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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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Math Expert
Joined: 02 Sep 2009
Posts: 58427
If |a/b| and |x/y| are reciprocals and a/b*x/y < 0, which of the follo  [#permalink]

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13 Aug 2018, 04:38
10
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Difficulty:

55% (hard)

Question Stats:

60% (01:53) correct 40% (02:01) wrong based on 232 sessions

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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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Math Expert
Joined: 02 Aug 2009
Posts: 8006
Re: If |a/b| and |x/y| are reciprocals and a/b*x/y < 0, which of the follo  [#permalink]

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13 Aug 2018, 09:59
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1
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 if $$\frac{a}{b}*\frac{x}{y} < 0$$, means (a/b)*(x/y)=-1
Thus a/b=-(y/x)

D
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Re: If |a/b| and |x/y| are reciprocals and a/b*x/y < 0, which of the follo   [#permalink] 13 Aug 2018, 09:59
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