Problem Solving

The number 75 can be written as the sum of the squares of 3 different positive integers. What is the sum of these integers?

a) 17
b) 16
c) 15
d) 14
e) 13

not sure of a better way to do it, but you should know that the largest of the three digits should be less than 9, since 9^2 = 81 is greater than 75. So you have numbers 1 through 8.

From then on, its a plug and chug game. Take 8^2 = 64, leaving 11. There is no combination of 2 numbers whose sum will give you this. Move on.

7^2 = 49, leaving a difference of 26. Are there 2 numbers whose squares sum up to 26? Yes, 5^2 + 1^2 = 25 + 1 = 26.

So your digits are 1,5,7, and sum of these is 13. Choice E.