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# If x and y are integers and x/y is also an integer, is x an even numbe

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Math Expert
Joined: 02 Aug 2009
Posts: 7334
If x and y are integers and x/y is also an integer, is x an even numbe  [#permalink]

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11 Mar 2018, 06:52
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Difficulty:

65% (hard)

Question Stats:

53% (01:35) correct 47% (01:47) wrong based on 109 sessions

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If x and y are integers and $$\frac{x}{y}$$ is also an integer, is x an even number?

(1) $$\frac{x}{y}$$ is odd.
(2) $$\frac{y}{2}$$ is odd.

New question - chetan

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
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Re: If x and y are integers and x/y is also an integer, is x an even numbe  [#permalink]

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11 Mar 2018, 08:23
If x and y are integers and x/y is also an integer, is x an even number?

(1) x/y is odd. It is clearly insufficient. For example, we can have 6/2 giving answer odd, and x = even, Also we can have 9/3 is odd, while x is odd.
Not sufficient.

(2) y/2is odd. This clearly means y is even.
Also, it is given x/y is an integer. Hence x has to be an even integer. because odd/even will not be an integer.
Sufficient.

Takeaway: x/y is not an integer if x is odd and y is even.
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Re: If x and y are integers and x/y is also an integer, is x an even numbe  [#permalink]

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11 Mar 2018, 11:41
1
chetan2u wrote:
If x and y are integers and $$\frac{x}{y}$$ is also an integer, is x an even number?

(1) $$\frac{x}{y}$$ is odd.
(2) $$\frac{y}{2}$$ is odd.

New question - chetan

Some important properties - If the solution of the expression $$\frac{x}{y}$$ is an integer,

EVEN/EVEN = ODD or EVEN
EVEN/ODD = EVEN
ODD/ODD = ODD
ODD/EVEN = Cannot be an integer

Now coming back to the question

(1) $$\frac{x}{y}$$ is odd.
Here x and y both could be either even or odd (Insufficient)

(2) $$\frac{y}{2}$$ is odd.
This is only possible when y is even Since, y is even, x also has to be even
as we know that the solution is an integer (Sufficient - Option B)

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Joined: 31 May 2017
Posts: 318
Re: If x and y are integers and x/y is also an integer, is x an even numbe  [#permalink]

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11 Mar 2018, 12:38
Now coming back to the question

(1) x/y is odd.
Here x and y both could be either even or odd
- Not Sufficient

(2) Y/2 is odd.
This is possible only when Y is even. If Y is even , X has to be even. This option is sufficient.

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Joined: 18 Jun 2017
Posts: 48
Re: If x and y are integers and x/y is also an integer, is x an even numbe  [#permalink]

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26 Mar 2018, 08:04
According to method of discrete number listing.

1] x/y is odd --> x/y can be 1,3,5,7
So x=5y if y=1 then X is 5 and odd, also if y=2 then x=10 and even.
Hence not sufficient.

2] y/2 is odd --> y/2=1,3,5,7
So y can be 2,6,10,14 always even.
For X/Y to be integer taking Y as even. X must be even, Hence B.
Re: If x and y are integers and x/y is also an integer, is x an even numbe   [#permalink] 26 Mar 2018, 08:04
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