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# If x and y are positive integers and x is a multiple of y,

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Director
Joined: 03 Jul 2003
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If x and y are positive integers and x is a multiple of y, [#permalink]  13 Dec 2003, 20:54
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If x and y are positive integers and x is a multiple of y, is y = 2?
(1) y ≠ 1
(2) x + 2 is a multiple of y.
SVP
Joined: 30 Oct 2003
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Location: NewJersey USA
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I think the answer should be E.

A ) not sufficient
B ) x + 2 = m * y
from problem stem x = n * y
so n * y + 2 = m * y hence y(m-n) = 2
Only if m-n = 1 y = 2 otherwise y can take any value. So B is not sufficient.
Manager
Joined: 26 Dec 2003
Posts: 227
Location: India
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C? becoz from (1) we cant say anything and from (2) y can be 1 or 2 but by combining both statements we can say that y=2.
Intern
Joined: 13 Jan 2004
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G+ DS-4-22 [#permalink]  13 Jan 2004, 04:37
1) is not sufficient as Y could be many different int.

2) If X is a multiple of Y then X = kY

Then X+2 = kY + 2

KY is clearly divisible by Y, so for the sum kY + 2 to be divisible by Y, 2 must also be divisible by Y.

If 2 is div. by Y then Y = 1 or 2.

Still insufficient as there are two possible values for Y.

Taken together the two statements lead to only one possible value for Y, i.e. Y=1.

so (c)
SVP
Joined: 30 Oct 2003
Posts: 1797
Location: NewJersey USA
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Kudos [?]: 41 [0], given: 0

You are right The answer should be C
For example X = 20 and X =22 are mutiples of 2
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