Add any three numbers of the following and answer should be 60
2 , 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58

Hit and trial, no other way. Its all about how you see numbers, the better you see numbers the lesser iterations required to get the results. 

x+y+z=60

Fix the value of x to some random number( say 38), now we have 22 more units to be divided between  "y" and "z", so by randomly looking at numbers we can say that there are no results possible.

Choose another no. as "x"( say 30) , so we have 30 units between "y" and "z", still not able to reach conclusion. 

Choose another no as "x"(say 26), so we have 34 units between "y" and "z", still not able to sum up to 60.

SO after analyzing all probabilities, I came to conclusion that it is indeed a trap question!! and no real solution exists. 

But a smart  solution, not a mathematical is,
58+2=60, here we have used rather 3 digits(not numbers) to reach our goal.