OG If q, s and t are all different numbers

[AbeNeedsAnswers]

If q, s and t are all different numbers, is q < s < t?

(1) t - q = |t - s| + |s - q|
(2) t > q

A

[NandishSS]

Bumping!!!

[NandishSS]

HI Guru,

Easily eliminated B. How to solve the que within 2 min?

Thanks
Nandish

[GMATGuruNY]

If q, s and t are all different numbers, is q < s < t?

(1) t - q = |t - s| + |s - q|
(2) t > q

Statement 1:
Since q, s and t are different numbers, and an absolute cannot be negative, we get:
t-q = positive + positive = positive.
Since t-q > 0, we get:
t>q.

Test an EASY CASE:
t=2 and q=0.
Plugging t=2 and q=0 into t - q = |t - s| + |s - q| , we get:
2 = |2-s| + |s|.
Given that q, s and t are different numbers, |2-s| + |s] = 2 only if s is between q=0 and t=2:
s=1 --> |2-1| + |1] = 2+1 = 2.
s=0.5 --> |2-0.5| + |0.5] = 1.5 + 0.5 = 2.
If s not between q=0 and t=2, then |2-s| + |s] ≠ 2.
s=3 --> |2-3| + |3] = 1+3 = 4.
s=-1 --> |2-(-1)| + |-1] = 3+1 = 4.
The cases in green imply the following:
To satisfy the equation in Statement 1, s must be between q and t, with the result that q < s < t.
Thus, the answer to the question stem is YES.
SUFFICIENT.

Statement 2:
If q=0, s=1 and t=2, then the answer to the question stem is YES.
If q=0, t=2 and s=3, then the answer to the question stem is NO.
Since the answer is YES in the first case but NO in the second case, INSUFFICIENT.

The correct answer is A.

[Scott@TargetTestPrep]

If q, s and t are all different numbers, is q < s < t?

(1) t - q = |t - s| + |s - q|
(2) t > q

We need to determine whether q < s < t, given that q, s, and t are all different numbers.

Statement One Alone:

t - q = |t - s| + |s - q|

Since q, s, and t are different numbers, both |t - s| and |s - q| are positive quantities, and their sum |t - s| + |s - q| will also be positive. This also makes the left-hand side t - q positive. Since t - q > 0, we have t > q.

We know t > q, but we still have to determine whether s is between them. That is, is q < s < t? We have three scenarios to consider.

(1) If q < s < t, then t > s and s > q, and then:

t - q = t - s + s - q

t - q = t - q

We see that this equation holds true: t - q = |t - s| + |s - q|, and furthermore q < s < t.

(2) If s < q < t, then t > s and q > s, and thus t -s is positive while s - q is negative, and we have:

|t - s| + |s - q|

t - s + [-(s - q)]

t - s - s + q

t - 2s + q ≠ t - q

Since t - 2s + q ≠ t - q, the equation does not hold and we can't have s < q < t.

(3) If q < t < s, then s > t and s > q, and thus t - s is negative while s - q is positive, and we have:

|t - s| + |s - q|

-(t - s) + s - q

-t + s + s - q

-t + 2s - q

Since -t + 2s - q ≠ t - q, we see that the equation does not hold, so we can't have q < t < s.

We see that only scenario 1 is true if t - q = |t - s| + |s - q,| and we do have q < s < t. Statement one alone is sufficient.

Statement Two Alone:

t > q

We know t > q, but we still have to determine whether s is between them. It's possible that q < s < t, but it is also possible that s < q < t or q < t < s. Since we don't know anything about s, we can't determine which case is valid. Statement two alone is not sufficient.

Answer: A

[ceilidh.erickson]

HI Guru,

Easily eliminated B. How to solve the que within 2 min?

Thanks
Nandish

Here's an unsatisfying answer: I don't think there is a way for most people to solve this in less than 2 min. Questions that require you to test cases are often very time-consuming. One of the hardest things about the GMAT is that no one - not even the experts! - will have time to carefully solve every single question. You must make decisions to skip (guess & move on) on certain questions so you can commit the time to others.

When practicing, take the time to think: is this a question that's worth 3 min? If you have a high likelihood of getting it right, then yes, spending 3 min on this one (and skipping something else) is the right move. If you've done a lot of problems and concluded that you don't get many of the absolute-value-testing-cases-DS questions right, then you'll want to skip it.

An important part of doing well on the GMAT is learning enough about yourself to know how to pick your battles!

[Brent@GMATPrepNow]

If q, s and t are all different numbers, is q < s < t?

(1) t - q = |t - s| + |s - q|
(2) t > q

A

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