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If a/b<c/d & bd < 0, which of the following inequalities must be true?

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If a/b<c/d & bd < 0, which of the following inequalities must be true?  [#permalink]

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New post 25 Apr 2019, 10:13
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  65% (hard)

Question Stats:

50% (01:57) correct 50% (02:01) wrong based on 42 sessions

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If a/b<c/d & bd < 0, which of the following inequalities must be true?

I. ad -bc < 0
II. bc -ad > 0
III. ad -bc > 0


A. I only
B. II only
C. III only
D. I and II
E. II and III
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Re: If a/b<c/d & bd < 0, which of the following inequalities must be true?  [#permalink]

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New post 25 Apr 2019, 22:42
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mangamma wrote:
If a/b<c/d & bd < 0, which of the following inequalities must be true?

I. ad -bc < 0
II. bc -ad > 0
III. ad -bc > 0


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


\(\frac{a}{b}<\frac{c}{d}\)
Since bd < 0,, we can multiply the inequality by bd and change the inequality sign..
\(bd*\frac{a}{b}>bd*\frac{c}{d}......ad>bc...ad-bc>0\)

Option III is exactly the same, so correct..

let us see the other options..
I. ad -bc < 0...opposite of ad-bc>0..Not true
II. bc -ad > 0...bc>ad or ad-bc<0...Same as option I..Not true

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Re: If a/b<c/d & bd < 0, which of the following inequalities must be true?   [#permalink] 25 Apr 2019, 22:42
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If a/b<c/d & bd < 0, which of the following inequalities must be true?

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