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# If (a - b)c = 0, which of the following CANNOT be true

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If (a - b)c = 0, which of the following CANNOT be true [#permalink]  04 Mar 2017, 03:49
Expert's post
00:00

Question Stats:

71% (00:31) correct 28% (00:33) wrong based on 39 sessions

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 $$c \neq 0$$
[Reveal] Spoiler: OA

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Re: If (a - b)c = 0, which of the following CANNOT be true [#permalink]  09 Mar 2017, 19:24
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Expert's post
Explanation

The best way to go about it is to check options one by one..

A) a - b > 0 and c=0 ................ (a - b)c = 0 as c=0 true

B) a=b and c different from 0 .................. a-b=0 so (a - b)c = 0 true

C) a=b and c=0 ........................... both a-b and c terms are 0 so (a - b)c = 0 true

D) a different from b and c=0 .................... c=0 so (a - b)c = 0 holds true

E) a different from b and c different from 0 ........... $$a - b \neq 0$$ and $$c \neq 0$$ so $$(a - b)c \neq 0$$.

Hence option E is correct.
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Sandy
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Re: If (a - b)c = 0, which of the following CANNOT be true [#permalink]  24 Mar 2017, 06:23
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Expert's post
Carcass wrote:

If (a - b)c = 0, which of the following CANNOT be true?

A) a - b > 0 ad c=0

B) a=b and c different from 0

C) a=b and c=0

D) a different from b and c=0

E) a different from b and c different from 0

Given: (a - b)c = 0
Here we have something TIMES something else = 0
So, EITHER a - b = 0 OR c = 0
In other words, EITHER a = b OR c = 0

Statement E says that a DOES NOT EQUAL b and c DOES NOT EQUAL 0
This statement is false.

[Reveal] Spoiler:
E

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

Re: If (a - b)c = 0, which of the following CANNOT be true   [#permalink] 24 Mar 2017, 06:23
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