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.
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