New GMATprep 2.1 Qn - Inequality - Can some experts help - The Beat The GMAT Forum

New GMATprep 2.1 Qn - Inequality - Can some experts help

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kaps786: Senior | Next Rank: 100 Posts; Posts: 52; Joined: Sat Aug 13, 2011 8:34 am; Thanked: 2 times

by kaps786 » Sun May 27, 2012 11:47 pm

This is from GMATprep latest version

Is x>y ?

1. x/4=y^2 (x divided by 4=y^2)

2. X>1

OA is C

Please explain your approach, and address any underlying concepts this question tests. Essentially how to think about conceptually addressing this problem

I tried algebra first and didnt seem to go anywhere, then I tried number plugging but had lost time by then.

Will appreaciate as many creative solutions as possible.

Thanks
Kapks

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Source: Beat The GMAT — Data Sufficiency | Sun May 27, 2012 11:47 pm

aneesh.kg: Master | Next Rank: 500 Posts; Posts: 385; Joined: Mon Apr 16, 2012 8:40 amFollowed by: 29 members; Location: Pune, India; Thanked: 186 times

by aneesh.kg » Mon May 28, 2012 12:07 am

kaps786 wrote:This is from GMATprep latest version

Is x>y ?

1. x/4=y^2 (x divided by 4=y^2)

2. X>1

OA is C

Statement(1):
x = 4(y)^2
Checking for values of x and y when x is NOT greater than y, or x =< y:
(Substituting x in terms of y. This is the KEY Step!)
4y^2 =< y
y*(4y - 1) =< 0
0 =< y =< 1/4
In terms of x:
4*(0)^2 =< x =< 4*(1/4)^2
0 =< x =< 1/4.
Conclusion: x =< y when y is between 0 and 1/4, x is between 0 and 1/4. x > y at all other other values of x and y.
INSUFFICIENT

Statement(2):
x > 1. No information on y.
INSUFFICIENT

Combining the two statements,
x =< y only when 0 =< x =< 1/4 (Based on Statement(1))
Since x > 1, x has to be greater than y.
The answer is YES!

[spoiler](C)[/spoiler] is correct.

P.S.:
Read this to learn how to to solve quadratic inequalities easily: The Critical Points Method https://www.beatthegmat.com/critical-poi ... tml#465861

Aneesh Bangia
GMAT Math Coach
[email protected]

GMATPad:
Facebook Page: https://www.facebook.com/GMATPad

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GMAT/MBA Expert

Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon May 28, 2012 7:44 am

kaps786 wrote:Is x > y?

1. x/4 = yÂ²
2. x > 1

If you have fundamental ideas about graphs of quadratic equations, this can be solved much more easily and in much less time. See the following diagram.

Clearly from the figure, for x < 0.25, y > x but for x > 0.25, x > y.

Hence, combining both statements we have, x > 1 ---> x > y

The correct answer is C.

Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

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