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# If x and y are integers greater than 1, is x a multiple of

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Senior Manager
Joined: 24 Mar 2011
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26 Jul 2011, 21:28
1
KUDOS
i think A.

Yalephd wrote:
If X and Y are integers greater than 1, is X a multiple of Y?

$$(1) 3Y^2 + 7Y = X$$

$$(2) X^2 - X$$ is a multiple of $$Y.$$

1st statement - Y(3Y+1) = X implies that... X is a multiple of Y... - sufficient

2nd Statement - i am not sure the best way... but i tried to use some arbitrary smart #s which will give me X>1.
X(X-1) is multiple of Y... so ex- if Y=6, then X =3.. so X is not a multiple of Y.
or Y = 12, then X = 4 again X is not a multiple of Y.

so not sufficient.
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26 Jul 2011, 22:13
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KUDOS
The answer should be (A) - statement (1) alone is sufficient to answer the question.

Consider statement (1) first:
X = 3Y^2 + 7Y
=> X = Y (3Y + 7)
=> X = Y * some number
Therefore X is a multiple of Y. So statement (1) alone is sufficient.

Next consider statement 2:
X^2 - X is a multiple of Y
=> kY = X(X-1) where k is any integer >= 1
=> X = kY/(X-1) = [k/(X-1)]Y
Therefore X is a multiple of Y depending on whether k/(X-1) is an integer or not.
For k = 4 and X = 5, this works. For k=5, X=5 it does not work.
Therefore statement (2) alone is insufficient to answer the question.

Hence (A) is the correct answer choice.
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27 Jul 2011, 06:39
agdimple333, GyanOne,
Thank you.

GyanOne, I like your approach in evaluating statement 2.
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27 Jul 2011, 10:46
A is enough
B - > Y is a multiple of X
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Is x multiple of y [#permalink]

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29 Sep 2011, 08:28
If x and y are integers greater than 1, is x is a multiple of y ?

(1) 3 y^2 + 7y = x
(2) x^2 - x is a multiple of y

Sorry If I have repeated the question in the forum, but I searched for it in the existing questiosn, but couldn't find it
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Re: GMATPrep DS: Is x a multiple of y [#permalink]

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01 Oct 2011, 01:59
themagiccarpet wrote:
If x and y are integers greater than 1, is x a multiple of y?

(1) 3y^2 + 7y = x
(2) x^2 - x is a multiple of y

(a) x = y(3y+7) => x =ky (for a given y)
Sufficient

(b) x(x-1) = ky
if k =1, then x(x-1) = y, hence not x is not a multiple of y.
if k =(x-1), then x = y, hence not x is a multiple of y
Not sufficient

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Re: GMATPrep DS: Is x a multiple of y   [#permalink] 01 Oct 2011, 01:59

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