What is the units digit of the positive integer x?

Data is sufficient if we can find a unique value for the units digit of positive integer x. If we get more than one value, data is not sufficient.

Statement 1:The units digit of x^2 is greater than the units digit of x^3
Approach: Look for more than one value that will satisfy the above condition.
Possibility 1: x = 3. Units digit of x^2 is 9 and units digit of x^3 is 7.
Possibility 2: x = 4. Units digit of x^2 is 6 and units digit of x^3 is 4

More than one possibility exists. Statement 1 alone is not sufficient.

Statement 2: The units digit of x is greater than the units digit of x^2
Approach: Look for more than one value that will satisfy the above condition.
Possibility 1: x = 8. Units digit of x^2 is 4.
Possibility 2: x = 9. Units digit of x^2 is 1.

More than one possibility exists. Statement 2 alone is not sufficient.

Combine the statements:The units digit of x^2 is greater than the units digit of x^3 and The units digit of x is greater than the units digit of x^2
Approach: List units digit of x, x^2 and x^3 for all 10 units digits

1. x = 1, x^2 = 1, x^3 = 1. Does not satisfy.
2. x = 2, x^2 = 4, x^3 = 8. Does not satisfy.
3. x = 3, x^2 = 9, x^3 = 7. Does not satisfy.
4. x = 4, x^2 = 6, x^3 = 4. Does not satisfy.
5. x = 5, x^2 = 5, x^3 = 5. Does not satisfy.
6. x = 6, x^2 = 6, x^3 = 6. Does not satisfy.
7. x = 7, x^2 = 9, x^3 = 3. Does not satisfy.
8. x = 8, x^2 = 4, x^3 = 2. Satisfies both conditions.
9. x = 9, x^2 = 1, x^3 = 9. Does not satisfy.
10. x = 0, x^2 = 0, x^3 = 0. Does not satisfy.

The only value that satisfies both conditions is 8. So, we can find a unique value using the two statements.
Choice C is the answer.