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Is x^3 > y^2?

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Is x^3 > y^2? [#permalink]

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New post 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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Re: X^3>y^2 [#permalink]

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New post 23 May 2010, 02:38
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Expert's post
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.

Answer: C.
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Re: Is x^3 > y^2? [#permalink]

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

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New post 07 Jan 2015, 12:10
Expert's post
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.

Final Answer:
[Reveal] Spoiler:
C


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