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

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Math Expert
Joined: 02 Sep 2009
Posts: 58340
If 2ab - c = 2a(b - c), which of the following must be true?  [#permalink]

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26 May 2016, 11:58
1
6
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Difficulty:

35% (medium)

Question Stats:

66% (01:23) correct 34% (01:40) wrong based on 205 sessions

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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

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Joined: 05 Oct 2015
Posts: 5
Location: India
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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26 May 2016, 12:21
1
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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28 May 2016, 06:48
c(1-2a)=0; so if a=0 then c=0
Math Expert
Joined: 02 Aug 2009
Posts: 7957
Re: If 2ab - c = 2a(b - c), which of the following must be true?  [#permalink]

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28 May 2016, 10:16
jurin wrote:
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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28 May 2016, 11:01
1
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

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

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09 Feb 2019, 05:18
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

if 2ab -c = 2ab - 2ac

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

E
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Re: If 2ab - c = 2a(b - c), which of the following must be true?   [#permalink] 09 Feb 2019, 05:18
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