If x is a positive number less than 10, is z greater than the average of x and 10
1) On the number line, z is closer to 10 than it is to x
2) z=5x
1) On the number line, z is closer to 10 than it is to x
2) z=5x
Let's plug in some values.
For statement 1, let's say x=8. That would make the average of x and 10 = 9. For z to be closer to 10 than it is to x, z would have to be greater than 9, so also greater than the average of x and 10. The same thing would happen if you plugged in x=6. The average of x and 10 is now 8. z would have to be greater than 8 to be closer to 10 than to x. This is always going to be the case, since z will always have to be at least a tiny bit above the average in order to be closer to 10 than to x. So, this is sufficient.
For statement 2, let's again say that x=8. z would then be 40, which is well over 9, the average of x and 10.
Now let's say that x=.0000001 (or, as close to zero as possible). That would make the average of x and 10 = 5 (plus a tiny, tiny bit). z would then be .0000005, which is less than the average of x and 10. So, not sufficient, since we said "yes" and "no" to this statement.
I'm going to say the correct choice is A.
