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Intern  S
Joined: 07 May 2015
Posts: 42
Location: India
Schools: Darden '21
GPA: 4
Is g < g^2 < g^3, for all real values of g?  [#permalink]

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5 00:00

Difficulty:   65% (hard)

Question Stats: 48% (01:55) correct 52% (01:45) wrong based on 40 sessions

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Is $$g< g^2 < g^3$$, for all real values of $$g$$?

(1) $$g < g^3$$
(2) $$g^3 > g^2$$

Originally posted by reynaldreni on 28 Sep 2018, 07:37.
Last edited by Bunuel on 28 Sep 2018, 08:53, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert V
Joined: 02 Aug 2009
Posts: 8197
Re: Is g < g^2 < g^3, for all real values of g?  [#permalink]

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1
1
Is $$g< g^2 < g^3$$, for all real values of $$g$$?

(1) $$g < g^3$$..
$$g^3-g>0......g(g^2-1)>0$$
So two cases..
1) g<0, then g^2<1.....so -1<g<0...then g^2>g^3>g
2) g>0, then g^2>1....so g>1...then g^3>g^2>g
Insufficient

(2) $$g^3 > g^2$$
g^3-g^2>0...g^2(g-1)>0
g^2>0, so g>1..
So g^3>g^2>g
Sufficient

B
_________________
Math Expert V
Joined: 02 Aug 2009
Posts: 8197
Re: Is g < g^2 < g^3, for all real values of g?  [#permalink]

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reynaldreni wrote:
Is $$g< g^2 < g^3$$, for all real values of $$g$$?

(1) $$g < g^3$$
(2) $$g^3 > g^2$$

Another way..
1) g<g^3
This happens in two cases..
a) g is between 0 to -1
Let g=-1/2..
So (-1/2)^2 >(-1/2)^3>(-1/2)
b) g >1
Say g=2
2^3>2^2>2
Insufficient

2) g^3>g^2
So g is positive and >1
Take any value and Ans will be yes
Sufficient

B
_________________ Re: Is g < g^2 < g^3, for all real values of g?   [#permalink] 28 Sep 2018, 10:07
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# Is g < g^2 < g^3, for all real values of g?  