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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42 GPA: 3.82
If x>y, is x^2>xy?  [#permalink]

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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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Retired Moderator P
Joined: 22 Aug 2013
Posts: 1428
Location: India
Re: If x>y, is x^2>xy?  [#permalink]

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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.

Manager  S
Joined: 22 May 2017
Posts: 118
Re: If x>y, is x^2>xy?  [#permalink]

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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
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Retired Moderator D
Joined: 25 Feb 2013
Posts: 1178
Location: India
GPA: 3.82
If x>y, is x^2>xy?  [#permalink]

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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  B
Joined: 22 Nov 2017
Posts: 25
Location: United States
Concentration: Technology, Healthcare
Re: If x>y, is x^2>xy?  [#permalink]

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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??

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Intern  B
Joined: 22 Nov 2017
Posts: 25
Location: United States
Concentration: Technology, Healthcare
Re: If x>y, is x^2>xy?  [#permalink]

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I stand corrected. Fraction will also satisfy the conditon.

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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If x>y, is x^2>xy?  [#permalink]

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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:
$$x^2>xy$$
$$⇔ x^2-xy > 0$$
$$⇔ x(x-y) > 0$$
$$⇔ x > 0$$ 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.
_________________ Re: If x>y, is x^2>xy?   [#permalink] 19 Jan 2018, 01:16
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