### Instruction: If the tens digit of positive integer x is 6 and the tens digit of positive integer y is 6, how many possible values of the tens digit of 2(x+y) can there be?
Answer Choices: (A) 2 (B) 3 (C) 4 (D) 5 (E) 6.### Response: Let's solve the multi-choice question step by step.
We only need to consider the tens and ones digits of x and y, and the last two digits can be represented as 60 + p and 60 + q respectively.
2(60+p+60+q)= 240 + 2(p + q).
2(p+q) can range from 0 up to a maximum value of 36 when p=q=9.
Then the tens and ones digits of 2(x+y) can range from 40 up to 76.
There can be 4 possibilities for the tens digit.
The answer is C.