If a/b<c/d & bd < 0, which of the following inequalities must be true? : Problem Solving (PS)

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

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Director

Joined: 25 Dec 2018

Posts: 620

Location: India

Concentration: General Management, Finance

Schools: Tippie '22, Imperial '21, AGSM '20, SMU '20

GMAT Date: 02-18-2019

GPA: 3.4

WE: Engineering (Consulting)

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

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25 Apr 2019, 09:13

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75% (hard)

Question Stats:

46% (01:58) correct

54% (01:52) wrong

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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

Spoiler: OA

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Joined: 02 Aug 2009

Posts: 8586

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

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25 Apr 2019, 21:42

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

C
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Re: If a/b<c/d & bd < 0, which of the following inequalities must be true? [#permalink] 25 Apr 2019, 21:42

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

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