\(abc\ne 0\) and \(\dfrac3{a} + \dfrac3{b} = \dfrac3{c}.\) What is the sum \(a+b?\)
(1) \(ab=c\)
(2) \(ab=ac+bc\)
[spoiler]OA=A[/spoiler]
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\(abc\ne 0\) and \(\dfrac3{a} + \dfrac3{b} = \dfrac3{c}.\) What is the sum \(a+b?\)
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So, we know \(\dfrac3{a} + \dfrac3{b} = \dfrac3{c}.\) Taking LCM, we get \(\dfrac {3(a+b)}{ab} = \dfrac3{c}.\)
\(a+b=\dfrac{ab}c\)
Let's take each statement one by one.
(1) \(ab=c\)
\(\dfrac{ab}c=1\)
Thus, \(a+b=\dfrac{ab}c=1\). Sufficient.
(2) \(ab=ac+bc\)
\(\dfrac{ab}c=a+b\)
Insufficient. We already know this.
Correct answer: A
Hope this helps!
-Jay
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