NP pg 38 #16

[mobenny]

Are there any tricks to solve this question faster. Or, does it just take a while any way you look at it?

I can answer it correctly, but it takes me more than 2 min.

Thanks,

Moses

[JonathanSchneider]

Actually, yes. First, notice that John will get either 2, 5, 7, or 11 points whenever he participates. This should tell you right away that we're probably dealing with primes. Now, note that we want to find the product of the individual point values, and that this value will be equal to 84,700.

So, start by finding the prime factors of 84,700. I'll show you how I'd break that down, line by line:

84,700
847 * 100
77 * 11 * 100 (I found 77 because I knew 7 and 11 were likely involved.)
2 * 2* 5 * 5 * 7 * 11 * 11 (100 is two 2's and two 5's)
So, you have a total of 7 numbers, or 7 times that John competed.

I did that in under 2 minutes.

HOWEVER, note that not all of our SG problems are two-minute problems. So, if a problem takes you more than 2 minutes, so be it. You actually do not need to be timing yourself for these. Just time yourself for OG problems and CATs (as well as our Question Banks online, if you do them).