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 500,000 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: If abc = b3 , which of the following must be true? [#permalink]

Show Tags

20 Feb 2011, 08:41

4

This post received KUDOS

abc = b^3 implies abc - b^3 = 0 or b*(ac-b^2)=0 which implies either b=0 or ac=b^2 so, either of them or both of them can be true, but none of them must be true. Answer A

Hi Bunuel, Request you to post your reasoning. Here is how I approached this one- abc = b^3 abc-b^3 =0 b(ac-b^2)=0 Hence either b=0 or ac=b^2

However b=0 is not a solution. Could you please shed some light on how to approach must be true or could be true questions. Thanks H

If abc = b^3 , which of the following must be true? I. ac = b^2 II. b = 0 III. ac = 1

A. None B. I only C. II only D. I and III E. II and III

\(abc = b^3\) --> \(b(ac-b^2)=0\) --> EITHER \(b=0\) OR \(ac=b^2\), which means that NONE of the option MUST be true.

For example if \(b=0\) then \(ac\) can equal to any number (not necessarily to 0 or 1), so I and III are not always true, and if \(ac=b^2\) then \(b\) can also equal to any number (not necessarily to 0), so II is not always true.

OA is definitely A. Folks may be little bit confused at option *i and iii* (3) tells us that ac=1. So what? Is b also 1 or equal to 0? Can't figure it out. Move further. If some part of multiplication is 0, there is no need to ans. That question. It doesnt satisfy the condition: abc=b^3.

NOTE:WHEN YOU ARE TACKLING "MUST BE TYPE" QUESTION, always try to find out " entire set" instead of "sub set" cz subset answers "what should be" rather than "what must be". If you are an accountant, you may consider it equivalent to " Bad debt reserve".

This tells us that either b = 0 OR \(ac = b^2\). At least one of these 2 'must be true'.

So can I say b must be equal to 0? No! It is possible but it is also possible that instead, \(ac = b^2\). So can I say ac must be equal to \(b^2\)? No! It is possible but it is also possible that instead, b = 0. So can I say that b = 0 AND \(ac = b^2\)? No! It is possible but it is also possible that only one of them is true. So can I say that b = 0 OR \(ac = b^2\)? Yes, I can! One of them must be true.

If one of the options were 'I or II', that would have been true.
_________________

Re: If abc = b^3 , which of the following must be true? [#permalink]

Show Tags

08 Oct 2014, 22:47

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 abc = b^3 , which of the following must be true? [#permalink]

Show Tags

10 Oct 2015, 20:57

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.
_________________

Why is it wrong to divide both sides by b at the start?

Another way to understand this:

When you divide by b, you are assuming that b is not 0. Is it a fair assumption? No. You are losing on a possible solution of the equation.

How can I make abc = b^3? I can do that by either making b = 0 or making ac = b^2.

But if you divide by b, you get only one solution: ac = b^2 and that means I must be true. Actually, the answer is none because there is another possibility and that is b = 0.
_________________

Re: If abc = b^3 , which of the following must be true? [#permalink]

Show Tags

15 Mar 2016, 00:51

nikhilsrl wrote:

If abc = b^3 , which of the following must be true?

I. ac = b^2 II. b = 0 III. ac = 1

A. None B. I only C. II only D. I and III E. II and III

This is from Kaplan CAT. I am not quite sure how they arrived at the answer.

HERE the question is asking us which statement must be true Hence we can discard all of them as we can make each one of them untrue by taking the other leftover equations true. Hence A
_________________

Give me a hell yeah ...!!!!!

gmatclubot

Re: If abc = b^3 , which of the following must be true?
[#permalink]
15 Mar 2016, 00:51

After days of waiting, sharing the tension with other applicants in forums, coming up with different theories about invites patterns, and, overall, refreshing my inbox every five minutes to...

I was totally freaking out. Apparently, most of the HBS invites were already sent and I didn’t get one. However, there are still some to come out on...

In early 2012, when I was working as a biomedical researcher at the National Institutes of Health , I decided that I wanted to get an MBA and make the...