tonebeeze wrote: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

0<x<10, Is z > (10+x)/2 ?
=> Is 2z > (10+x) ?

Statement 1:

See the number line drawn below :-

0.......x.....a.....10........

a = avg of (x and 10) = (10+x)/2

As per the first statement, z lies between either a and 10 or right side of 10 (means z>10).

In both the cases: z> (10+x)/2 -> sufficient

Statement 2:
z = 5x
So, 2z > (10+x) ?
=> 10x > (10+x) ?
=> x > 10/9 ? --- Insufficient (As x can be 0<x<10/9 or 10/9<=x<10 and in these two cases the inequality will be either true or false).

So, A

For statement (2) I did this:

(2) z = 5x

0< x <10
0< 5x < 50 (multiplied by 5)
0 < z < 50 (substitute 5x by z)

Is z> (x+10)/2? Insufficient as z could be very close to 0 or very close to 50.

Correct me if I'm wrong...

tonebeeze wrote: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

The average of any 2 numbers is the value right in the middle (equidistant from each number):

For example:
Given 0 and 10, the average = (0+10)/2 = 5, which is halfway between 0 and 10 on the number line.
Given 1/8 and 5/8, the average = (1/8 + 5/8)/2 = 3/8, which is halfway between 1/8 and 5/8 on the number line.

In the problem above, the order of the values is:

0-----x-----10

Statement 1: Z is closer to 10 than it is to X
If Z is closer to 10 than it is to X, then Z is greater than the value halfway between X and 10. Thus, Z is greater than the average.
Sufficient.

Statement 2: Z = 5X
If X=2, then Z = 5*2 = 10, which is closer to 10 than it is to 2. Thus, Z is greater than the average of 2 and 10.
If X=1/2, then Z = 5*(1/2) = 5/2, which is closer to 1/2 it is than to 10. Thus, Z is less than the average of 1/2 and 10.
Z can be both greater than and less than the average.
Insufficient.

The correct answer is A.