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Re: If abc = b3 , which of the following must be true? [#permalink]
20 Feb 2011, 07:41

1

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

Re: If abc = b3 , which of the following must be true? [#permalink]
30 Mar 2012, 09:55

1

This post received KUDOS

Expert's post

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 --> EITHERb=0ORac=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".

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