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

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

by Max@Math Revolution » Tue Jan 16, 2018 11:57 pm
[GMAT math practice question] 1.17

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

1) $$x>0$$
2) $$y>0$$
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Source: — Data Sufficiency |
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by GMATGuruNY » Wed Jan 17, 2018 3:47 am
Max@Math Revolution wrote:[GMAT math practice question] 1.17

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

1) $$x>0$$
2) $$y>0$$
Statement 1:
Since x>0, we can safely multiply both sides of x>y by x:
x*x > x*y
x² > xy.
Thus, the answer to the question stem is YES.
SUFFICIENT.

Statement 2:
Since x>y and y>0, x>0.
Thus, Statement 2 implies the same information as Statement 1.
Since Statement 1 is sufficient, so is Statement 2.
SUFFICIENT.

The correct answer is D.
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by Max@Math Revolution » Fri Jan 19, 2018 12:09 am
=>
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
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