com ... why did you choose C , can you pls explain ?

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Re: DS + Algebra [#permalink]

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New post 18 Mar 2009, 03:28
Agree with B

x + y = integer -- 1) is Y an integer?

1)
x - y = int1 --- 2)

so solving both 1 and 2, we get 2y = int2 - int1
So we can say weather Y is an integer. coz (int2 - int1)/2 may not be an integer.

2) x + y + y = integer

So y is definely an integer integer - integer

B

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Re: DS + Algebra [#permalink]

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New post 18 Mar 2009, 04:37
My choice is also B

given x+y=integer-----(1)

Statement 1: x-y=integer-----------(2)
(1)-(2) --------> 2y=integer
now y may be an integer or may not be eg if y=2.5 still 2y=5 an integer Insuff

Statemnet 2: x+2y=intger
x+y+y =integer
now x+y=integer
hence y=integer Suff

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Re: DS + Algebra [#permalink]

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New post 18 Mar 2009, 08:58
What about the case where x=1.5 and y=0.5 ? In this case, x+y is an integer, and x+2y also gives an integer even when y is not an integer. You could also have x=1 and y=2, and again x+y gives an integer, as does x+2y .... so how can it be B ?

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Re: DS + Algebra [#permalink]

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New post 18 Mar 2009, 17:31
when x=1.5 and y=0.5 ... In this case, x+y is an integer = 2
BUT x+2y gives 1.5 + 1.0 = 2.5 hence not an integeer

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Re: DS + Algebra [#permalink]

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New post 18 Mar 2009, 22:53
x+2y= 2.5 ---------> not an integer

pmenon wrote:
What about the case where x=1.5 and y=0.5 ? In this case, x+y is an integer, and x+2y also gives an integer even when y is not an integer. You could also have x=1 and y=2, and again x+y gives an integer, as does x+2y .... so how can it be B ?

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Re: DS + Algebra   [#permalink] 18 Mar 2009, 22:53
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