Vincen wrote: ↑Sun May 09, 2021 2:18 pm
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) \(z = 5x\)
Answer:
A
Source: Official Guide
Target question: Is z greater than the mean of x and 10?
Statement 1: On the number line, z is closer to 10 than it is to x.
IMPORTANT: On the number line, the mean of two numbers will lie at the
midpoint between those two numbers.
So, the mean of x and 10 will lie
halfway between x and 10.
So, if z is closer to 10 than it is to x, then
z must lie to the right of the midpoint between x and 10.
This means that
z must be greater than the mean of x and 10
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: z = 5x
There are several pairs of numbers that meet this condition. Here are two:
Case a: x=1, z=5, in which case
z is less than the mean of x and 10 (mean = 5.5)
Case b: x=4, z=20, in which case
z is greater than the mean of x and 10 (mean = 7)
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
