Bunuel wrote:

For any integers a and b, min(a, b) and max(a, b) denote the minimum and maximum of a and b, respectively. For example, min(1, 2) = 1 and max(1, 2) = 2. If x, y, and z are integers, what is max(y, 8)?

(1) min(9, x) = y

(2) min(6, z) = y

Question: What is max(y, 8)?

To find max(y, 8), we need to know if y > 8 or not.

If y = 8.1 or 9 or 10 or any value greater than 8, max(y, 8) would be y.

Otherwise, max(y, 8) would be 8. If y = 8 or if y < 8, the answer would be 8.

Essentially, the question is: Is y > 8?

1. Statement 1: min(9, x) = y

i.e., if x < 9, min(9, x) = x = y

if x = 9 or x > 9, min(9, x) = 9 = y

But, we don't know the value of x. Therefore, we cannot know if y = 9 or if y = x . If x = 8.5, y could be 8.5. If x = 5, y could be 5. If x = 10, y could be 9. Hence, this statement isn't sufficient to know if y > 8.

2. Statement 2: min(6, z) = y

i.e., if z < 6, min(6, z) = z = y

if z = 6 or z > 6, min(6, z) = 6 = y

Therefore, irrespective of z's value, it is clear that y will not be greater than 6, i.e.,

y = 6 or y < 6.

Thus, the question is y > 8 can be answered with this statement.

Since statement 1 is not sufficient and only statement 2 is sufficient, answer is

B.