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

Question

(1) 2x/y is an integer
(2) y is an odd integer.

timeishere · Answer

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.

DeeptiM · Answer

I have the same answer explanation but somehow part C didnt make sense to me..

timeishere · Answer

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.

GMATinsight · Answer

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

SchruteDwight · Answer

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.

bumpbot · Answer

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

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