Vincen 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 OA is A.
I thought the right option should be E. I need a clarification here. Thanks.
Hi Vincen,
Let's list down the given information.
1. 0 < x < 10
2. Average of x and 10 = (x + 10)/2
3. z is any number, we do not have any information.
You must know that average of two numbers lies in the mid of the two numbers.
Thus,
x ≤ (x + 10)/2 ≤ 10
This implies that the average cannot be less than the smaller number and greater than the larger number.
We have to determine whether z is greater than (x + 10)/2.
Statement 1: On the number line, z is closer to 10 than it is to x.
Case 1: Say z > 10.
Refer to the following depiction in the number line.
0----x-----Av.----10----z
Since Av. would lie between x and 10, and z > 10, we see that z > Av. The answer is Yes.
Case 2: Say z ≤ 10.
Refer to the following depiction in the number line.
0----x-----Av.------z--10
Since Av. would lie exactly in mid of x and 10, it (Av.) would be equidistant from x and 10. Again, since it is given that z is closer to 10 than it is to x, we can ascertain that z > Av. The answer is Yes. Sufficient.
Hope this helps!
Download free ebook:
Manhattan Review GMAT Quantitative Question Bank Guide
-Jay
__________________________________
Manhattan Review GMAT Prep
Locations:
New York |
Warsaw |
Cape Town |
Madrid | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor!
Click here.
