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If q, s and t are all different numbers, is q < s < t?
(1) t - q = |t - s| + |s - q|
(2) t > q
A
(1) t - q = |t - s| + |s - q|
(2) t > q
A
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OG If q, s and t are all different numbers
Source: Beat The GMAT — Data Sufficiency |
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GMATGuruNY
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Statement 1:AbeNeedsAnswers wrote:If q, s and t are all different numbers, is q < s < t?
(1) t - q = |t - s| + |s - q|
(2) t > q
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.
Last edited by GMATGuruNY on Mon Feb 05, 2018 9:01 am, edited 1 time in total.
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Scott@TargetTestPrep
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We need to determine whether q < s < t, given that q, s, and t are all different numbers.AbeNeedsAnswers wrote:If q, s and t are all different numbers, is q < s < t?
(1) t - q = |t - s| + |s - q|
(2) t > q
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
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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.NandishSS wrote:HI Guru,
Easily eliminated B. How to solve the que within 2 min?
Thanks
Nandish
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!
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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Brent@GMATPrepNow
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Given: q, s, and t are all different numbersAbeNeedsAnswers wrote:If q, s and t are all different numbers, is q < s < t?
(1) t - q = |t - s| + |s - q|
(2) t > q
A
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
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Brent
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