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11 Mar 2018, 07:52
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B
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Difficulty:
55%
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Question Stats:
50% (01:33) correct
50%
(01:46)
wrong
based on 134
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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
(1) \(\frac{x}{y}\) is odd.
(2) \(\frac{y}{2}\) is odd.
New question - chetan
11 Mar 2018, 09:23
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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.
(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.
11 Mar 2018, 12:41
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chetan2u
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)
