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a*b = ab/(a + b) for all a, b that satisfy a ≠ -b. What is the value

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Bunuel
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a*b = ab/(a + b) for all a, b that satisfy a ≠ -b. What is the value [#permalink] New post   22 Jul 2019, 01:32
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\(a \circ b = \frac{ab}{a+b}\) for all a, b that satisfy \(a ≠ -b\). What is the value of \((–4) \circ 2\)?

A. \(-4\)

B. \(-2\)

C. \(-\frac{4}{3}\)

D. \(\frac{4}{3}\)

E. \(4\)
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E
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a*b = ab/(a + b) for all a, b that satisfy a ≠ -b. What is the value [#permalink] New post   22 Jul 2019, 02:36
Bunuel wrote:
\(a \circ b = \frac{ab}{a+b}\) for all a, b that satisfy \(a ≠ -b\). What is the value of \((–4) \circ 2\)?

A. \(-4\)

B. \(-2\)

C. \(-\frac{4}{3}\)

D. \(\frac{4}{3}\)

E. \(4\)


Given: \(a \circ b = \frac{ab}{a+b}\) for all a, b that satisfy \(a ≠ -b\).
Asked: What is the value of \((–4) \circ 2\)?

\((–4) \circ 2 = \frac{(-4)*2}{-4+2}= \frac{-8}{-2} = 4\)

IMO E
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Re: a*b = ab/(a + b) for all a, b that satisfy a ≠ -b. What is the value [#permalink] New post   23 Jul 2019, 04:34
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Solution


Given:
    • \(a ∘ b = \frac{ab}{a+b}\)
    • a ≠ −b

To find:
    • The value of (–4)∘2

Approach and Working Out:
    • \((–4)∘2 = \frac{-4*2}{(-4 + 2)} = \frac{-8}{-2} = 4\)

Hence, the correct answer is Option E.

Answer: E

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Re: a*b = ab/(a + b) for all a, b that satisfy a -b. What is the value [#permalink] New post   08 Aug 2022, 00:27
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Given that \(a \circ b = \frac{ab}{a+b}\) and we need to find the value of \((–4) \circ 2\)

To find \((–4) \circ 2\) we need to compare what is before and after \(\circ\) in \((–4) \circ 2\) and \(a \circ b\)

=> We need to substitute a with -4 and b with 2 in \(a \circ b = \frac{ab}{a+b}[/m to get the value of [m](–4) \circ 2\)

=> \(-4 \circ 2 = \frac{-4*2}{-4+2}\) = \(\frac{-8}{-2}\) = 4

So, Answer will be E
Hope it helps!

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Re: a*b = ab/(a + b) for all a, b that satisfy a -b. What is the value [#permalink]
08 Aug 2022, 00:27
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