Number Properties (3rd ed): Chapter 1 question 17:

by **Eric_J** Sun Oct 26, 2008 1:48 pm

a, b and c are positive integers. If a < b <c and abc = 286, what is c-b?

The official answer and explanation is 2. it is based on the prime factorization of the number 286 into 2, 11 and 13, which it then says are the values of a, b and c, respectively, so 13-11 is 2. I get that.

What I don't understand is why this is the ONLY answer - for example:

a=1
b=2
c=143

seems as though it would also satisfy the question. (1,2 and 143 are positive integers, their product is 286), so the answer could also be 141.

The official answer states that a,b and c must be greater than 1, but I'm not sure where that is coming from - if the question stated that a,b and c were PRIME integers, that restriction would make sense, but as written I think the question has multiple correct answers - can someone clarify what I'm missing?

Thanks,

Eric

by **sumi** Tue Oct 28, 2008 6:22 pm

Ha!
Nice catch, I actually noticed the same issue. My mind was going through DS mentality and I almost said (E) Insufficient. Haha! Before I realized it was a PS type question.

I wrote down both answers and then checked the answers and have come to a conclusion that there was a mistype.

If the question said a, b and c are prime integers then it would not be a problem.

Agreed?

Sumi

by **RonPurewal** Sat Nov 15, 2008 7:25 am

apparently both of you failed telepathy class. ;)
the problem was supposed to broadcast strong subliminal messages of greater-than-one-ness.

nice catch. it will be noted, and fixed in the next edition (which is some way off at this point).