If a 0, is a 1? (1) a*b a + b (2) a/b b/a

Question

If  a>0 , is  a>1 ?

(1)  a*b>a+b

(2)  \frac{a}{b}>\frac{b}{a}

IanStewart · Answer

If a = 1/10, and b = -10, then both statements are true, but a is not greater than 1. But if a = 3 and b = 2, then again both statements are true and a is greater than 1. So the answer is E.

If you knew b was positive (which we don't) then Statement 1 would be sufficient alone, since if a < 1, ab would be less than b, and therefore less than a+b if a > 0, so it would be impossible for Statement 1 to be true if a < 1 were true, meaning a > 1 (a cannot equal 1 either, for the same reason).

If a > 0, is a > 1? (1) a*b > a + b (2) a/b > b/a

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