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

Lets approach the easier statement (2) first: -

z = 5x and x < 10 lets pick nos

x = 4; Arithematic Mean = (4+10)/2 = 7 and z = 5x4 = 20, So z>arithematic mean.

No lets assume x = 1/4, Arithematic mean = (1/2+10)2 = 5.25, and z = 5x1/2 = 2.5, so z< arithematic mean.

So (2) is insufficient, the answer choices boils down to A & D

Now look at (1)

On number line Z is closer to 10 than x.

Assume x =2, then A.M = 6. If Z has to be closer to 10 then the Z > 6 so Z > A.M
Assume x = 6 then A.M = 8, then Z >9 so Z > A.M

for all +ve values of x<10, Z > A.M Hence (1) is sufficient.

Answer is (A)

Great explanation!! Thanks a lot. (A) is the right answer.