math contest question

My favorite math question was number 15.

In the multiplication show, P and Q ecah represent a single digit, and the product is 32951. What is the value of P + Q?

39P x Q3 = 32951

First, you know that 3 x P has to be a digit that ends in a 1, because the product ends in a 1. Therefore, 3 x 7 = 21.
Now we made an educated guess that P = 7, So than you plug in:
397 x 3 to get the first product.
397 x 3 = 1191.
Now you have to find out that, 32951 (the ending product)- 1191 (The first product) = x (The second product)
Therefore x + 1191 = 3295.
which is 31760.
Than you have to say that Q x 7 = a digit that ends in a 6.
So you make an educated guess that Q would = to 8.
than you plug in 397 x 83 which equals to 32951.
than you add Q + P = 7 + 8 = 15.
Thus, your answer would be 15.

I like this question because at first it seems really hard, but if you use logic to figure it out, it is actually a simple question. AFter I figured out the answer, I felt really smart! ^^