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If ab = ac is b = 2 ?

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If ab = ac is b = 2 ? [#permalink] New post 16 Jan 2013, 07:57
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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.

Please explain this in detail.

Thanks & Regards
Vinni
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Re: If ab = ac is b = 2 ? [#permalink] New post 16 Jan 2013, 09:01
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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.

Please explain this in detail.

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.

Answer: B.


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.
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Manager
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Re: If ab = ac is b = 2 ? [#permalink] New post 16 Jan 2013, 09:45
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, 09:45
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