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If 2ab - c = 2a(b - c), which of the following must be true?

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If 2ab - c = 2a(b - c), which of the following must be true? [#permalink]

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New post 26 May 2016, 10:58
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A
B
C
D
E

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  35% (medium)

Question Stats:

62% (01:02) correct 38% (01:00) wrong based on 209 sessions

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Joined: 05 Oct 2015
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GMAT 1: 700 Q50 V34
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Re: If 2ab - c = 2a(b - c), which of the following must be true? [#permalink]

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New post 26 May 2016, 11:21
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2ab - c = 2a(b - c)

=> 2ab - c = 2ab - 2ac
=> - c = - 2ac
=> c = 2ac
=> c - 2ac = 0
=> c (1 - 2a) = 0
Either c = 0 or 1 - 2a = 0 i.e. a = 1/2.
Hence, E
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Re: If 2ab - c = 2a(b - c), which of the following must be true? [#permalink]

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New post 28 May 2016, 05:48
What about answer choice A?
c(1-2a)=0; so if a=0 then c=0
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Re: If 2ab - c = 2a(b - c), which of the following must be true? [#permalink]

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New post 28 May 2016, 09:16
jurin wrote:
What about answer choice A?
c(1-2a)=0; so if a=0 then c=0


If 2ab - c = 2a(b - c), which of the following must be true?

so as you have shown c(1-2a) = 0
(A) a=0 and c=0
This is NOT necessarily MUST

Yes this is ONE value which fits in, BUT we are looking for MUST be TRUE....
If a= 1/2...then c(1-2a) = 0
or c=0..... then c(1-2a) = 0...

SO it is MUST that either of two c=0 or a=1/2 has to be true for the equation to hold good...
Even (A) contains c=o..
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Re: If 2ab - c = 2a(b - c), which of the following must be true? [#permalink]

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New post 28 May 2016, 10:01
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Bunuel wrote:
If 2ab - c = 2a(b - c), which of the following must be true?

(A) a=0 and c=0
(B) a=1/2 and b=2
(C) b=1 and c=0
(D) a=1 or b=0
(E) a=1/2 or c=0



2ab-c = 2a (b-c)

2ab - c = 2ab - 2ac

c= 2ac

2ac-c = 0
c(2a-1) = 0

Either c = 0; or a = 1/2

E is the answer
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Re: If 2ab - c = 2a(b - c), which of the following must be true? [#permalink]

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New post 11 Aug 2017, 05:00
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Re: If 2ab - c = 2a(b - c), which of the following must be true?   [#permalink] 11 Aug 2017, 05:00
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