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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8235
GMAT 1: 760 Q51 V42 GPA: 3.82

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Difficulty:

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Question Stats: 75% (01:01) correct 25% (01:43) wrong based on 4 sessions

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If $$x$$ and $$y$$ are integers, is $$4x^2-y^2$$ an odd number?

1) $$x$$ is an odd number

2) $$y$$ is an odd number

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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8235
GMAT 1: 760 Q51 V42 GPA: 3.82

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Official Solution:

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.

Modifying the question:

In order for $$4x^2 - y^2$$ to be odd, $$y^2$$ must be odd since $$4x^2$$ is always even. This is equivalent to $$y$$ being odd. So, the question asks if y is odd.

Condition 1)

If y is an odd number, then both $$2x + y$$ and $$2x - y$$ are odd numbers and $$(2x+y)(2x-y)$$ is an odd number.

If y is an even number, both $$2x + y$$ and $$2x - y$$ are even numbers and $$(2x+y)(2x-y)$$ is an even number.

Since the question does not have a unique answer, condition 1) is not sufficient.

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Intern  B
Joined: 20 Apr 2019
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Suppose if x = 0 ? Then just by stating y is odd will not fetch anything meaningful.
Hence x is odd is required, just to make sure x is not 0. Re: M60-23   [#permalink] 18 May 2019, 06:33
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# M60-23

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