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# If G^2 < G, which of the following could be G?

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Intern
Status: Aiming for 750+
Joined: 16 Oct 2013
Posts: 21
GMAT Date: 05-05-2014
If G^2 < G, which of the following could be G?  [#permalink]

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21 Jan 2014, 23:31
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5% (low)

Question Stats:

89% (00:38) correct 11% (01:09) wrong based on 146 sessions

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If G^2 < G, which of the following could be G?

(A) 1
(B) 23/7
(C) 7/23
(D) -4
(E) -2

I do not understand this basic and I need clarification on this question...

G raised to the power of 2 < G
=> G raised to the power of 2 -G < 0
=> G(G-1) < 0
=> Either G < 0 OR G-1 < 0
=> G < 0 or G < 1
=> G must be less than 0.

So, shouldn't the negative numbers be the possible values of G?

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Re: If G2 < G, which of the following could be G?  [#permalink]

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22 Jan 2014, 00:00
1
flower07 wrote:
(A) 1
(B) 23/7
(C) 7/23
(D) -4
(e) -2

I do not understand this basic and I need clarification on this question...

G raised to the power of 2 < G
=> G raised to the power of 2 -G < 0
=> G(G-1) < 0
=> Either G < 0 OR G-1 < 0
=> G < 0 or G < 1
=> G must be less than 0.

So, shouldn't the negative numbers be the possible values of G?

For your question why negative numbers cannot be a value of G.

we have the inequality as $$G^2$$<G.

When simplified we get G<0 or G<1.

G can never be less than zero, since $$G^2$$ is less than G.

If G is negative, for example G= -2 then $$G^2$$ becomes 4 which contradicts the statement $$G^2$$<G.

So choose the value which is less than 1 and by POE we get $$7/23$$

Hope it helps

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Joined: 02 Sep 2009
Posts: 58311
Re: If G^2 < G, which of the following could be G?  [#permalink]

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23 Jan 2014, 03:45
1
flower07 wrote:
If G^2 < G, which of the following could be G?

(A) 1
(B) 23/7
(C) 7/23
(D) -4
(E) -2

I do not understand this basic and I need clarification on this question...

G raised to the power of 2 < G
=> G raised to the power of 2 -G < 0
=> G(G-1) < 0
=> Either G < 0 OR G-1 < 0
=> G < 0 or G < 1
=> G must be less than 0.

So, shouldn't the negative numbers be the possible values of G?

One can solve this question algebraically (check the links at the end of the post) or simply go through the options.

First of all notice that G cannot possibly be negative, because if G is negative then $$G^2=positive$$ and in this case $$(G^2=positive)>(G=negative)$$, which contradicts the given condition that $$G^2 < G$$. Discard D and E.

Clearly, G cannot be 1 either: in this case $$G^2 = G$$. Discard A.

The same way, G cannot be greater than 1: in this case $$G^2 > G$$. Discard B.

Only option C remains: if $$0<G<1$$, then $$G^2 < G$$. For example, $$(\frac{1}{2})^2<\frac{1}{2}$$.

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Re: If G^2 < G, which of the following could be G?  [#permalink]

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02 Mar 2018, 10:38
flower07 wrote:
If G^2 < G, which of the following could be G?

(A) 1
(B) 23/7
(C) 7/23
(D) -4
(E) -2

In order for G^2 to be less than G, G must be a value between 0 and 1. Thus, G could be 7/23.

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Re: If G^2 < G, which of the following could be G?   [#permalink] 02 Mar 2018, 10:38
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