AJ1012
If p, s, and t are positive integer, is |ps - pt| > p(s - t) ?
(1) p < s
(2) s < t
Target question: Is |ps - pt| > p(s - t) ?In other words,
Is |ps - pt| > ps - pt?This is a good candidate for
rephrasing the target question.
KEY CONCEPT: |x - y| can be thought as the DISTANCE between x and y on the number line.
For example, |3 - 10| = the DISTANCE between 3 and 10 on the number line.
And |6 - 1| = the DISTANCE between 6 and 1 on the number line.
IMPORTANT: We can also find the distance 6 and 1 on the number line by simply subtracting 6 - 1 to get 5, so why do we need absolute values? Can't we just conclude that |x - y| = x - y?
Great questions, me!
For SOME values of x and y, it's true that |x - y| = x - y, and for other values it is NOT the case that |x - y| = x - y
For example, if x = 5 and y = 2, then we get: |5 - 2| = 5 - 2. In this case |x - y| = x - y
Likewise, if x = 11 and y = 3, then we get: |11 - 3| = 11 - 3. In this case |x - y| = x - y
And, if x = 7 and y = 7, then we get: |7 - 7| = 7 - 7. In this case |x - y| = x - y
CONVERSELY, if x = 4 and y = 6, then we get: |4 - 6| = 4 - 6. In this case |x - y|
≠ x - y
Likewise, if x = 5 and y = 20, then we get: |5 - 20| = 5 - 20. In this case |x - y|
≠ x - y
And, if x = 0 and y = 1, then we get: |0 - 1| = 0 - 1. In this case |x - y|
≠ x - y
Notice the |x - y| = x - y IS true when x > y, and |x - y| = x - y is NOT true when x < y
If x < y, then |x - y| = some POSITIVE value, and x - y = some NEGATIVE value.
This means that, if x < y, then |x - y| > x - y
The target question asks
Is |ps - pt| > ps - pt?According to our conclusion above, if ps > pt, then |ps - pt| = ps - pt and . . .
if
ps < pt, then |ps - pt| > ps - ptThis means we can REPHRASE the target question....
REPHRASED target question:
Is ps < pt?We can make things even easier, if we notice that, since p is POSITIVE, we can safely take the inequality
ps < pt and divide both sides by p to get:
s < t?.
RE-REPHRASED target question: Is s < t?At this point, it will be very easy to analyze the answer choices....
Statement 1: p < sSince there's no information about t, there's no way to answer the
RE-REPHRASED target question with certainty.
Statement 1 is NOT SUFFICIENT
Statement 2: s < tPerfect!
The answer to the RE-REPHRASED target question is
YES, s IS less than tSince we can answer the
RE-REPHRASED target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent