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Difficulty:
35%
(medium)
Question Stats:
67% (01:28) correct
33%
(01:44)
wrong
based on 428
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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
_________________
(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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ashutoshyadav1707
Joined: 05 Oct 2015
Last visit: 03 Oct 2018
Posts: 5
Location: India
GMAT 1: 700 Q50 V34
WE:Education (Education)
GMAT 1: 700 Q50 V34
Posts: 5
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
=> 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
jurin
Joined: 12 Jul 2015
Last visit: 12 Feb 2018
Posts: 7
Location: Canada
Concentration: Strategy, Finance
Schools: Ivey '17 Queens'17 Desautels '17
GPA: 3.62
WE:Project Management (Energy)
Schools: Ivey '17 Queens'17 Desautels '17
Posts: 7
What about answer choice A?
c(1-2a)=0; so if a=0 then c=0
c(1-2a)=0; so if a=0 then c=0
jurin
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..
_________________
Bunuel
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
KanishkM
Joined: 09 Mar 2018
Last visit: 18 Dec 2021
Posts: 755
Location: India
Schools: DeGroote'21 Desautels '21 NUS '21
Schools: DeGroote'21 Desautels '21 NUS '21
Posts: 755
Bunuel
if 2ab -c = 2ab - 2ac
-c = - 2ac
2ac - c = 0
c(2a - 1) = 0
c= 0 & a=1/2
E
Posts: 4
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?
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?
Vineela.mk
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.
_________________
Vineela.mk
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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Vineela.mk
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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