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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
