The number of 75 can be written as the sum

dtl wrote:Is there any quick method to approach this question instead of testing cases?

there's no other method.
on the other hand, your question suggests that you consider testing cases "slow" -- which means that your approach probably lacks organization. if your testing of cases is properly organized, it should be quite fast.

as just one example, you could organize the cases according to the single biggest possible number, and work your way down.

* 9^2 is more than 75, so the biggest possible single number is 8.

* if one of the numbers is 8, then 8^2 = 64. that leaves 75 - 64 = 11 for the other two numbers.
there are no two integers whose squares add up to 11 (a fact you can figure out in about five seconds), so 8 can't be one of the numbers.

* if one of the numbers is 7, then 7^2 = 49, leaving 75 - 49 = 26 for the other two numbers.
you can make 26 = 5^2 + 1^2.
so, your numbers are 7, 5, and 1.

fast and painless.

dtl wrote:The number of 75 can be written as the sum of the squares of 3 different positive integer. What's the sum of these 3 integer?

A. 17
B. 16
C. 15
D. 14
E. 13

Is there any quick method to approach this question instead of testing cases? Please help.. Thank you!

Refer to the post: https://www.beatthegmat.com/sum-of-squar ... 00899.html