What is the value of 1/a + 1/b + 1/c ?

Question

What is the value of  \frac{1}{a} + \frac{1}{b} + \frac{1}{c}  ?

(1)  a + b = \frac{5}{6}

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

DS21203

GMATinsight · Answer

Question:  \frac{1}{a} + \frac{1}{b} + \frac{1}{c}  = ?

Statement 1 :  a + b = \frac{5}{6}

No information about c hence

NOT SUFFICIENT

Statement 2 :  \frac{bc + ac + ab}{abc} = \frac{12}{13}

i.e.  \frac{bc}{abc}+\frac{ac}{abc}+\frac{ab}{abc} = (1/a)+(1/b)+(1/c) = \frac{12}{13}

SUFFICIENT

Answer: Option B

Siak0730 · Answer

statement 1: a+b = 5/6
clearly, not sufficient, as we cant solve two variable a and b with 1 equation
also, no information about c

statement 2 :  \frac{bc + ac + ab}{abc} = \frac{12}{13} 
the above equation can be written as 
(bc/abc) + (ac/abc) + (ab/abc) = 12/13
or 1/a + 1/b + 1/c =12/13
and therefore, sufficient.
answer B

BrentGMATPrepNow · Answer

Target question :    What is the value of  \frac{1}{a} + \frac{1}{b} + \frac{1}{c}  ?

Statement 1 :  a + b = \frac{5}{6}   
Since we have no information about the value of c, there's no way to answer the  target question  with certainty
Statement 1 is NOT SUFFICIENT

Statement 2 :  \frac{bc + ac + ab}{abc} = \frac{12}{13}

Key concept:  \frac{w+x+y}{z} = \frac{w}{z} + \frac{x}{z} + \frac{y}{z}

So we can take:  \frac{bc + ac + ab}{abc} = \frac{12}{13}

And rewrite the fractions as follows:  \frac{bc}{abc} + \frac{ac}{abc} + \frac{ab}{abc}= \frac{12}{13}

Simplify each fraction to get:  \frac{1}{a} + \frac{1}{b} + \frac{1}{c}= \frac{12}{13}

Voila!! The answer to the target question is  12/13

Since we can answer the  target question  with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

Kinshook · Answer

Asked: What is the value of  \frac{1}{a} + \frac{1}{b} + \frac{1}{c}  ?

(1)  a + b = \frac{5}{6} 
Since c is unknown
NOT SUFFICIENT

(2)  \frac{bc + ac + ab}{abc} = \frac{12}{13} 
 \frac{1}{a} + \frac{1}{b} + \frac{1}{c} = \frac{12}{13}  
SUFFICIENT

IMO B

NitishJain · Answer

Nothing is available in the question stem, let's analyze the statements:

Statement I:: a + b = 5/6

We can write it as 1/3 + 1/2, so a and b can be 1/2, 1/3 or vice versa but we don't need exact values for a & b but still value for c is not available.

Hence  NOT SUFFICIENT

A & D gone.

STATEMENT II:: bc+ac+ab/abc=12/13

Let's separate out the numerator ==> bc/abc + ac/abc + ab/abc = 12/13
==> 1/a + 1/b + 1/c = 12/13
 SUFFICIENT

Hence  B

japo17 · Answer

Question is solved if we find the value of a, b and c. Statement 1 is not sufficient as we are missing information about c. Statement 2 is sufficient. if we are careful enough to separate each fraction and simplify as they use the same denominator. After this simplification we get the value of the expression the problem is asking for.

Answer is B.

Posted from my mobile device

Answer is B.

Posted from my mobile device

bumpbot · Answer

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What is the value of 1/a + 1/b + 1/c ?

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What is the value of 1/a + 1/b + 1/c ?

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