GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 24 Apr 2019, 21:15

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern
Joined: 05 Jan 2014
Posts: 9
GMAT Date: 01-15-2014
If a = 3bc, what is the value of c?  [#permalink]

### Show Tags

Updated on: 05 Jan 2014, 06:36
2
00:00

Difficulty:

95% (hard)

Question Stats:

33% (01:46) correct 67% (01:39) wrong based on 191 sessions

### HideShow timer Statistics

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

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

Originally posted by werbliben on 05 Jan 2014, 06:19.
Last edited by Bunuel on 05 Jan 2014, 06:36, edited 1 time in total.
Edited the OA.
Intern
Joined: 05 Jan 2014
Posts: 9
GMAT Date: 01-15-2014
Re: If a = 3be, what is the value of c?  [#permalink]

### Show Tags

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?
Math Expert
Joined: 02 Sep 2009
Posts: 54496
Re: If a = 3be, what is the value of c?  [#permalink]

### Show Tags

05 Jan 2014, 06:35
1
1
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?
_________________
Intern
Joined: 05 Jan 2014
Posts: 9
GMAT Date: 01-15-2014
Re: If a = 3bc, what is the value of c?  [#permalink]

### Show Tags

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 =)
Manager
Joined: 04 Oct 2013
Posts: 151
Location: India
GMAT Date: 05-23-2015
GPA: 3.45
Re: If a = 3bc, what is the value of c?  [#permalink]

### Show Tags

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.
Math Expert
Joined: 02 Sep 2009
Posts: 54496
Re: If a = 3bc, what is the value of c?  [#permalink]

### Show Tags

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.
_________________
Intern
Joined: 05 Jan 2014
Posts: 9
GMAT Date: 01-15-2014
Re: If a = 3bc, what is the value of c?  [#permalink]

### Show Tags

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.
Manager
Joined: 04 Oct 2013
Posts: 151
Location: India
GMAT Date: 05-23-2015
GPA: 3.45
Re: If a = 3bc, what is the value of c?  [#permalink]

### Show Tags

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).
Intern
Joined: 14 May 2014
Posts: 13
GMAT 1: 760 Q50 V42
Re: If a = 3be, what is the value of c?  [#permalink]

### Show Tags

06 Jun 2014, 11:29
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?
Math Expert
Joined: 02 Sep 2009
Posts: 54496
Re: If a = 3be, what is the value of c?  [#permalink]

### Show Tags

06 Jun 2014, 11:37
1
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.
_________________
Intern
Joined: 14 May 2014
Posts: 13
GMAT 1: 760 Q50 V42
Re: If a = 3be, what is the value of c?  [#permalink]

### Show Tags

06 Jun 2014, 11:44
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?
Math Expert
Joined: 02 Sep 2009
Posts: 54496
Re: If a = 3be, what is the value of c?  [#permalink]

### Show Tags

06 Jun 2014, 11:48
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.
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 10624
Re: If a = 3bc, what is the value of c?  [#permalink]

### Show Tags

14 Jul 2017, 22:57
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If a = 3bc, what is the value of c?   [#permalink] 14 Jul 2017, 22:57
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.