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

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Re: If a = 3bc, what is the value of c? [#permalink]
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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 =)
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Re: If a = 3bc, what is the value of c? [#permalink]
werbliben wrote:
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 =)

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.
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Re: If a = 3bc, what is the value of c? [#permalink]
arunspanda wrote:
werbliben wrote:
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 =)

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.

Yes, if it's given that abc does not equal 0, then the answer is B.
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Re: If a = 3bc, what is the value of c? [#permalink]
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.
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Re: If a = 3bc, what is the value of c? [#permalink]
werbliben wrote:
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.

The quoted text is from the guide published on 24th April, 2012 (Kindle Edition).
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Re: If a = 3be, what is the value of c? [#permalink]
Hi Bunuel,

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?
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Re: If a = 3be, what is the value of c? [#permalink]
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faamir wrote:
Hi Bunuel,

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?

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.
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Re: If a = 3be, what is the value of c? [#permalink]
Bunuel wrote:
faamir wrote:
Hi Bunuel,

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?

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.

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?
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Re: If a = 3be, what is the value of c? [#permalink]
faamir wrote:
Bunuel wrote:
faamir wrote:
Hi Bunuel,

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?

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.

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?

___________________
Absolutely. From a/b=4/3 it follows that neither of them can be 0.
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Re: If a = 3bc, what is the value of c? [#permalink]
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Re: If a = 3bc, what is the value of c? [#permalink]
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