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

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New post 11 Mar 2018, 07:52
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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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Re: If x and y are integers and x/y is also an integer, is x an even numbe [#permalink]

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New post 11 Mar 2018, 09:23
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.

Answer is B

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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New post 11 Mar 2018, 12:41
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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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Re: If x and y are integers and x/y is also an integer, is x an even numbe [#permalink]

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New post 11 Mar 2018, 13:38
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.

Answer: B
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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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New post 26 Mar 2018, 09:04
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, 09:04
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