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If |a/b| and |x/y| are reciprocals and

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If |a/b| and |x/y| are reciprocals and [#permalink] New post 12 Aug 2018, 09:54
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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. \(\frac{y}{x} > \frac{a}{b}\)
[Reveal] Spoiler: OA

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Re: If |a/b| and |x/y| are reciprocals and [#permalink] New post 13 Sep 2018, 12:32
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using the definition of absolute values, we can say a/b is either y/x or -y/x. but as the second condition implies, these two fractions hold opposite signs.

so a/b=-y/x
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Re: If |a/b| and |x/y| are reciprocals and [#permalink] New post 10 Jun 2020, 16:34
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Carcass 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. \(\frac{y}{x} > \frac{a}{b}\)


We can either try to apply some number sense or simply test some values.

I have a feeling the latter might be faster.

If |a/b| and |x/y| are reciprocals, AND (a/b)(x/y) < 0, then it could be the case that: a = 1, b = 1, x = 1 and y = -1

Now check out the choices....

A. \((1)(1) < 0\) NOT TRUE

B. \(\frac{1}{1} (\frac{1}{-1}) < -1\) NOT TRUE

C. \(\frac{1}{1} < 1\) NOT TRUE

D. \(\frac{1}{1} = \frac{-(-1)}{1}\) TRUE!

E. \(\frac{-1}{1} > \frac{1}{1}\) NOT TRUE

Answer: D

Cheers,
Brent
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Re: If |a/b| and |x/y| are reciprocals and [#permalink] New post 28 Oct 2020, 23:39
As, (a/b)(x/y)<1; one of the terms (a/b) or (x/y) must be negative.
Again, MOD(a/b)=1/MOD(x/y)= MOD(y/x).......(i)
When, (a/b)=-ve; MOD(a/b)= -(a/b), then y/x must be positive.
From (i) we get, -(a/b)= (x/y)
So, answer is "D"
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Re: If |a/b| and |x/y| are reciprocals and [#permalink] New post 07 Nov 2020, 02:14
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If |a/b| and |x/y| are reciprocals, AND (a/b)(x/y) < 0, then it could be the case that: a = 1, b = 1, x = 1 and y = -1


Doesn't a or b have to be negative if a/b and x/y are reciprocals? a/b is the multiplicative inverse of x/y and a/b * x/y must equal 1. 1/1 * 1/-1 = -1

correct oa should be A and C
Re: If |a/b| and |x/y| are reciprocals and   [#permalink] 07 Nov 2020, 02:14
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