New GMATprep 2.1 Qn - Inequality - Can some experts help

[kaps786]

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

[aneesh.kg]

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

[Anurag@Gurome]

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.



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.