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]

20 Feb 2011, 08:19

00:00

Question Stats:

35% (01:24) correct

64% (00:45) wrong

based on 28 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, 10:44, edited 1 time in total.

Edited the question

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

20 Feb 2011, 08:41

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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]

30 Mar 2012, 10:12

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]

30 Mar 2012, 10:55

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imhimanshu 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

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]

31 Mar 2012, 07:44

Thanks Bunuel.. you are awesum :-)

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Number properties [#permalink]

06 May 2012, 17:10

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

1) ac= b^2
2) b=0
3) ac=1

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

Is this correct representation of Actual GMAT questions , looks tricky

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Re: Number properties [#permalink]

06 May 2012, 18:34

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: Number properties [#permalink]

06 May 2012, 22:36

Joy111 wrote:

Merging similar questions. please ask if anything remains unclear.
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Re: If abc = b^3 , which of the following must be true? [#permalink]

12 Jun 2012, 05:07

nikhilsrl wrote:

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] 12 Jun 2012, 05:07

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

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