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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: 53020
If 2ab - c = 2a(b - c), which of the following must be true?  [#permalink]

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26 May 2016, 10:58
1
5
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Difficulty:

35% (medium)

Question Stats:

67% (01:23) correct 33% (01:37) wrong based on 157 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: 6
Location: India
GMAT 1: 700 Q50 V34
WE: Education (Education)
Re: If 2ab - c = 2a(b - c), which of the following must be true?  [#permalink]

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26 May 2016, 11:21
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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Joined: 12 Jul 2015
Posts: 11
Concentration: Strategy, Finance
GPA: 3.62
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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, 05:48
c(1-2a)=0; so if a=0 then c=0
Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: If 2ab - c = 2a(b - c), which of the following must be true?  [#permalink]

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28 May 2016, 09:16
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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
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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, 10:01
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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Joined: 09 Mar 2018
Posts: 1001
Location: India
Re: If 2ab - c = 2a(b - c), which of the following must be true?  [#permalink]

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09 Feb 2019, 04:18
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, 04:18
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