sjgudapa wrote:

I agree with the solution . It is D.

When I looked at the problem. I thought I should use permutations rather than combinations. My solution was not one of the answer choices and hence switched to Combinations.

Could somebody explain , why combinations should have been the choice in lay man terms.

Thanks a lot

I would suggest to forget about combinations, permutations, factorials...

Think of the real process and translate the steps into simple arithmetic operations:

For a triangle, we need three different vertices, which are not all three on the same line.

Choose one vertex, say A, from the points on the line with the 7 points and the two other vertices, say B and C, from the points on the line with the 8 points.

For A we have 7 choices, and for each of these, for B 8 choices, then for C 7 choices. This will translate into 7 * 8 * 7 choices, but we must divide by 2, because choosing first B, then C, will produce the same triangle as choosing first C and then B. So, we can get 7 * 8 * 7/2 distinct triangles.

Repeat the above process for triangles with vertex A on the line with 8 points, and vertices B and C on the line with 7 points.

This will give you 8 * 7 * 6 / 2 triangles.

All the triangles chosen above are distinct. Therefore, the total number of triangles is 7 * 4 * 7 + 4 * 7 * 6 = 28(7 + 6) = 28 * 13 <--- this should end in 4, and luckily, we have just one answer which ends in 4. If there would have been more than one answer which ends in 4, we should have carried out the multiplication or do some other estimate.

So, the correct answer is 364.

Answer: D

_________________

PhD in Applied Mathematics

Love GMAT Quant questions and running.