# Math

A history quiz consists of 60 points and contains questions that ate either true/false or multiple-choice. If a true/false question is worth 3 points and a multiple-choice question is worth 8 points, and the quiz has at least one question of each type, what is a possible number of multiple choice questions on the quiz?

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1. If there are m 8-point questions and t T/F questions, you need

8m+3t = 60
m >= 1 and t >= 1
So, clearly m <= 7 since 8*8 > 60

So, just list the possibilities:
1*8=8 and 3 does not divide 60-8=52
2*8=16; 3∤44
3*8+12*3 = 60 ok!

you might want to check for other answers in the same way

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