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a,b,c,and d are positive

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Carcass
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a,b,c,and d are positive [#permalink] New post   09 Mar 2021, 05:00
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a,b,c,and d are positive integers such that \(\frac{a}{b}< \frac{c}{d}\)

Quantity A
Quantity B
\([\frac{c}{b}][\frac{a}{d}]\)
\(\frac{c}{d}\)


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

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Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Re: a,b,c,and d are positive [#permalink] New post   09 Mar 2021, 09:18
Carcass wrote:
a,b,c,and d are positive integers such that \(\frac{a}{b}< \frac{c}{d}\)

Quantity A
Quantity B
\([\frac{c}{b}][\frac{a}{d}]\)
\(\frac{c}{d}\)


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.


\(\frac{a}{b} < \frac{c}{d}\)

Since, we have all 4 positive integers, we can say: \(ad < bc\)

Col. A: \(\frac{ac}{bd}\)
Col. B: \(\frac{c}{d}\)

Cross-Multiply the denominators;

Col. A: \(acd\)
Col. B: \(bcd\)

Eliminating \(cd\);

Col. A: \(a\)
Col. B: \(b\)

We do not know any relation between \(a\) and \(b\)!

Hence, option D
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Re: a,b,c,and d are positive [#permalink]
09 Mar 2021, 09:18
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