If \(x\) is a positive number less than \(10,\) is \(z\) greater than the average (arithmetic mean) of \(x\) and \(10?\)

[Vincen]

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

[Brent@GMATPrepNow]

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