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Is a^3 > a^2 ? (1) 1/a > a (2) a^5 > a^3

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vaibhav1221
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Is a^3 > a^2 ? (1) 1/a > a (2) a^5 > a^3 [#permalink] New post  09 Aug 2018, 06:25
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Is \(a^3>a^2\)?


(1) \(\frac{1}{a} > a\)

(2) \(a^5>a^3\)
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Re: Is a^3 > a^2 ? (1) 1/a > a (2) a^5 > a^3 [#permalink] New post  09 Aug 2018, 07:22
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vaibhav1221 wrote:
Is \(a^3>a^2\)?

1. \(\frac{1}{a} > a\)

2. \(a^5>a^3\)


Re-phrasing question stem:-
\(a^3>a^2\)
Or, \(a^3-a^2>a^2-a^2\)
Or, \(a^2(a-1)>0\)
Or, \(a^2(a+1)(a-1)>0\)
Or, \(a>1\)

Re-phrased question stem:- Is a>1 ?

St1:- \(\frac{1}{a} > a\)
Or, \(\frac{1}{a}-a>a-a\)
Or, \(\frac{1-a^2}{a}>0\)
Or, \(\frac{-(a-1)(a+1)}{a}>0\)
Or, \(a<-1\) or, \(0<a<1\) (Answer to question stem is No)

Sufficient.

St2:- \(a^5>a^3\)
Or, \(a^5-a^3>a^3-a^3\)
Or, \(a^3(a^2-1)>0\)
Or, \(a^3(a-1)(a+1)>0\)
Or, \(-1<a<0\) or,\(a>1\)
Insufficient.

Ans. (A)
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Re: Is a^3 > a^2 ? (1) 1/a > a (2) a^5 > a^3 [#permalink] New post  05 Nov 2019, 00:27
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PKN how did you arrive Or, a2(a+1)(a−1)>0
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Is a^3 > a^2 ? (1) 1/a > a (2) a^5 > a^3 [#permalink] New post  03 May 2023, 05:10
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vaibhav1221 wrote:
Is \(a^3>a^2\)?


(1) \(\frac{1}{a} > a\)

(2) \(a^5>a^3\)


Each statement indicates that \(a\) is NONZERO, with the result that \(a^4\) is POSITIVE.

In S1, if we multiply both sides by \(a^4\), we get:
\(a^4 * \frac{1}{a} > a * a^4\)
\(a^3 > a^5\)

The resulting inequality contradicts S2, which states that \(a^5 > a^3\).
Implication:
This problem is invalid.
On the GMAT, the two statements cannot contradict each other.
What is the source of this problem?
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Is a^3 > a^2 ? (1) 1/a > a (2) a^5 > a^3 [#permalink]
03 May 2023, 05:10
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