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# If ab = ac is b = 2 ?

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Manager
Joined: 14 Dec 2011
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If ab = ac is b = 2 ? [#permalink]

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16 Jan 2013, 08:57
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If ab = ac is b = 2 ?

(1) c = 1
(2) a is a prime number and c is NOT a prime number

I got this step correct $$a(b-c)=0$$ : either $$a=0$$ or $$b=c$$

But (1), i selected this one as the answer along with (2)
Not sure why this isn't correct. My understanding says b = 1 because b = c, which is 1.
Not able to understand (1)'s explanation:- $$c=1$$ . If $$a=0$$ then $$b$$ can take any value irrespective of the value of $$c$$ . Not sufficient.

Thanks & Regards
Vinni
Math Expert
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Re: If ab = ac is b = 2 ? [#permalink]

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16 Jan 2013, 10:01
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Expert's post
vinnik wrote:
If ab = ac is b = 2 ?

(1) c = 1
(2) a is a prime number and c is NOT a prime number

I got this step correct $$a(b-c)=0$$ : either $$a=0$$ or $$b=c$$

But (1), i selected this one as the answer along with (2)
Not sure why this isn't correct. My understanding says b = 1 because b = c, which is 1.
Not able to understand (1)'s explanation:- $$c=1$$ . If $$a=0$$ then $$b$$ can take any value irrespective of the value of $$c$$ . Not sufficient.

Thanks & Regards
Vinni

OFFICIAL SOLUTION:
If $$ab=ac$$ is $$b=2$$?

Notice that we cannot reduce $$ab=ac$$ by $$a$$ and write $$b=c$$, since $$a$$ can be zero and division by zero is not allowed. $$ab=ac$$ --> $$a(b-c)=0$$ --> either $$a=0$$ or $$b=c$$.

(1) $$c=1$$ --> if $$a=0$$ then $$b$$ can tale any value irrespective of the value of $$c$$. Not sufficient.

(2) $$a$$ is a prime number and $$c$$ is NOT a prime number --> $$a=prime$$ means that $$a\neq{0}$$, so it must be true that $$b=c$$. Now, since also given that $$c\neq{prime}$$ then $$b$$ is also not equal to a prime number so it cannot equal to a prime number 2. Sufficient.

As for your question. We have that either a=0 OR b=c.

Now, if for (1) a=0, then b can take ANY value. Consider a=0, c=1 and b=(any value) --> ab=ac=0.

Hope it's clear.
_________________
Manager
Joined: 14 Dec 2011
Posts: 76
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Re: If ab = ac is b = 2 ? [#permalink]

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16 Jan 2013, 10:45
Bunuel wrote:
As for your question. We have that either a=0 OR b=c.

Now, if for (1) a=0, then b can take ANY value. Consider a=0, c=1 and b=(any value) --> ab=ac=0.

Hope it's clear.

ab = ac
0 * b = 0 * 1

got it. Thank you.

Regards
Vinni
Re: If ab = ac is b = 2 ?   [#permalink] 16 Jan 2013, 10:45
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# If ab = ac is b = 2 ?

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