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ab/a+b=1/6

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ab/a+b=1/6 [#permalink] New post   11 Dec 2023, 00:07
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\(\frac{ab}{a+b}=\frac{1}{6}\)


Quantity A
Quantity B
1/a + 1/b
6



A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.



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C
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Re: ab/a+b=1/6 [#permalink] New post   12 Dec 2023, 13:33
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We're given equivalent fractions, so cross multiply to get
\(6ab = a+b\)

Divide both sides by ab to isolate 6 (which is quantity B)
\(6 = \frac{a+b}{ab} = \frac{1}{a} + \frac{1}{b}\)
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Re: ab/a+b=1/6 [#permalink] New post   25 Dec 2023, 09:04
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ab/a+b = 1/6 = reciprocate = 6
Quantity A = 1/a+1/b = a+b/ab = 6
hence both are equal.
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ab/a+b=1/6 [#permalink] New post   29 Jan 2024, 21:37
Quantity A

\(\dfrac{1}{a}+\dfrac{1}{b}\)

adding the two fractions, we get

\(\dfrac{a+b}{ab}\)

We know that

\(\dfrac{ab}{a+b} = \frac{1}{6}\)

\(\text{ since } \frac{a+b}{ab}\) is its reciprocal, its value will be \(6\)

\(\dfrac{a+b}{ab} = 6 = \dfrac{1}{a}+\dfrac{1}{b}\)

Quantity B

\(6\)

BOTH quantities are EQUAL

The answer is C.
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ab/a+b=1/6 [#permalink]
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