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

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

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New post 21 Jan 2014, 23:31
1
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A
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C
D
E

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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?

What I am missing, please?
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Re: If G2 < G, which of the following could be G?  [#permalink]

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New post 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?

What I am missing, please?


Hi, the Answer is C.

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 :)

Also Please read the rules for posting before posting any question
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Re: If G^2 < G, which of the following could be G?  [#permalink]

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New post 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?

What I am missing, please?


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, \((\frac{1}{2})^2<\frac{1}{2}\).

Answer: C.


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

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New post 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.

Answer: C
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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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