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# If x>y, is x^2>xy?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42
GPA: 3.82

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17 Jan 2018, 01:04
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Difficulty:

55% (hard)

Question Stats:

56% (01:33) correct 44% (01:16) wrong based on 78 sessions

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[GMAT math practice question]

If $$x>y$$, is $$x^2>xy$$?

$$1) x>0$$
$$2) y>0$$

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Retired Moderator Joined: 22 Aug 2013 Posts: 1428 Location: India Re: If x>y, is x^2>xy? [#permalink] ### Show Tags 17 Jan 2018, 10:58 1 MathRevolution wrote: [GMAT math practice question] If $$x>y$$, is $$x^2>xy$$? $$1) x>0$$ $$2) y>0$$ x^2 > xy can also be written as: x^2 - xy > 0 OR x (x-y) > 0. Since we are already given that x > y, this means x-y > 0. So x also must be positive in order for x(x-y) to be greater than 0. So, in summary, if x > y, then x^2 will be > xy if x > 0, else not. (1) x > 0 Given directly. Sufficient. (2) y > 0 So y is positive, and we are given that x > y, so x also must be positive. Sufficient. Hence D answer Manager Joined: 22 May 2017 Posts: 118 Re: If x>y, is x^2>xy? [#permalink] ### Show Tags 17 Jan 2018, 11:01 i.) if x > 0 x is +ve , y can be 0/-ve /+ve eg 1) 1> 0 1^2 > 1*0 1> 0 eg 2) 1>-1 1^2 > 1*-1 1>-1 any value y which is less than x in this case satisfies the 2.) y > 0 in this case both x and y are +ve so this case also always satisfies hence D _________________ Kudos please if explanation helped ------------------------------------------------------------------------------------------------- Don't stop when you are tired , stop when you are DONE . Retired Moderator Joined: 25 Feb 2013 Posts: 1178 Location: India GPA: 3.82 If x>y, is x^2>xy? [#permalink] ### Show Tags 17 Jan 2018, 11:02 MathRevolution wrote: [GMAT math practice question] If $$x>y$$, is $$x^2>xy$$? $$1) x>0$$ $$2) y>0$$ Simplify the question stem $$x^2>xy=>x^2-xy>0$$ $$=>x(x-y)>0=>$$ $$x>0$$ or $$x-y>0$$ Given $$x>y$$ or $$x-y>0$$, so the question is asking Is $$x>0$$? Statement 1: Directly provides the answer. Sufficient Statement 2: as $$y>0$$ and $$x>y$$ so $$x>0$$. Sufficient Option D Intern Joined: 22 Nov 2017 Posts: 25 Location: United States Concentration: Technology, Healthcare Re: If x>y, is x^2>xy? [#permalink] ### Show Tags 17 Jan 2018, 11:14 X and Y can be fraction as well right. Say x is 1/5 and Y is 1/4 and so X>Y. But X^2 (1/25) is less than xy (1/20). So sinse type of x and y is not mentioned wont the answer be E?? Sent from my SAMSUNG-SM-J120A using GMAT Club Forum mobile app Intern Joined: 22 Nov 2017 Posts: 25 Location: United States Concentration: Technology, Healthcare Re: If x>y, is x^2>xy? [#permalink] ### Show Tags 17 Jan 2018, 11:16 I stand corrected. Fraction will also satisfy the conditon. Sent from my SAMSUNG-SM-J120A using GMAT Club Forum mobile app Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8017 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If x>y, is x^2>xy? [#permalink] ### Show Tags 19 Jan 2018, 01:16 => 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: $$x^2>xy$$ $$⇔ x^2-xy > 0$$ $$⇔ x(x-y) > 0$$ $$⇔ x > 0$$ since $$x > y$$ (which implies that $$x – y > 0$$). So, the question is equivalent to asking ‘is $$x > 0$$?’. Since condition 1) is same as the modified question, it is sufficient. Condition 2): Since x > y, condition 2) ($$y > 0$$) implies that $$x > 0$$. Condition 2) is also sufficient. Therefore, the answer is D. Note: The VA approach tells us that the answer is most likely to be D, since this is a CMT(Common Mistake Type) 4B question. Condition 1) is easy to check, but condition 2) is more difficult to work with. If you can’t figure out condition 2), you should choose D as the answer. Answer: D _________________ 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$79 for 1 month Online Course"
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Re: If x>y, is x^2>xy?   [#permalink] 19 Jan 2018, 01:16
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