If \(p, s,\) and \(t\) are positive integer, is \(|ps - pt| > p(s - t)?\)

(1) \(p < s\)

(2) \(s < t\)

Answer: B

Source: Official Guide

## If \(p, s,\) and \(t\) are positive integer, is \(|ps - pt| > p(s - t)?\)

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## Your Answer

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## Global Stats

**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 - pt**

This 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 < s**

Since there's no information about t, there's no way to answer the RE-REPHRASED target question with certainty.

Statement 1 is SUFFICIENT

**Statement 2: s < t**

Perfect!

The answer to the RE-REPHRASED target question is YES, s IS less than t

Since we can answer the RE-REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,

Brent