What is the value of \(\dfrac1{a}+\dfrac1{b}+\dfrac1{c}?\)

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What is the value of \(\dfrac1{a}+\dfrac1{b}+\dfrac1{c}?\)

(1) \(a+b=\dfrac56\)

(2) \(\dfrac{bc+ac+ab}{abc}=\dfrac{12}{13}\)

Answer: B

Source: GMAT Prep

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$$What\ is\ the\ value\ \frac{1}{a}+\frac{1}{b}+\frac{1}{c}?$$
Statement 1: a + b = 5/6
From the question stem; find the lcm
$$\frac{bc+ac+ab}{abc}=\frac{c\left(b+a\right)+ab}{abc}$$
$$=\frac{\frac{5}{6}c+ab}{abc}$$
$$=\frac{5c+6ab}{6abc}$$
Since the value of c is not stated, then, the target question cannot be answered. Therefore, statement 1 is NOT SUFFICIENT.

$$Statement\ 2:\frac{bc+ac+ab}{abc}=\frac{12}{13}$$
From the question stem; find the lcm
$$\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{bc+ac+ab}{abc}=\frac{12}{13}$$
The target question equals 13. Therefore, statement 2 is SUFFICIENT.

Since only statement B is sufficient, then option B is the correct answer.