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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6985
GMAT 1: 760 Q51 V42
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If x and y are integers, is 4x^2-y^2 an odd number?  [#permalink]

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Updated on: 09 Feb 2018, 22:00
00:00

Difficulty:

25% (medium)

Question Stats:

76% (00:53) correct 24% (01:11) wrong based on 78 sessions

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[GMAT math practice question]

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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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Originally posted by MathRevolution on 06 Feb 2018, 23:46. Last edited by amanvermagmat on 09 Feb 2018, 22:00, edited 2 times in total. changed y2 to y^2 DS Forum Moderator Joined: 21 Aug 2013 Posts: 1431 Location: India Re: If x and y are integers, is 4x^2-y^2 an odd number? [#permalink] ### Show Tags 07 Feb 2018, 01:36 MathRevolution wrote: [GMAT math practice question] If $$x$$ and $$y$$ are integers, is $$4x^2-y2$$ an odd number? 1) $$x$$ is an odd number 2) $$y$$ is an odd number I believe it should read as '4x^2 - y^2' Since x,y are integers:- 4x^2 is always going to be even, so whether 4x^2 - y^2 will be odd or not, depends on whether y is odd or not. (1) x is an odd number, but nothing about y. Not sufficient. (2) y is odd, so 4x^2 - y^2 = even - odd = odd. So sufficient. Hence B answer Intern Joined: 23 Oct 2017 Posts: 5 Concentration: International Business, General Management Re: If x and y are integers, is 4x^2-y^2 an odd number? [#permalink] ### Show Tags 07 Feb 2018, 01:58 If x and y are integers, is $$4x^2-y2 an odd number?$$ 4x2 would be even whether x is odd or even. The answer depends on the value of y alone. If y is odd, y2 is odd. therefore 4x2-y2 = even-odd = odd (sufficient). So the correct choice is B Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6985 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If x and y are integers, is 4x^2-y^2 an odd number? [#permalink] ### Show Tags 09 Feb 2018, 00:40 => 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. Thus, the answer is B. 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. Therefore, the answer is B. Answer: B _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Re: If x and y are integers, is 4x^2-y^2 an odd number?  [#permalink]

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12 Feb 2018, 16:13
MathRevolution wrote:
[GMAT math practice question]

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

Let’s recall some facts about odds and evens: (1) Even x even = even and even x odd = even. Thus, 4x^2 will always be an even number. (2) Odd x odd = odd. So if y is odd, then y^2 will be odd.

Thus, in order for 4x^2 - y^2 to be odd, y must be odd.

Statement One Alone:

x is an odd number

Since we know nothing regarding y, statement one alone is not sufficient to answer the question.

Statement Two Alone:

y is an odd number

Since y is odd, 4x^2 - y^2 must be odd since even - odd = odd. Statement two alone is sufficient to answer the question.

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Re: If x and y are integers, is 4x^2-y^2 an odd number?   [#permalink] 12 Feb 2018, 16:13
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