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Difficulty:
15%
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Question Stats:
88% (00:55) correct
13%
(00:38)
wrong
based on 40
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If \((a - b)c = 0\), which of the following CANNOT be true?
A) \(a - b > 0\) and \(c=0\)
B) \(a=b\) and \(c \neq 0\)
C) \(a=b\) and \(c=0\)
D) \(a \neq b\) and \(c=0\)
E) \(a \neq b\) and \(c \neq 0\)
A) \(a - b > 0\) and \(c=0\)
B) \(a=b\) and \(c \neq 0\)
C) \(a=b\) and \(c=0\)
D) \(a \neq b\) and \(c=0\)
E) \(a \neq b\) and \(c \neq 0\)
31 Jul 2022, 12:43
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Bunuel
If \((a - b)c = 0\), which of the following CANNOT be true?
A) \(a - b > 0\) and \(c=0\)
B) \(a=b\) and \(c \neq 0\)
C) \(a=b\) and \(c=0\)
D) \(a \neq b\) and \(c=0\)
E) \(a \neq b\) and \(c \neq 0\)
A) \(a - b > 0\) and \(c=0\)
B) \(a=b\) and \(c \neq 0\)
C) \(a=b\) and \(c=0\)
D) \(a \neq b\) and \(c=0\)
E) \(a \neq b\) and \(c \neq 0\)
\((a - b)c = 0\) : If the product of 2 terms is 0, there can be three different cases (First term 0, Second term 0, Both terms 0)
Case 1: \(a-b = 0 => a=b\) and \(c \neq 0\)
Case 2: \(c = 0\) and \(a - b \neq 0 => a \neq b\)
Case 3: \(c = 0\) and \(a - b = 0 => a = b\)
Now, if you look at the options
A) \(a - b > 0\) and \(c=0\)
It can be true because if \(c=0\) then \(a-b\) can be anything
B) \(a=b\) and \(c \neq 0\)
It can be true because it matches perfectly with our Case 1
C) \(a=b\) and \(c=0\)
It can be true because it matches perfectly with our Case 3
D) \(a \neq b\) and \(c=0\)
It can be true because it matches perfectly with our Case 2
E) \(a \neq b\) and \(c \neq 0\)
Now this cannot be true. Because if \(c \neq 0\) and a \neq b[/m] it means that neither terms of the product are equal to 0. Then the original condition does not work
Answer - E
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