If a = 3bc, what is the value of c?

Question

(1) a = 10 - b
(2) 3a = 4b

werbliben · Answer

Hopefully this wasn't posted before. At least I wasn't able to find this task on the forum :roll:

The answer given by the authors of the textbook is B. Their solution suggests dividing the equation in the 2nd statement by b , thus transforming it to the form c = 1/3*a/b . This would be true if not for the circumstance that we cannot divide by b unless we prove it isn't 0. Both the initial equation a=3be and the one in the 2nd statement give us no information about possible value of b or a , but by using 1st statement in combination with the 2nd one we can prove that both a and b are non-zero, after which we have legitimate power to do the transformation described above. But in that case the answer should be C, not B. Am I missing something or is this a typo?

Bunuel · Answer

Yes, you are right. The answer cannot be B, it's C. For (2) if a=b=0, then c can be any number.

Hope it's clear.

P.S. Are you sure that it's MGMAT question?

werbliben · Answer

Thanks again =)

Well, yes, I've found this one on page 115 of the 5th edition of Algebra MGMAT Strategy guide. It's given as an example, not in a problem set, and, what's more, the explanation is ended in a rather unusual fashion: instead of naming the letter of the correct answer, the textbook says: "Statement 2 by itself allows us to solve for a/b". So, either a typo or great troubles await me in the Reading comprehension section =)

arunspanda · Answer

The example question in the guide asks "  If a = 3bc, and  abc does not equal 0 , what is the value of c?

(1)  a = 10 - b  
(2)  3a = 4b   "

With the condition  abc not equal to zero , the value of a/b from statement (2) is sufficient to evaluate  c  uniquely from equation  a = 3bc .
Hence, the answer is (B) in the strategy guide.

Bunuel · Answer

Yes, if it's given that abc does not equal 0, then the answer is B.

werbliben · Answer

arunspanda

There is no mention of the abc =/= 0 condition in my edition, they should've updated this task in the subsequent editions, although I thought the 5th, published in 2012, was the latest to date.

arunspanda · Answer

The quoted text is from the guide published on 24th April, 2012 (Kindle Edition).

faamir · Answer

Hi Bunuel,

Please help me out here.
Doesn't 3a = 4b mean a/b=4/3 ? Doesn't this imply a not= 0 and b not= 0. In this case shouldn't the answer be B?

Bunuel · Answer

If we are not given that a and b does not equal 0, then from 3a=4b we cannot write a/b=4/3. Because 3a=4b also holds when a=b=0, and in this case a/b=0/0=undefined not 4/3.

faamir · Answer

Thanks Bunuel.

If instead of the 2nd statement being 3a=4b, we were given a/b=4/3, can we then deduce a not=0 and b not=0 ? Would the answer then have been B?

Bunuel · Answer

___________________
Absolutely. From a/b=4/3 it follows that neither of them can be 0.

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If a = 3bc, what is the value of c?

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If a = 3bc, what is the value of c?

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