• 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

Is x^2>xy?

This topic has 5 expert replies and 0 member replies

GMAT/MBA Expert

Is x^2>xy?

Post

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 World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Only $99 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

  • +1 Upvote Post
  • Quote
  • Flag
Post
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.

_________________
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!

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

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

Is x^2>xy?

1) x>y
2) y>0
x² > xy is true only if x is NONZERO, in which case we can safely divide by x², since the square of a nonzero value must be positive:
x²/x² > (xy)/x²
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:
No information about x.
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 correct answer is C.

_________________
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.
For more information, please email me at GMATGuruNY@gmail.com.
Student Review #1
Student Review #2
Student Review #3



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

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.
Post
GMATGuruNY wrote:
Max@Math Revolution wrote:
[Math Revolution GMAT math practice question]

Is x^2>xy?

1) x>y
2) y>0
Since x² > xy implies that x is NONZERO, we can safely divide by x², which must be equal to a POSITIVE VALUE:
x²/x² > (xy)/x²
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:
No information about x.
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 correct answer is C.
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!

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
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 x² > xy implies that x is NONZERO, we can safely divide by x², which must be equal to a POSITIVE VALUE:
x²/x² > (xy)/x²
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 x² > 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.
For more information, please email me at GMATGuruNY@gmail.com.
Student Review #1
Student Review #2
Student Review #3

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.

GMAT/MBA Expert

Legendary Member
Joined
24 Jul 2015
Posted:
1760 messages
Followed by:
28 members
Upvotes:
19
GMAT Score:
Most Active Expert
Post
=>

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 ‘yes’.
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 ‘yes’.
If x = 1, y = 2, then we have x^2

Therefore, C is the answer.
Answer: C

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.

_________________

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 $99 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

  • +1 Upvote Post
  • Quote
  • Flag
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep

Top First Responders*

1 fskilnik@GMATH 88 first replies
2 Brent@GMATPrepNow 49 first replies
3 Jay@ManhattanReview 43 first replies
4 GMATGuruNY 30 first replies
5 Rich.C@EMPOWERgma... 26 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description fskilnik@GMATH

GMATH Teacher

173 posts
2 image description Scott@TargetTestPrep

Target Test Prep

143 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

104 posts
4 image description Max@Math Revolution

Math Revolution

87 posts
5 image description GMATGuruNY

The Princeton Review Teacher

74 posts
See More Top Beat The GMAT Experts