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

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Q50  V36
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Re: If x is an integer, is x/y an integer? [#permalink]
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]
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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

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If x is an integer, is x/y an integer? [#permalink]
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]
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Re: If x is an integer, is x/y an integer? [#permalink]
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