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
If q, s, and t are all different numbers, is q < s < t ?
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Given: q, s, and t are all different numbersBTGModeratorVI wrote: ↑Sun Aug 02, 2020 6:55 amIf 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
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