Statement 1 : Keith Pat Steve
x 2 x
Total = 3x
Not enough information to solve for x
Statement 1 not sufficient

Statement 2 : Keith. Pat. Steve
x 109-x
126-(109-x)
= 17+ x
Total = x + 17 + x + 109 - x
= 126 + x
Not enough information to solve for x
Statement 2 not sufficient

Statement 1 and 2 together :

Keith. Pat. Steve
x. 17+x. 109-x
Keith+ pat = 2*steve
x + 17+ x = 2*(109-x)

Can be solved for x

Statement 1 and 2 together are sufficient

Hence C.

Question stem asks for the sum of K+S+P.

Statement 1) gives you only something like a ratio : K+P=1/2 S --> Not sufficient
Statement 2) gives you only K+S=109 P+S=126 --> 3 variables, two equations --> Not sufficient.

Together they yield: one ratio between K+P and S ; K+S=109; P+S=126. Now you can rearrange K+S=109 to K=109-S . & P+S=126 to P=126-S
Now you can express both K and P in times of S and hence you can insert them in equation ratio from 1 and you have one equation with just one variable left : S. Hence, you can solve for S and since you know how S+P depend on S you know that you can calculate the sum of K+P+S

Hence, C