GeminiHeat wrote:
If \(G^2 < G\), which of the following could be G?
(A) 1
(B) 23/7
(C) 7/23
(D) −4
(E) -1
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
Answer: C
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.
Answer: C