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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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Math Expert
Joined: 02 Sep 2009
Posts: 57152
a*b = ab/(a + b) for all a, b that satisfy a ≠ -b. What is the value  [#permalink]

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22 Jul 2019, 01:32
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Difficulty:

15% (low)

Question Stats:

88% (00:30) correct 13% (00:39) wrong based on 24 sessions

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

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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]

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23 Jul 2019, 04:34

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.

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