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If |a/b| and |x/y| are reciprocals and [#permalink]
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Question Stats: 76% (01:10) correct 23% (01:24) wrong based on 106 sessions
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]
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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 GRE Instructor Joined: 10 Apr 2015
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Re: If |a/b| and |x/y| are reciprocals and [#permalink]
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Expert's post
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

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com Intern Joined: 22 Oct 2019
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Re: If |a/b| and |x/y| are reciprocals and [#permalink]
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)
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Re: If |a/b| and |x/y| are reciprocals and [#permalink]
Quote:
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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