PSAT abstract inequality question.

[ElijahRockers]

p<q, r<s, and r<q.

Which of the following statements must be true?

I. p<s
II. s<q
III. r<p

The correct answer could be either one statement, a combination of statements, or none of the statements. Came across this question while helping some high school students prepare for their SATs and I'm embarassed to say it stumped me.

 

[Mentallic]

Try drawing an unlabelled number line, and place 4 points on the line. For the first, p<s, let's assume that p>s. Since for the first two criteria p<q and r<s, this means that the only way the order can fit is if it's r,s,p,q, and since the last criteria r<q holds as well, that means we've found a scenario where p is not less than s, so I. is not necessarily true.

 

[ElijahRockers]

Yea, I pretty much came to the conclusion that none of the three statements are necessarily true.

 

[Mentallic]

Yep, precisely.