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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## If x and y are integers, is 4x^2-y^2 an odd number? tagged by: Max@Math Revolution ##### This topic has 2 expert replies and 0 member replies ### GMAT/MBA Expert ## If x and y are integers, is 4x^2-y^2 an odd number? [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 _________________ Math Revolution 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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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.

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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 Email to : info@mathrevolution.com ### GMAT/MBA Expert GMAT Instructor Joined 09 Apr 2015 Posted: 1465 messages Followed by: 19 members Upvotes: 39 Max@Math Revolution 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. Answer: B • FREE GMAT Exam Know how you'd score today for$0

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