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If x is an integer, is x/y an integer?

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DeeptiM
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If x is an integer, is x/y an integer? [#permalink] New post  14 Aug 2011, 13:15
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If x is an integer, is x/y an integer?

(1) 2x/y is an integer
(2) y is an odd integer.
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timeishere
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Re: If x is an integer, is x/y an integer? [#permalink] New post  14 Aug 2011, 13:19
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DeeptiM wrote:
If x is an integer, is x/y an integer?
(1) 2x/y is an integer
(2) y is an odd integer.

Can someone help me explain part C of the question??


Answer is C.
Taking only 1. Not sufficient, as x/y can be 1/2
Taking only 2. Not sufficient, we dont know anything about x

Taking both - 2x/y is integer when y is odd integer.
Y can not divide 2 (as odd cannot divide even)
Hence, y must divide x.
Therefore x/y is integer.
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DeeptiM
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Re: If x is an integer, is x/y an integer? [#permalink] New post  14 Aug 2011, 13:36
I have the same answer explanation but somehow part C didnt make sense to me..
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timeishere
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Re: If x is an integer, is x/y an integer? [#permalink] New post  14 Aug 2011, 14:06
DeeptiM wrote:
I have the same answer explanation but somehow part C didnt make sense to me..


Given is 2 * (X/Y) is integer

In case, X/Y is not integer but still the above fact is true=> Only possible when Y=2 => But this violated Statement 2.

If Y = Even (i.e 2) Then the constant 2 already extra available, can cancel the 3 in denominator. and X may or may not be a multiple of 2. Thus, we cannot say whether X/Y is integer or not.

When Y is Odd. Take Y=3.
Now, 2*(X/3) Can be an integer when X is a multiple of 3, which will cancel the 3 in denominator.
or we can write X= aY, where a is a constant integer.

Thus X/Y is an integer.

Hope clear.
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Re: If x is an integer, is x/y an integer? [#permalink] New post  27 Jul 2015, 01:06
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DeeptiM wrote:
If x is an integer, is x/y an integer?
(1) 2x/y is an integer
(2) y is an odd integer.

Can someone help me explain part C of the question??


Question : is x/y an integer?

Statement 1: 2x/y is an integer

Case-1: x = 3 and y = 2 and 2x/y is an integer but x/y is NOT an Integer
Case-2: x = 4 and y = 2 and 2x/y is an integer and x/y is an Integer too.
NOT SUFFICIENT

Statement 2: y is an odd integer

Case-1: x = 4 and y = 3 and but x/y is NOT an Integer
Case-2: x = 3 and y = 3 and and x/y is an Integer.
NOT SUFFICIENT

Combining the two statements:
if y is odd and 2x/y is an integer then y can't be influenced by the factor 2 in Numerator of 2x/y and hence
for 2x/y to be an Integer, x/y must be an Integer as well.
SUFFICIENT

Answer: option C
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If x is an integer, is x/y an integer? [#permalink] New post  04 Nov 2019, 00:25
We need to know that \(2*Z=Z\) whereby \(Z\) stands for integer.

If we combine both statements we get

\(\frac{2*Z_1}{Z_2}=Z_3\) and since \(Z_2=odd\) the 2 cannot cancel it out, implying that \(\frac{Z_1}{Z_2}=Z_4\) as otherwise the equation would not hold.
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Re: If x is an integer, is x/y an integer? [#permalink] New post  20 Dec 2022, 08:00
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Re: If x is an integer, is x/y an integer? [#permalink]
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