2 Questions...

1) How much time should be spent on a problem like this? I imagine even when you are very efficient, it's going to take a long time.

2) Is there an alternative method that can be applied to reduce the burden of testing all of those numbers?

Follow Up...

Is the quick answer that in order for (2/7)y to have a positive integer x as the average, y must be a multiple of 7? Since y is 1, 2, 3, 4, 5, or 6, it is impossible for (E) to be the answer.

All of the explanations make sense, but what I found to be missing was how you arrive at (6,8) or (8,6) and the additional coordinate variations. Here is what I did to methodically solve for them: a^2 + b^2 = c^2, we know that c=10 a^2 + b^2 = 100 a a^2 b √b c^2 1 1 99 9√11 does not work 2 4 96 ...

Okay, if i'm interpreting things correctly, it looks like your question boils down to why we have to account for order when drawing a red and a white marble but not when drawing two reds. Ultimately it comes to this: If you are drawing one of each, you will either need to get a red and then a white...