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

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mangamma
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If a/b<c/d & bd < 0, which of the following inequalities must be true? [#permalink] New post  25 Apr 2019, 10:13
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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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chetan2u
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Re: If a/b<c/d & bd < 0, which of the following inequalities must be true? [#permalink] 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] New post  30 Jun 2020, 03:11
a/b<c/d
a/b - c/d<0
ad-bc/bd<0
this means ad-bc and bd have opp signs
bd<0 (given)
hence ad-bc>0 option III
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Re: If a/b<c/d & bd < 0, which of the following inequalities must be true? [#permalink] New post  30 Jun 2023, 09:16
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Re: If a/b<c/d & bd < 0, which of the following inequalities must be true? [#permalink]
30 Jun 2023, 09:16
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