If x/y is an integer, which of the following must also be an integer?

Question

I. xy
II. y/x
III. x

A. I alone
B. II alone
C. III alone
D. I and III
E. None of the above

sowragu · Answer

Lets take X = 4/3 and Y = 2/3

Then X/Y = 2 which is an integer.

But XY = 4/3 * 2/3 = 8/9 --> Not an integer.
Y/X = 2/3 divided by 4/3 = 2/4 = 1/2 Not an integer.
X alone is 4/3. Not an integer.

Hence E. None of the above.

kzivrev · Answer

Since it is not stated that X or Y or both are integers, that implies that X and Y can be any number, fractions as well, so all posabilities are open, hence answer should be NONE of the ABOVE

TeamGMATIFY · Answer

Given : x/y is an integer.
This means x is a multiple of y
 We do not know if they are integers or not.

Assume x = 1/2 and y = 1/4
Therefore x/y = 2

I. xy = 1/2*1/4 = 1/8 Not an integer
II. y/x = (1/4)/(1/2) = 1/2 Not an integer
III. x = 1/2 Not an integer.

Therefore none of the statements are always true.
Option E

mejia401 · Answer

IMO E.

None of the above. Take, for example:
 x = \frac{1}{2} 
 y = \frac{1}{4}

\frac{x}{y}  is an integer but none else is. The questions asks for which ones MUST be an integer and none of them are.

amanvermagmat · Answer

This question can best be tested by taking 'decimal' values of x and y both, which should yield an integer for x/y. That is how most of the people have done, and I did the same way.

I took x = 4.5 and y = 1.5 so that x/y = 4.5/1.5 = 3, which is an integer. In this case,

xy = 4.5 * 1.5, NOT an integer
y/x = 1.5/4.5, NOT an integer 
x = 4.5, NOT an integer

None of the three have to be necessarily be an integer, though they might be an integer (eg, if we take x=2, y=2 and then all three statements would give an integer value).

Hence  E answer

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If x/y is an integer, which of the following must also be an integer?

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If x/y is an integer, which of the following must also be an integer?

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