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03 May 2022, 02:30
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
91% (00:50) correct
9%
(01:06)
wrong
based on 55
sessions
History
Date
Time
Result
Not Attempted Yet
If \(\frac{1}{x} + \frac{1}{y} = \frac{1}{3}\), then \(\frac{xy}{x + y} =\)
(A) 1/5
(B) 1/3
(C) 1
(D) 3
(E) 5
(A) 1/5
(B) 1/3
(C) 1
(D) 3
(E) 5
03 May 2022, 06:12
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If \(\frac{1}{x} + \frac{1}{y} = \frac{1}{3}\), then \(\frac{xy}{x + y} =\)
(A) 1/5
(B) 1/3
(C) 1
(D) 3
(E) 5
(A) 1/5
(B) 1/3
(C) 1
(D) 3
(E) 5
Given: \(\frac{1}{x} + \frac{1}{y} = \frac{1}{3}\)
Rewrite the left side with common denominators: \(\frac{y}{xy} + \frac{x}{xy} = \frac{1}{3}\)
Simplify the left side: \(\frac{x+y}{xy} = \frac{1}{3}\)
Useful property: If \(abcd ≠ 0\), and \(\frac{a}{b} = \frac{c}{d}\), then it's also true that \(\frac{b}{a} = \frac{d}{c}\)
So take the reciprocal of both sides: \(\frac{xy}{x+y} = \frac{3}{1} = 3\)
Answer: D
