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

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If abc = b^3 , which of the following must be true? [#permalink] New post 20 Feb 2011, 07:19
00:00
A
B
C
D
E

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  55% (hard)

Question Stats:

50% (01:51) correct 50% (00:45) wrong based on 171 sessions
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.
[Reveal] Spoiler: OA

Last edited by Bunuel on 30 Mar 2012, 09:44, edited 1 time in total.
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Re: If abc = b3 , which of the following must be true? [#permalink] New post 20 Feb 2011, 07:41
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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
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Re: If abc = b3 , which of the following must be true? [#permalink] New post 30 Mar 2012, 09:12
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
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Re: If abc = b3 , which of the following must be true? [#permalink] New post 30 Mar 2012, 09:55
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imhimanshu wrote:
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.

Answer: A.

More Must or Could be True Questions with solutions to practice: search.php?search_id=tag&tag_id=193

Hope it helps.
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Re: If abc = b^3 , which of the following must be true? [#permalink] New post 31 Mar 2012, 06:44
Thanks Bunuel.. you are awesum :-)
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Re: Number properties [#permalink] New post 06 May 2012, 17:34
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".

Entire set= LCM
Suset =GCM.

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Re: If abc = b^3 , which of the following must be true? [#permalink] New post 12 Jun 2012, 04:07
Expert's post
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.


Responding to a pm:

I think I won't be able to take 'Must be true' for another week on my blog (Std Dev still not over). Hence, explaining this question right here.

Given: \(abc = b^3\)
\(abc - b^3 = 0\)
\(b(ac - b^2) = 0\)

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.
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Re: If abc = b^3 , which of the following must be true? [#permalink] New post 08 Oct 2014, 21:47
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Re: If abc = b^3 , which of the following must be true?   [#permalink] 08 Oct 2014, 21:47
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