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Is x^2 > x^3 (1) x^3 > 0 (2) x ≠ 1

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Bunuel
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Is x^2 > x^3 (1) x^3 > 0 (2) x ≠ 1 [#permalink] New post   20 Jan 2021, 06:38
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Is \(x^2 > x^3\) ?

(1) \(x^3 > 0\)

(2) \(x\neq{1}\)
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E
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Nipungupta9081
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Is x^2 > x^3 (1) x^3 > 0 (2) x ≠ 1 [#permalink] New post   Updated on: 20 Jan 2021, 07:21
IMO E

(1) x^3 > 0

This tells us X is positive = X could be 0 or 1.

X^2 = X^3 ------- INSUFFICIENT

(2) x≠1

X could be 0 or -1. --------- INSUFFICIENT

Joining both Statements

X^3 > 0 and X ≠ 1

Still cant get a definite value ------ INSFUFFIENT

Joining 1 + 2

Still INSUFFICIENT

Originally posted by Nipungupta9081 on 20 Jan 2021, 06:48.
Last edited by Nipungupta9081 on 20 Jan 2021, 07:21, edited 1 time in total.
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Re: Is x^2 > x^3 (1) x^3 > 0 (2) x ≠ 1 [#permalink] New post   20 Jan 2021, 07:05
(1) \(x^3\) > 0
means that x is +ve.
If x is greater than 1 than we get no.
If x is less than 1 than we get yes; x=\(\frac{1}{2}\), \(x^2\)=\(\frac{1}{4}\) and \(x^3\)=\(\frac{1}{8}\); \(x^2\)>\(x^3\)

Insufficient.

(2) x≠1
Clearly insufficient as we do not know the polarity of x.

1+2
Statement 1 still stands
Insufficient.

Option E
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Re: Is x^2 > x^3 (1) x^3 > 0 (2) x ≠ 1 [#permalink] New post   30 Jan 2021, 00:32
Question stem asks if x^2>x^3
Let's simplify the expression

x^2 - x^3 >0
x^2(1-x)>0
For this expression to be greater than 0 we should have both the terms x^2 and 1-x positive or negative. As x^2 is always nonnegative so 1-x needs to be positive as well for the expression to be greater than 0
So 1-x>0
1>x
So basically we have to find if x<1

Statement 1:
x^3>0
This tells us that x>0
The answer will be yes for range 0<x<1 but will be no for x>1
Hence Insufficient
Statement 2
x≠1
This only tells us that x can be any value other than 1. Not sufficient

Combining 2 statements also does not give us a definite answer. The answer will be yes for range 0<x<1 but will be no for x>1

Hence the answer is E
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Is x^2 > x^3 (1) x^3 > 0 (2) x 1 [#permalink] New post   28 Apr 2023, 06:12
Bunuel KarishmaB JeffTargetTestPrep ScottTargetTestPrep avigutman

Could one of the experts validate my reasoning please?

Pushing the question stem got me the following:

Is x^2 > 0 or is x > 1?

"x^2 > 0" doesn't tell us much as x could be positive or negative so I focused on whether x > 1. Is this the right approach?

S1. x^3 > 0
So x is positive but could be greater or lesser than 1
Insufficient

S2. x is not equal to 1
Clearly insufficient

Combining S1 and S2:
Still insufficient as x could be any value other than 1

Therefore, E
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Re: Is x^2 > x^3 (1) x^3 > 0 (2) x 1 [#permalink] New post   28 Apr 2023, 07:58
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achloes wrote:
Bunuel KarishmaB JeffTargetTestPrep ScottTargetTestPrep avigutman

Could one of the experts validate my reasoning please?

Pushing the question stem got me the following:

Is x^2 > 0 or is x > 1?

"x^2 > 0" doesn't tell us much as x could be positive or negative so I focused on whether x > 1. Is this the right approach?

S1. x^3 > 0
So x is positive but could be greater or lesser than 1
Insufficient

S2. x is not equal to 1
Clearly insufficient

Combining S1 and S2:
Still insufficient as x could be any value other than 1

Therefore, E


Your rephrasing of the question is not accurate. "Is x^2 > x^3?" can be rephrased as: Is 1 > x and x ≠ 0?



I recall you providing links to study inequality theory. Without a solid foundation, there's a risk of repeatedly making the same mistakes. Here are those links once again:

9. Inequalities



For more check Ultimate GMAT Quantitative Megathread



Hope it helps.

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Re: Is x^2 > x^3 (1) x^3 > 0 (2) x 1 [#permalink]
28 Apr 2023, 07:58
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