BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

GMAT ExAM INEQUALITY

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Tue Oct 06, 2015 6:21 am
rommysingh wrote:Is xy > x²y²?
(1) 14x² = 3
(2) y² = 1
xy > x²y² only if xy≠0, with the result that x²y² > 0 (since the square of a nonzero value must be positive).
Thus, we can safely divide each side by x²y², which must be a POSITIVE value:
(xy)/(x²y²) > (x²y²)/(x²y²)
1/xy > 1.

1/xy > 1 only if xy is a POSITIVE FRACTION between 0 and 1.
Question stem, rephrased:
Is xy a positive fraction between 0 and 1?

Statement 1: x² = 3/14, implying that x = ±√(3/14).
Statement 2: y² = 1, implying that y = ±1.

Both statements are satisfied if x=√(3/14) and y=1.
In this case, xy = √(3/14), which is a positive fraction between 0 and 1.
Both statements are satisfied if x=√(3/14) and y=-1.
In this case, xy = -√(3/14), which is NOT a positive fraction between 0 and 1.
Thus, the two statements combined are INSUFFICIENT.

The correct answer is E.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

by Max@Math Revolution » Thu Oct 08, 2015 3:46 am
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is xy > x^2y^2?
(1) 14x^2 = 3
(2) y^2 = 1

If we convert the original condition, we get (xy)^2-xy<0, xy(xy-1)<0 and ultimately we want to know whether 0<xy<1.
We have 2 variables, and hence we need 2 equations to match the number of variables; the conditions provide 2 equations, so the answer is likely to be (C).
Looking at the conditions together, x^2=3/14, x=-sqrt(3/14),sqrt(3/14) and y^2=1, y=-1,1, which means
The question is answered 'no' for xy=-sqrt(3/14) but 'yes' for xy=sqrt(3/14). No unique answer is given, and therefore the conditions are insufficient, making the answer (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.
Unlimited Access to over 120 free video lessons - try it yourself (https://www.mathrevolution.com/gmat/lesson)
See our Youtube demo (https://www.youtube.com/watch?v=R_Fki3_2vO8)
Top
Post new topic Post Reply
• Page 1 of 1