Bunuel 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
I received a PM about this question.
Here's my solution:
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 10Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: z = 5xThere 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:
Cheers,
Brent
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