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Re: If abc = b3 , which of the following must be true? [#permalink]
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
Re: If abc = b3 , which of the following must be true? [#permalink]
30 Mar 2012, 09:55
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Expert's post
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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.
Re: Number properties [#permalink]
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".
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]
08 Oct 2014, 21:47
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Re: If abc = b^3 , which of the following must be true? [#permalink]
10 Oct 2015, 19:57
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