Data Sufficiency

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



My answer is E but OA is A.
How can A be the answer?
If Z=9 ans X=8, Z is same as the average of X and 10
If Z=9 and X=6, Z is greater than the average of X and 10
If Z=2 and X=1, Z is less than the average of X and 10

Z is closer to 10 in all above case but can be same, greater, or less than the average of X and 10. What am I missing?

josephcho77, IMO A. Refer the approach below -


|-------------------------------------------------------------------------|
X Z 10

Now if Z is closer to 10 than X, (10 + X) / 2 should be some thing less than Z. So option - I gives the answer to the question. Are u getting me? Even if u take an example -
X = 1 and Z = 9
So (X + 10) / 2 = 5.5 where Z > 5.5. So option - I gives the answer.

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

let avg of of X & 10 be a so a will be midway between 10 & x

now since X < 10 hence the possibilty here is

x a 10 now if z is to the left a anywhere on the nos line then it will be closer to x & if z is to the right of a then only it is closer to 10 so SUFF

2) Z=5X

INSUFF

A

hope this makes sense