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14 Nov 2017, 07:46
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
42% (01:41) correct
58%
(01:13)
wrong
based on 62
sessions
History
Date
Time
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Not Attempted Yet
If \(x>y\) and \(y\) is a positive integer, is \(y\) even?
(1) \(xy\) is odd.
(2) \(x=y+2\)
self made
(1) \(xy\) is odd.
(2) \(x=y+2\)
self made
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
14 Nov 2017, 08:34
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We are not given whether x is an integer or not. But we know that y is a positive integer.
Statement 1: xy is odd. Now, if x is an integer, then y cannot be even, it has to be odd. Because product of two integers is odd ONLY if both are odd.
But if x is not an integer, then we cannot say. Eg - if x is 2.5 and y is 2 then xy = 2.5*2 = 5 (odd). Here y is even still xy is odd.
So Insufficient.
Statement 2: x = y+2. This tells us that x is also an integer, and also either both x/y are odd, or both x/y are even. Insufficient.
Combining the two, we know that both x/y are integers and the product is odd. So BOTH x/y have to be odd. Thus y cannot be even. Sufficient.
Hence C answer
Statement 1: xy is odd. Now, if x is an integer, then y cannot be even, it has to be odd. Because product of two integers is odd ONLY if both are odd.
But if x is not an integer, then we cannot say. Eg - if x is 2.5 and y is 2 then xy = 2.5*2 = 5 (odd). Here y is even still xy is odd.
So Insufficient.
Statement 2: x = y+2. This tells us that x is also an integer, and also either both x/y are odd, or both x/y are even. Insufficient.
Combining the two, we know that both x/y are integers and the product is odd. So BOTH x/y have to be odd. Thus y cannot be even. Sufficient.
Hence C answer
14 Nov 2017, 08:37
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chetan2u
y = even ?
1) xy = od
x = 3, y = 1 => xy = odd NO, y is odd
x = \(\frac{5}{2}\), y = 2 => xy = odd YES, but y is even
2 different answers. Insufficient.
2) x = y + 2
Insufficient. Y could be odd or even
1+2)
xy = odd
x = y + 2 => x is also a positive integer
=> y has to be odd.
Sufficient. C is the answer.
