If x is a positive number less than 10, is z greater than the average (arithmetic mean) 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.

this means that it is the the right (larger) than the average (m) and so (1) is sufficient. We can rule out B,C,E.

2) z=5x

This one is trying to trap people who don't read the problem carefully. X is a positive number less than 10, not necessarly an integer. consider x=.1. Then the mean of x and 10 is 5.05. if z=5x, then z is .5 and is smaller than the mean. Now consider x=2. The mean of x and 10 is then 6. z=5x=10 and is larger than the mean. So 2 is not sufficient and the answer is A.