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If G^2 < G, which of the following could be G? : Problem Solving (PS)
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# If G^2 < G, which of the following could be G?

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

APPROACH #1: Properties of exponents
case i: If x > 1, then 0 < x < x²
case ii: If 0 < x < 1, then 0 < x² < x
case iii: If -1 < x < 0, then x < 0 < x²
case iv: If x < -1, then x < 0 < x²

Since G² < G, then we're dealing with case ii, which means 0 < x < 1

APPROACH #2: Process of elimination
(A) If G = 1, then G² = 1. These values don't satisfy the condition that G² < G. Eliminate A.
(B) If G = 23/7, then G² = 23²/7². These values don't satisfy the condition that G² < G. Eliminate B.
(C) If G = 7/23, then G² = 7²/23². These values DO satisfy the condition that G² < G
(D) If G = -4, then G² = 16. These values don't satisfy the condition that G² < G. Eliminate D.
(E) If G = -1, then G² = 1. These values don't satisfy the condition that G² < G. Eliminate E.
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Re: If G^2 < G, which of the following could be G? [#permalink]
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]
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Given that $$G^2$$ < G and we need to find a possible value of G from the answer choice

$$G^2$$ < G
=> $$G^2$$-G<0
=> G (G-1)<0
Product of two values < 0 => these two values will have OPPOSITE Signs

Now this will give us two cases

Case 1

G < 0 and G-1 > 0
=> G < 0 and G > 1
Intersection will give us NO SOLUTION in this case

Case 2

G > 0 and G-1 < 0
=> G > 0 and G < 1
=> 0 < G < 1

Only possible answer in this range is C

Hope it helps!

Watch the following video to learn the Basics of Inequalities

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