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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