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New GMATprep 2.1 Qn - Inequality - Can some experts help

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New GMATprep 2.1 Qn - Inequality - Can some experts help

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: — Data Sufficiency |
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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]

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by Anurag@Gurome » Mon May 28, 2012 7:44 am
kaps786 wrote:Is x > y?

1. x/4 = y²
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.

Image

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.
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