If the lengths of two sides of a certain triangle are 5 and 10, what

If the lengths of two sides of a certain triangle are 5 and 10, what is the length of the third side of the triangle

(1) Perimeter of the triangle is a multiple of 5
(2) The triangle is isosceles

We can modify the original condition and the question. If we designate the three sides of the triangle as x, we get 10-5<x<10+5, which is same as 5<x<15. There is 1 variable (x) in the original condition. In order to match the number of variables to the number of equations, we need 1 more equation. Since the condition 1) and the condition 2) each has 1 equation, there is high chance that D is the correct answer choice.
For the condition 1), since x=10, the answer is unique and the condition is sufficient.
For the condition 2), from 5:5:10 and 5:10:10, only 5:10:10 is possible. Hence, the answer is unique and the condition is sufficient. Therefore, the correct answer is D.
l For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.