M06-24

from ab = ac; => a(b-c) = 0;
it means
either a=0 or b=c.

Now,
from stat 1 we do not know what would be the value of a ?
if a = 0 then b can be take any value and equation ab = ac will still satisfy.right !
so stat 1 not sufficient.


from stat 2 we are given that a is not zero.
now if a is not zero, we can say b = c; (from either a= 0 or b = c).
and c is not a prime number, then b also wont be a prime number.
is b = 2 ? NO! (2 is a prime)
stat 2 is sufficient.

I think this is a high-quality question and I agree with explanation.

I think this is a high-quality question and I agree with explanation.

Good question. I missed to consider a=0 in option A and considered it as sufficient and marked C as answer incorrectly.

Thanks Bunuel for explanation

I think this is a high-quality question and I agree with explanation. Really good question !!!

I think this is a high-quality question and I agree with explanation. Oh boi

I think this is a high-quality question and I agree with explanation.

Hello, everyone. I approached this question as a scientist would, asking whether b COULD or MUST equal 2 and running a few trials. With Statement (1), if c = 1, we know that ab = a. Is b allowed to be 2 in such an equation? Sure, as long as a equals 0. But then this notion, that a = 0, leads to the thought that b could just as well be anything other than 2, and the equation would still be valid. Conflicting results mean that Statement (1) is NOT sufficient.

For Statement (2), the smallest prime number that a can be is 2. We can substitute this value right away into the given equation:

\((2)b = (2)c\)

We can divide out the 2's to reach a logical endpoint:

\(b = c\)

Now, can b equal 2? Well, if c is NOT a prime number, then no, b cannot be 2. There is no need to test other prime values for a, since 3, 5, 7, 11, 13, and so on would only lead to the same simplified equation, that b = c. In the end, if c is NOT prime and b equals c, then b CANNOT be 2. A single answer to the question, namely NO, is sufficient, so the answer must be (B).

I hope this post may help someone who may have assumed too much (or too little) and jumped to a rash conclusion. Good luck with your studies.

- Andrew

very interesting question, I keep forgetting to include the value 0.

any tips on when to consider the value 0?

It is important to never reduce an equation by a variable or by an expression that contains a variable, unless we are sure that the variable or expression is not equal to zero. Dividing by zero is undefined and not allowed.

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

I think this is a high-quality question and I agree with explanation.