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If |a/b| and |x/y| are reciprocals and a/b*x/y < 0, which of the follo

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Bunuel
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If |a/b| and |x/y| are reciprocals and a/b*x/y < 0, which of the follo [#permalink] New post   13 Aug 2018, 04:38
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If \(|\frac{a}{b}|\) and \(|\frac{x}{y}|\) are reciprocals and \(\frac{a}{b}*\frac{x}{y} < 0\), which of the following must be true?


A. \(ab < 0\)

B. \(\frac{a}{b} (\frac{x}{y}) < -1\)

C. \(\frac{a}{b} < 1\)

D. \(\frac{a}{b} = \frac{-y}{x}\)

E. \(\frac{y}{x} > \frac{a}{b}\)
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chetan2u
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If |a/b| and |x/y| are reciprocals and a/b*x/y < 0, which of the follo [#permalink] New post   13 Aug 2018, 09:59
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Bunuel wrote:
If \(|\frac{a}{b}|\) and \(|\frac{x}{y}|\) are reciprocals and \(\frac{a}{b}*\frac{x}{y} < 0\), which of the following must be true?


A. \(ab < 0\)

B. \(\frac{a}{b} (\frac{x}{y}) < -1\)

C. \(\frac{a}{b} < 1\)

D. \(\frac{a}{b} = \frac{-y}{x}\)

E. \(\frac{y}{x} > \frac{a}{b}\)



\(|\frac{a}{b}|\) and \(|\frac{x}{y}|\) are reciprocals, so \(|\frac{a}{b}|*|\frac{x}{y}|=1\)

But as \(\frac{a}{b}*\frac{x}{y} < 0\), one of the fraction is positive and other negative, that is the product of fractions is negative => \((\frac{a}{b})*(\frac{x}{y})=-1\)

Thus \(\frac{a}{b}=-(\frac{y}{x})\)

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prathyushaR
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Re: If |a/b| and |x/y| are reciprocals and a/b*x/y < 0, which of the follo [#permalink] New post   10 Jun 2020, 06:38
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Bunuel wrote:
If \(|\frac{a}{b}|\) and \(|\frac{x}{y}|\) are reciprocals and \(\frac{a}{b}*\frac{x}{y} < 0\), which of the following must be true?


A. \(ab < 0\)

B. \(\frac{a}{b} (\frac{x}{y}) < -1\)

C. \(\frac{a}{b} < 1\)

D. \(\frac{a}{b} = \frac{-y}{x}\)

E. \(\frac{y}{x} > \frac{a}{b}\)


the modulus fractions are reciprocals of each other : \(|\frac{a}{b}|\) * \(|\frac{x}{y}|\) =1
\(\frac{a}{b}*\frac{x}{y} < 0\) : the fractions have opposite signs (since product is negative)
thus \(\frac{a}{b}*\frac{x}{y} =-1 \)
\(\frac{a}{b} = \frac{-y}{x}\)
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Re: If |a/b| and |x/y| are reciprocals and a/b*x/y < 0, which of the follo [#permalink] New post   07 Jul 2020, 11:25
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DaniyalAlwani wrote:
chetan2u

In you explanation you assumed product of both the reciprocals equals to 1. Why is that? Question doesn't mention it plus it could've also said a/b * b/a. Then it would've been fair for product to be 1. Kindly explain please


question mentions that a/b and x/y are reciprocals i.e reciprocals of each other, so product will be 1, As product is less than < 0, so a/b*x/y = -1.

Hope i am able to make it clear
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If |a/b| and |x/y| are reciprocals, then, which of the following must [#permalink] New post   24 Jun 2021, 02:44
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Bunuel wrote:
If \(|\frac{a}{b}|\) and \(|\frac{x}{y}|\) are reciprocals, then, which of the following must be true?


(A) \(ab < 0\)

(B) \(\frac{a}{b}*\frac{x}{y }< -1\)

(C) \(\frac{a}{b }< 1\)

(D) \(\frac{a}{b }= -\frac{y}{x}\)

(E) \(\frac{y}{x }> \frac{a}{b}\)



I think something is missed. The facts given in the question are not enough to go further. (such as signs of x and y or correlation between variables)
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DaniyalAlwani
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Re: If |a/b| and |x/y| are reciprocals and a/b*x/y < 0, which of the follo [#permalink] New post   06 Jun 2020, 05:11
chetan2u

In you explanation you assumed product of both the reciprocals equals to 1. Why is that? Question doesn't mention it plus it could've also said a/b * b/a. Then it would've been fair for product to be 1. Kindly explain please
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Re: If |a/b| and |x/y| are reciprocals and a/b*x/y < 0, which of the follo [#permalink] New post   07 Jan 2022, 03:08
Bunuel
It is given that |a/b| and |x/y| are reciprocals (implies a=y and b=x) therefore, there product should always be 1, because if one of them a (or b) is negative we will always have one more negative i.e y (or x) and product of two negative is positive.

Therefore, the condition given (a/b)*(x/y) < 0 is not a valid condition. As reciprocals are true irrespective of absolute values.

Or please let me know if I am missing something here.
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Re: If |a/b| and |x/y| are reciprocals and a/b*x/y < 0, which of the follo [#permalink] New post   09 Apr 2023, 11:51
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Re: If |a/b| and |x/y| are reciprocals and a/b*x/y < 0, which of the follo [#permalink]
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