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# Given that ab< 0 and a > b, which of the following must be true?

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Manager
Joined: 12 Jun 2016
Posts: 224

Kudos [?]: 48 [0], given: 152

Location: India
WE: Sales (Telecommunications)
Given that ab< 0 and a > b, which of the following must be true? [#permalink]

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18 Aug 2017, 23:20
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15% (low)

Question Stats:

73% (00:44) correct 27% (00:39) wrong based on 62 sessions

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Given that $$ab< 0$$ and $$a > b$$, which of the following must be true?

I. $$a>0$$

II. $$b>0$$

III. $$\frac{1}{a} > \frac{1}{b}$$

A. I only
B. II Only
C. I and III Only
D. II and III Only
E. I, II and III
[Reveal] Spoiler: OA

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Kudos [?]: 48 [0], given: 152

Math Expert
Joined: 02 Sep 2009
Posts: 43306

Kudos [?]: 139263 [1], given: 12781

Given that ab< 0 and a > b, which of the following must be true? [#permalink]

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19 Aug 2017, 02:36
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susheelh wrote:
Given that $$ab< 0$$ and $$a > b$$, which of the following must be true?

I. $$a>0$$

II. $$b>0$$

III. $$\frac{1}{a} > \frac{1}{b}$$

A. I only
B. II Only
C. I and III Only
D. II and III Only
E. I, II and III

$$ab< 0$$ means that a and b have different signs. Since also given that a > b, then a > 0 > b (a and b have different signs).

So, I is true and II is not.

Next, 1/a = 1/(positive) = (positive) and 1/b = 1/(negative) = (negative), thus 1/a > 1/b. III is true too.

Hope it's clear.
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Kudos [?]: 139263 [1], given: 12781

Given that ab< 0 and a > b, which of the following must be true?   [#permalink] 19 Aug 2017, 02:36
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