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Is x^3 > y^2?

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23 May 2010, 00:33
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Is x^3 > y^2?

(1) y = x^2
(2) x > x^2
[Reveal] Spoiler: OA

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23 May 2010, 02:38
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dimitri92 wrote:
Is X^3>y^2

1) y=x^2

2) x>x^2

Is $$x^3>y^2$$?

(1) $$y=x^2$$ --> question becomes: is $$x^3>x^4$$? Not sufficient. (For $$0<x<1$$ answer is YES but for other values of $$x$$ answer is NO)

(2) $$x>x^2$$. No info about $$y$$. Not sufficient. But form this statement: $$x^2-x<0$$ --> $$0<x<1$$.

(1)+(2) For any value of $$x$$ from the range $$0<x<1$$ (from 2) inequality $$x^3(1-x)>0$$ holds true. Sufficient.

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Re: Is x^3 > y^2? [#permalink]

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07 Jan 2015, 05:56
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Re: Is x^3 > y^2? [#permalink]

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07 Jan 2015, 12:10
Hi All,

This question can be solved by TESTing VALUES and using the Number Properties that are built-into this question to our advantage.

We're asked if X^3 > Y^2. This is a YES/NO question.

Fact 1: Y = X^2

IF....
X = 0
Y = 0
Is 0^3 > 0^2? The answer to the question is NO.

X = 1/2
Y = 1/4
Is (1/2)^3 > (1/4)^2? The answer to the question is YES.
Fact 1 is INSUFFICIENT

Fact 2: X > X^2

This tells us nothing about Y, so we can quickly deduce that it's insufficient.

However, this info provides us with some serious RESTRICTIONS about X...
X CANNOT be 0
X CANNOT be negative
X CANNOT be greater than or equal to 1
X CAN ONLY BE a POSITIVE FRACTION (that info will come in handy in just a moment).
Fact 2 is INSUFFICIENT.

Combined, we know...
Y = X^2
X is a POSITIVE FRACTION

Under these restrictions, we can rewrite the original question
Is X^3 > Y^2?
as...
Is X(X^2) > X^2?

Since X must be a positive fraction, X^3 will always be SMALLER than X^2, so the answer to the question is ALWAYS NO.
Combined, SUFFICIENT.

[Reveal] Spoiler:
C

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Re: Is x^3 > y^2?   [#permalink] 07 Jan 2015, 12:10
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