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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
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A
B
C
D
E

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  35% (medium)

Question Stats:

50% (01:57) correct 50% (00:42) wrong based on 62 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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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 --> 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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Number properties [#permalink] New post 06 May 2012, 16:10
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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] 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: Number properties [#permalink] New post 06 May 2012, 21:36
Expert's post
Joy111 wrote:
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


Merging similar questions. please ask if anything remains unclear.
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PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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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] 12 Jun 2012, 04:07
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