which must be true?

Question

if p < q , r < s , and r < q , which of the following must be true ?

Answer 1

The easiest way to visualise this sort of problem is to use a straight line with markers representing the quantities.

There are 5 arrangements of markers that obey the given rules. I'll represent them by writing the order from left to right:

1. prqs
2. prsq
3. rpqs
4. rpsq
5. rspq

For example, prqs means p<r<q<s. Each configuration shows the relative position of the markers along the line. Since each obeys the rules, it's clear that, for example, it's not possible to draw a conclusion about the relationship between p and r: p<r appears in 1 and 2, and r<p appears in 3, 4 and 5. No statement can be made about p and r. The same goes for p and s, and s and q.