If a = 3bc and abc ≠ 0, what is the value of c ?

Question

(1) a = 10 − b
(2) 3a = 4b

chetan2u · Answer

a=3bc

(1) a = 10 − b
Substitute in  a=3bc.....10-b=3bc .....Two variables
Insuff

(2) 3a = 4b
Substitute in  a=3bc........3a=3*3bc.........4b=9bc .....
We can cancel out b as b≠ 0, so  4=9c.......c=\frac{4}{9} 
Suff

B

GMATinsight · Answer

Given: a = 3bc

Question : c = ?

Statement (1) a = 10 − b

I.e. 10 − b = 3bc

But we can't eliminate b from the equation to find c hence

NOT SUFFICIENT

Statement (2) 3a = 4b

I.e. (4/3)*b = 3bc

I.e. c = 4/9 hence

SUFFICIENT

Answer: Option B

CrackverbalGMAT · Answer

From the question data we know that a=3bc and from the question stem, we know that we are trying to find the value of c.

Let’s try to express c in terms of the other two variables by re-organising them. When we do this, we get,

c =  \frac{a}{3b} . Let’s call this equation 1.

From this, we understand that we need the values of a and b or a relation between them to find the value of c.

From statement I alone, a = 10-b. Substituting this in equation 1, we have c =  \frac{10-b }{ b} . This is not sufficient to find the value of c since we still need the value of b. 
Statement I alone is insufficient. Answer options A and D can be eliminated. Possible answer options are B, C or E.

From statement II alone, we have 3a = 4b or a =  \frac{4b }{ 3} . Substituting this in equation 1, we have, 
c =  \frac{4b}{9b}  =  \frac{4}{9} .
Statement II alone is sufficient to give us a unique value for c. Answer options C and E can be eliminated.

The correct answer option is B .

Hope that helps!

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If a = 3bc and abc ≠ 0, what is the value of c ?

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GMAT Data Sufficiency (DS) Questions

If a = 3bc and abc ≠ 0, what is the value of c ?

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