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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: For integers a, b, and c, if ab = bc, then which of the foll [#permalink]
11 Feb 2013, 14:22

5

This post received KUDOS

Expert's post

3

This post was BOOKMARKED

emmak wrote:

For integers a, b, and c, if ab = bc, then which of the following must also be true?

A. a = c B. a^2*b=b*c^2 C. a/c = 1 D. abc > bc E. a + b + c = 0

\(ab = bc\) --> \(ab-bc=0\) --> \(b(a-c)=0\)--> \(b=0\) or \(a=c\).

A. a = c. If \(b=0\), then this option is not necessarily true.

B. a^2*b=b*c^2 --> \(b(a^2-c^2)=0\) --> \(b(a-c)(a+c)=0\). Now, since \(b=0\) or \(a=c\), then \(b(a-c)(a+c)\) does equal to zero. So, we have that this options must be true.

C. a/c = 1. If \(b=0\), then this option is not necessarily true.

D. abc > bc. If \(b=0\), then this option is not true.

E. a + b + c = 0. If \(b=0\), then this option is not necessarily true (if b=0 then a+c can take any value this option is not necessarily true.).

Re: For integers a, b, and c, if ab = bc, then which of the foll [#permalink]
11 Jun 2013, 19:47

Bunuel wrote:

emmak wrote:

For integers a, b, and c, if ab = bc, then which of the following must also be true?

A. a = c B. a^2*b=b*c^2 C. a/c = 1 D. abc > bc E. a + b + c = 0

\(ab = bc\) --> \(ab-bc=0\) --> \(b(a-c)=0\)--> \(b=0\) or \(a=c\).

B. a^2*b=b*c^2 --> \(b(a^2-c^2)=0\) --> \(b(a-c)(a+c)=0\). Now, since \(b=0\) or \(a=c\), then \(b(a-c)(a+c)\) does equal to zero. So, we have that this options must be true.

Answer: B.

for answer choice B, could you also say that if a = -c it also equals zero?

Also, why do all of the possible answers equaling zero in choice B mean that B must be true?

Re: For integers a, b, and c, if ab = bc, then which of the foll [#permalink]
11 Jun 2013, 20:21

dhlee922 wrote:

Bunuel wrote:

\(ab = bc\) --> \(ab-bc=0\) --> \(b(a-c)=0\)--> \(b=0\) or \(a=c\).

B. a^2*b=b*c^2 --> \(b(a^2-c^2)=0\) --> \(b(a-c)(a+c)=0\). Now, since \(b=0\) or \(a=c\), then \(b(a-c)(a+c)\) does equal to zero. So, we have that this options must be true.

Answer: B.

for answer choice B, could you also say that if a = -c it also equals zero?

The point here is that analyzing the initial equation ab = bc, we know that either b = 0 or a = c. Plugging in either of these values results in b(a-c)(a+c) being equal to zero. I think you're confusion comes from extracting "a = -c" from "b(a-c)(a+c) = 0" as opposed to extracting information from the original equation ab = bc (which is what we need to do).

dhlee922 wrote:

Also, why do all of the possible answers equaling zero in choice B mean that B must be true?

Continuing from above: So recall that from the first equation, b = 0 or a = c. The expanded term b(a-c)(a+c) is an alternate expression for the second option; i.e, the fact that both of the possible necessary truths (b = 0; a = c) lead to b(a-c)(a+c) = 0 means that the equivalent expression, a^2 * b = b * c^2 must also be true.

Re: For integers a, b, and c, if ab = bc, then which of the foll [#permalink]
12 Jun 2013, 14:29

i'm still a little confused by the answer choices.

is it because the question stem equates to B=0 OR A=C

so for answer choice A, A doesnt have to equal C because the B equaling 0 will just make the whole expression 0

but then for answer choice B, since B=0 OR A=C, since 1 or the 3 groups in parentheses will be 0, it will make the whole expression 0, therefore B must be true?

Re: For integers a, b, and c, if ab = bc, then which of the foll [#permalink]
12 Jun 2013, 14:34

dhlee922 wrote:

i'm still a little confused by the answer choices.

is it because the question stem equates to B=0 OR A=C

so for answer choice A, A doesnt have to equal C because the B equaling 0 will just make the whole expression 0

but then for answer choice B, since B=0 OR A=C, since 1 or the 3 groups in parentheses will be 0, it will make the whole expression 0, therefore B must be true?

Yes, exactly. We know that or b=0 or a-c=0 ( or both) .

We can rewrite B as \(b(a-c)(a+c)\), and since at least one of the terms is 0, the whole expression is 0. _________________

It is beyond a doubt that all our knowledge that begins with experience.

Re: For integers a, b, and c, if ab = bc, then which of the foll [#permalink]
12 Jun 2013, 14:38

Expert's post

dhlee922 wrote:

i'm still a little confused by the answer choices.

is it because the question stem equates to B=0 OR A=C

so for answer choice A, A doesnt have to equal C because the B equaling 0 will just make the whole expression 0

but then for answer choice B, since B=0 OR A=C, since 1 or the 3 groups in parentheses will be 0, it will make the whole expression 0, therefore B must be true?

Yes, for A, if b=0, then a may or may not equal to c.

As for B, since b=0 or a=c (a-c=0), then b(a-c)(a+c)=0 must be true, since either the first or the second multiple (or both) is 0.

Re: For integers a, b, and c, if ab = bc, then which of the foll [#permalink]
30 Jul 2014, 05:53

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. _________________

I am not panicking. Nope, Not at all. But I am beginning to wonder what I was thinking when I decided to work full-time and plan my cross-continent relocation...

Over the last week my Facebook wall has been flooded with most positive, almost euphoric emotions: “End of a fantastic school year”, “What a life-changing year it’s been”, “My...