Statement 1:We know nothing on a or b yet, we cannot simplify this to a < b so cannot prove a < b. Some examples we can use here:
\(2^3 < 3^2\) => \(a < b\) . Yes.
\(5^2 < 2^5\) => \(a > b\). No.
Statement 2:This tells us a and b have the same sign. However, we cannot simplify this expression. Insufficient.
Combined:Positive a and b give a > b from (2). Negative a and b give a < b from (2). We just need to find a case for each scenario that satisfies (1) to say insufficient.
For the positive case, we can recycle \(5^2 < 2^5\). For the negative case, we can let \(b\) be a negative odd number and \(a\) be a negative even number.
\((-4)^{-3} < (-3)^{-4}\) for example will satisfy (1) and also give us a < b. Therefore combined it is still insufficient.
Ans: E
Bunuel wrote:
Is a < b?
(1) \(a^b < b^a\)
(2) \(\frac{a}{b} > 1\)
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