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

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Joined: 05 Jan 2014
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If a = 3bc, what is the value of c? [#permalink]

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05 Jan 2014, 06:19
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If a = 3bc, what is the value of c?

(1) a = 10 - b
(2) 3a = 4b
[Reveal] Spoiler: OA

Last edited by Bunuel on 05 Jan 2014, 06:36, edited 1 time in total.
Edited the OA.

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

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05 Jan 2014, 06:27
werbliben wrote:
If a = 3be, what is the value of c?

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

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

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?

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

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05 Jan 2014, 06:35
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werbliben wrote:
werbliben wrote:
If a = 3bc, what is the value of c?

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

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

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?

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

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05 Jan 2014, 06:56
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]

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06 Jan 2014, 02:06
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]

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06 Jan 2014, 02:45
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]

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06 Jan 2014, 04:39
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]

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06 Jan 2014, 08:44
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]

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06 Jun 2014, 11:29
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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06 Jun 2014, 11:37
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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]

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06 Jun 2014, 11:44
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]

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06 Jun 2014, 11:48
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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14 Jul 2017, 22:57
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Re: If a = 3bc, what is the value of c?   [#permalink] 14 Jul 2017, 22:57
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