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

Let's take each statement one by one.

(1) t – q = |t – s| + |s – q|

Since |t – s| and |s – q| are positive, we have t – q positive; thus, t > q.

Case 1: Say q < s < t

We have t – q = |t – s| + |s – q|

t – q = t – s + s – q
t – q = t – q

This case holds true. The answer is yes.

Case 2: Say s < q < t

We have t – q = |t – s| + |s – q|

t – q = t – s – s + q; since s < q
t – q = t –2s + q

This case does not hold true.

Case 3: Say q < t < s

We have t – q = |t – s| + |s – q|

t – q = –t + s + s – q; since t < s
t – q = –t + 2s – q

This case does not hold true.

Thus, only Case 1 is applicable. The answer is yes. Sufficient.

(2) t > q

Certainly, insufficient.

The correct answer: A

Hope this helps!

-Jay
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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