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

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Bunuel
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If 2ab - c = 2a(b - c), which of the following must be true? [#permalink] New post   26 May 2016, 11:58
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A
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E

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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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E
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Re: If 2ab - c = 2a(b - c), which of the following must be true? [#permalink] New post   26 May 2016, 12:21
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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] New post   28 May 2016, 06:48
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] New post   28 May 2016, 10:16
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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] New post   28 May 2016, 11:01
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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] New post   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] New post   16 Sep 2023, 05:39
Why is a = 0 and c = 0 not a solution?

2ab - c = 2ab - 2ac

If we substitute a = 0, and c = 0, then 2ab - c = 0, and 2ab - 2ac = 0. Why the substitution not allowed here?
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Re: If 2ab - c = 2a(b - c), which of the following must be true? [#permalink] New post   16 Sep 2023, 06:33
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Vineela.mk wrote:
Why is a = 0 and c = 0 not a solution?

2ab - c = 2ab - 2ac

If we substitute a = 0, and c = 0, then 2ab - c = 0, and 2ab - 2ac = 0. Why the substitution not allowed here?


When you substitute c=0, then we get 2ab=2ab, meaning an and b can be any value on earth as both sides will always remain equal.
So, why should it be a MUST that a=0?
Even if \(a\neq 0\), 2ab-c=2a(b-c) when c=0.
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Re: If 2ab - c = 2a(b - c), which of the following must be true? [#permalink] New post   16 Sep 2023, 06:37
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Vineela.mk 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

Why is a = 0 and c = 0 not a solution?

2ab - c = 2ab - 2ac

If we substitute a = 0, and c = 0, then 2ab - c = 0, and 2ab - 2ac = 0. Why the substitution not allowed here?


From 2ab - c = 2a(b - c), we get:
2ab - c = 2ab - 2ac
c - 2ac = 0
c(1 - 2a) = 0

This gives two possible solutions:

c = 0 (and in this case, a can be any value)
a = 1/2 (and in this case, c can be any value)

Answer: E.

To address your doubt: the question asks "which of the following must be true?" a=0 AND c=0 is NOT always true. For instance, if a = 1/2, c can be any value, not just 0.

Hope it's clear.
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Re: If 2ab - c = 2a(b - c), which of the following must be true? [#permalink] New post   16 Sep 2023, 09:45
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Vineela.mk wrote:
Why is a = 0 and c = 0 not a solution?

2ab - c = 2ab - 2ac

If we substitute a = 0, and c = 0, then 2ab - c = 0, and 2ab - 2ac = 0. Why the substitution not allowed here?


Though you have already got two perfect explanations, let me add one last point here: this is a 'must be true' question, not 'could be true'. It is a tricky point of distinction that GMAT loves to test on :)
Check this post for an explanation of this distinction: https://anaprep.com/algebra-must-be-tru ... questions/
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Re: If 2ab - c = 2a(b - c), which of the following must be true? [#permalink]
16 Sep 2023, 09:45
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