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

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Fri Jun 01, 2018 1:11 am

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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

[spoiler]OA=A[/spoiler].

I don't understand this PS question. Why is A the correct choice? Can anyone explain this to me? Please.

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Source: Beat The GMAT — Problem Solving | Fri Jun 01, 2018 1:11 am

regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

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

by regor60 » Fri Jun 01, 2018 5:26 am

Try some numbers

Let B=0, then A*0*C = 0

Test the first possibility: Does A*C have to equal B^2= 0 for the above to be true ? No, A and C could be any number

Second possibility can't be ruled out since we assumed it above

Third possibility: Does A*C = 1. Not necessarily, per the first possibility

Now, try some new numbers to see if B=0 is required

Let A=1, B=1 and C=1. Do these multiplied together = B^3 =1 ? Yes. Is B=0 ?, No. Therefore the second possibility, B=0 isn't necessarily true

Answer None, A

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deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

RE:

by deloitte247 » Sat Jun 02, 2018 2:54 pm

$$abc=b^3$$
$$b\left(ac-b^2\right)=0$$
$$So,\ it\ is\ either\ b=0,\ or\ ac=b^2$$
Therefore, NONE of the given option is true
if b=0, then 'ac' will be equal to any number which makes option I and III very uncertain.

Also, If 'ac=b^2' then 'b' can also be any number so Option II is also uncertain.

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

hi

by Jeff@TargetTestPrep » Sun Jun 03, 2018 5:28 pm

Gmat_mission 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

abc - b^3 = 0

b(ac - b^2) = 0

(b = 0) or (ac - b^2 = 0 ---> ac = b^2)

Since it's either b = 0 or ac = b^2, so neither one is a must true statement. Also, nowhere we can conclude that ac = 1. So none of the statements is a must true.

Answer: A

Jeffrey Miller
Head of GMAT Instruction
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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