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If |ab| > ab, which of the following must be true?

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If |ab| > ab, which of the following must be true?  [#permalink]

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New post Updated on: 19 Jan 2017, 23:37
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If \(|ab| > ab\), which of the following must be true?

I. \(a < 0\)
II. \(b < 0\)
III. \(ab < 0\)

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

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Originally posted by hazelnut on 19 Jan 2017, 20:22.
Last edited by Bunuel on 19 Jan 2017, 23:37, edited 1 time in total.
Added the OA.
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Re: If |ab| > ab, which of the following must be true?  [#permalink]

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New post 19 Jan 2017, 21:17
C.

|ab|>ab implies that ab is -ve

So, either a is -ve or b is -ve but not both

if one of a and b is -ve then ab must be -ve.
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Re: If |ab| > ab, which of the following must be true?  [#permalink]

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New post 19 Jan 2017, 22:02
C.
ab<0 that means either a<0 or b<0

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Re: If |ab| > ab, which of the following must be true?  [#permalink]

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New post 03 Apr 2017, 11:07
Absolute value of an integer is always positive.
Thus we should consider the case when the integers can be negative as well.

Either of the two variables is negative because if both are then |ab|=ab.
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If |ab| > ab, which of the following must be true?  [#permalink]

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New post 03 Apr 2017, 13:14
Has to be C. A & B do not tell the sign of ab
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Re: If |ab| > ab, which of the following must be true?  [#permalink]

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New post 05 Aug 2018, 00:06
hazelnut wrote:
If \(|ab| > ab\), which of the following must be true?

I. \(a < 0\)
II. \(b < 0\)
III. \(ab < 0\)

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


If \(ab ≥ 0\) then \(|ab| = ab\)
In order for \(|ab| > ab\), we must have \(ab < 0\)
As long as a and b bear opposite signs, this will hold true.
So, C.
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If |ab| > ab, which of the following must be true?  [#permalink]

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New post 05 Aug 2018, 08:54
hazelnut wrote:
If \(|ab| > ab\), which of the following must be true?

I. \(a < 0\)
II. \(b < 0\)
III. \(ab < 0\)

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



Given

\(|ab| > ab\)

*** ab is on both sides. But the one with absolute value sign gives us positive value. It implies that ab <0 and when we put this negative value inside the absolute value sign it become positive. Thus absolute value part is greater.

The best answer is C.
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If |ab| > ab, which of the following must be true? &nbs [#permalink] 05 Aug 2018, 08:54
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