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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? [#permalink] New post 05 Jan 2014, 05:19
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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, 05:36, edited 1 time in total.
Edited the OA.
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Re: If a = 3be, what is the value of c? [#permalink] New post 05 Jan 2014, 05:27
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 :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?
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Re: If a = 3be, what is the value of c? [#permalink] New post 05 Jan 2014, 05:35
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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 :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?


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] New post 05 Jan 2014, 05:56
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] New post 06 Jan 2014, 01:06
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] New post 06 Jan 2014, 01:45
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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] New post 06 Jan 2014, 03:39
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] New post 06 Jan 2014, 07:44
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] New post 06 Jun 2014, 10:29
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?
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Re: If a = 3be, what is the value of c? [#permalink] New post 06 Jun 2014, 10:37
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faamir wrote:
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?


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] New post 06 Jun 2014, 10:44
Bunuel wrote:
faamir wrote:
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?


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] New post 06 Jun 2014, 10:48
Expert's post
faamir wrote:
Bunuel wrote:
faamir wrote:
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?


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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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: If a = 3be, what is the value of c?   [#permalink] 06 Jun 2014, 10:48
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