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

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Manager
Joined: 19 Nov 2017
Posts: 183
Location: India
Schools: ISB
GMAT 1: 670 Q49 V32
GPA: 4
Is a^3 > a^2 ? (1) 1/a > a (2) a^5 > a^3  [#permalink]

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09 Aug 2018, 06:25
2
00:00

Difficulty:

55% (hard)

Question Stats:

57% (01:45) correct 43% (01:51) wrong based on 30 sessions

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Is $$a^3>a^2$$?

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

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

_________________
Regards,

Vaibhav

Sky is the limit. 800 is the limit.

~GMAC
VP
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1028
WE: Supply Chain Management (Energy and Utilities)
Re: Is a^3 > a^2 ? (1) 1/a > a (2) a^5 > a^3  [#permalink]

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09 Aug 2018, 07:22
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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Regards,

PKN

Rise above the storm, you will find the sunshine
Re: Is a^3 > a^2 ? (1) 1/a > a (2) a^5 > a^3   [#permalink] 09 Aug 2018, 07:22
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# Is a^3 > a^2 ? (1) 1/a > a (2) a^5 > a^3

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