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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 ## Is x^2>xy? tagged by: Max@Math Revolution ##### This topic has 5 expert replies and 0 member replies ### GMAT/MBA Expert ## Is x^2>xy? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [Math Revolution GMAT math practice question] Is x^2>xy? 1) x>y 2) y>0 _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only Worldâ€™s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$99 for 3 month Online Course
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Max@Math Revolution wrote:
[Math Revolution GMAT math practice question]

Is x^2>xy?

1) x>y
2) y>0
$${x^2}\,\,\mathop > \limits^? \,\,\,xy\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,x\left( {x - y} \right)\,\,\mathop > \limits^? \,\,\,0$$
$$\left( 1 \right)\,\,x > y\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {1,0} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr \,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {0, - 1} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr} \right.$$
$$\left( 2 \right)\,\,y > 0\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {1,1} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr \,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {2,1} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.$$
$$\left( {1 + 2} \right)\,\,\,x > y > 0\,\,\,\,\, \Rightarrow \,\,\,\,\left\{ \matrix{ \,x > 0 \hfill \cr \,x - y > 0 \hfill \cr} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

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Max@Math Revolution wrote:
[Math Revolution GMAT math practice question]

Is x^2>xy?

1) x>y
2) y>0
xÂ² > xy is true only if x is NONZERO, in which case we can safely divide by xÂ², since the square of a nonzero value must be positive:
xÂ²/xÂ² > (xy)/xÂ²
1 > y/x
Question stem, rephrased:
Is y/x < 1?

Statement 1: x > y
If x=2 and y=1, then y/x =1/2. so the answer to the rephrased question stem is YES.
If x=-1 and y=-2, then y/x = 2, so the answer to the rephrased question stem is NO.
INSUFFICIENT.

Statement 2:
INSUFFICIENT.

Statements combined:
Since x > y > 0, x is POSITIVE, enabling us to safely simplify x > y by dividing both sides by x:
x/x > y/x
1 > y/x
y/x < 1
Thus, the answer to the rephrased question stem is YES.
SUFFICIENT.

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Last edited by GMATGuruNY on Tue Nov 06, 2018 2:52 am; edited 2 times in total

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GMATGuruNY wrote:
Max@Math Revolution wrote:
[Math Revolution GMAT math practice question]

Is x^2>xy?

1) x>y
2) y>0
Since xÂ² > xy implies that x is NONZERO, we can safely divide by xÂ², which must be equal to a POSITIVE VALUE:
xÂ²/xÂ² > (xy)/xÂ²
1 > y/x
Question stem, rephrased:
y/x < 1?

Statement 1: x > y
If x=2 and y=1, then y/x =1/2. so the answer to the rephrased question stem is YES.
If x=-1 and y=-2, then y/x = 2, so the answer to the rephrased question stem is NO.
INSUFFICIENT.

Statement 2:
INSUFFICIENT.

Statements combined:
Since x > y > 0, x is POSITIVE, enabling us to safely simplify x > y by dividing both sides by x:
x/x > y/x
1 > y/x
y/x < 1
Thus, the answer to the rephrased question stem is YES.
SUFFICIENT.

The reasoning that comes pre-statements (shown in red) is not correct.

In other words, the original question stem and the question stem rephrased (proposed) are not equivalent.

I explain: x CAN be zero (only in the original question stem) and, being so, the question asked is answered in the negative (for any real value of y that satisfies the corresponding statement).

More explicitly:

(1) (x,y) = (0,-1) is a possible particular case for which the answer to the question asked (in the original question stem) is NO.

(2) (x,y) = (0,1) is a possible particular case for which the answer to the question asked (in the original question stem) is NO.

Regards,
Fabio.

_________________
Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or https://GMATH.com.br (Portuguese version)
Course release PROMO : finish our test drive till 30/Nov with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount!

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fskilnik@GMATH wrote:
GMATGuruNY wrote:
Max@Math Revolution wrote:
[Math Revolution GMAT math practice question]

Is x^2>xy?

1) x>y
2) y>0
Since xÂ² > xy implies that x is NONZERO, we can safely divide by xÂ², which must be equal to a POSITIVE VALUE:
xÂ²/xÂ² > (xy)/xÂ²
1 > y/x
Question stem, rephrased:
y/x < 1?
The reasoning that comes pre-statements (shown in red) is not correct.

In other words, the original question stem and the question stem rephrased (proposed) are not equivalent.
For the purposes of a Y/N DS problem, the rephrase is the equivalent of the original question stem.
Original question stem: Is xÂ² > xy?
The answer will be YES if y/x is less than 1..
The answer will be NO if y/x is NOT less than 1.
Thus, the original question stem can be rephrased as follows:
Is y/x < 1?
If x=0, the answer is NO, since y/x is undefined and thus not less than 1.

_________________
Mitch Hunt
Private Tutor for the GMAT and GRE
GMATGuruNY@gmail.com

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.
Student Review #1
Student Review #2
Student Review #3

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### GMAT/MBA Expert

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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. We then recheck the question.
x^2>xy
=> x^2-xy > 0
=> x(x-y) > 0
=> x>0, x>y or x<0, x
Since we have 2 variables (x and y) and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
Since we have x > y and x > 0 from x > y > 0 which are a combined inequality of both conditions, both conditions together are sufficient.

Since this question is an inequality question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1) x > y
If x = 2, y = 1, then we have x^2>xy and the answer is â€˜yesâ€™.
If x = -1, y = -2, then we have x^2
Condition 2) y > 0
If x = 2, y = 1, then we have x^2>xy and the answer is â€˜yesâ€™.
If x = 1, y = 2, then we have x^2

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.

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