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

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Math Expert
Joined: 02 Sep 2009
Posts: 60463
If x/y is an integer, which of the following must also be an integer?  [#permalink]

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28 Feb 2016, 09:24
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66% (01:04) correct 34% (00:56) wrong based on 197 sessions

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

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

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Manager
Joined: 25 Dec 2012
Posts: 116
Re: If x/y is an integer, which of the following must also be an integer?  [#permalink]

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28 Feb 2016, 09:41
1
Bunuel wrote:
If x/y is an integer, which of the following must also be an integer?

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

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.
Intern
Joined: 06 Jun 2014
Posts: 41
Re: If x/y is an integer, which of the following must also be an integer?  [#permalink]

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29 Feb 2016, 14:18
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
Senior Manager
Joined: 20 Aug 2015
Posts: 382
Location: India
GMAT 1: 760 Q50 V44
Re: If x/y is an integer, which of the following must also be an integer?  [#permalink]

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03 Mar 2016, 03:05
Bunuel wrote:
If x/y is an integer, which of the following must also be an integer?

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

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
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Location: United States
WE: Corporate Finance (Manufacturing)
Re: If x/y is an integer, which of the following must also be an integer?  [#permalink]

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03 Mar 2016, 18:42
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.
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Joined: 22 Aug 2013
Posts: 1403
Location: India
Re: If x/y is an integer, which of the following must also be an integer?  [#permalink]

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21 Jun 2017, 21:26
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).

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Re: If x/y is an integer, which of the following must also be an integer?  [#permalink]

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24 Nov 2019, 03:28
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Re: If x/y is an integer, which of the following must also be an integer?   [#permalink] 24 Nov 2019, 03:28
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