BTGModeratorVI wrote: ↑Wed Feb 26, 2020 4:21 pm
If q, s, and t are all different numbers, is q < s < t ?
(1) t - q = |t - s| + |s - q|
(2) t > q
Answer:
A
Source: Official Guide
Given: q, s, and t are all different numbers
Target question: Is q < s < t ?
Statement 1: t - q = |t - s| + |s - q|
Since q, s, and t are all different numbers, we know that |t - s| is POSITIVE, and |s - q| is POSITIVE.
So, t - q = some positive number
From this we can conclude that:
q < t
On the number line we have something like this:
From here we need only determine whether s is
between q and t
To help us we can use a nice property that says:
|x - y| = the distance between x and y on the number line
For example: |3 - 10| = 7, so the distance between 3 and 10 on the number line is 7
So, the statement "t - q = |t - s| + |s - q|" tells us that: (the distance between t and q) = (the distance between t and s) + (the distance between s and q)
The ONLY time this equation holds true is when is
between q and t
Given this, it MUST be the case that
q < s < t
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: t > q
Since there is no information about s, we cannot answer the
target question with certainty.
Statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
