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If |a/b| and |x/y| are reciprocals and
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12 Aug 2018, 09:54
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. \(\frac{y}{x} > \frac{a}{b}\)
A. \(ab < 0\)
B. \(\frac{a}{b} (\frac{x}{y}) < -1\)
C. \(\frac{a}{b} < 1\)
D. \(\frac{a}{b} = \frac{-y}{x}\)
E. \(\frac{y}{x} > \frac{a}{b}\)
Re: If |a/b| and |x/y| are reciprocals and
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13 Sep 2018, 12:32
13 Sep 2018, 12:32
2
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
so a/b=-y/x
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Re: If |a/b| and |x/y| are reciprocals and
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10 Jun 2020, 16:34
10 Jun 2020, 16:34
2
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. \(\frac{y}{x} > \frac{a}{b}\)
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
