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

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VP
Joined: 23 Feb 2015
Posts: 1353
If a > 0, is a > 1? (1) a*b > a + b (2) a/b > b/a  [#permalink]

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17 Mar 2019, 08:43
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Difficulty:

55% (hard)

Question Stats:

53% (02:22) correct 47% (02:14) wrong based on 18 sessions

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If $$a>0$$, is $$a>1$$?

(1) $$a*b>a+b$$

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

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Re: If a > 0, is a > 1? (1) a*b > a + b (2) a/b > b/a  [#permalink]

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17 Mar 2019, 12:20
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).
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Re: If a > 0, is a > 1? (1) a*b > a + b (2) a/b > b/a   [#permalink] 17 Mar 2019, 12:20
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# If a > 0, is a > 1? (1) a*b > a + b (2) a/b > b/a

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