Problem Solving

This is probably, really simple, but I can't wrap my head around it.

#83, page 72: on the OG math workbook

If u > t, r > q, s > t, and t > r, which of the following must be true?

I u > s
II. s > q
III u > r.

case II and III, are straight forward and easy.


I drew the number line it looks like this:

Q------------r-----------t-------------u----------

The question is: where is 's' placed? between 't' and 'u,' or just in front of 'u'?

case I explanation tells me to draw the line, and plug in some arbitrary numbers. they pick, t = 2, u = 3, and s = 4, therefore it's obvious that u is not greater than s.

How did they come up with these numbers? what if I pick t = 2 u = 5, and s = 4? then U > S, and still follows all the premises...right?


What am I missing here?

The OG explanations are not great. This is the opinion of almost everyone


Coming to this problem:

I would write the inequalities as follows:

u>t r>q s>t t>r

It follows:

u>r t>q

u>q s>q


In must be true questiona statement that has to be true for all sets of values so if u can prove something is not true for 1 set of values then it is not part of the answer choice


Stmt I u>s may or may not be true.

The other question type is could be true -> This means if u can prove a statement is true for 1 set of values based on problem constraints if any then that statement will be part of you answer choice


Stmt II and III must be true

I dont understand how the OG says (not sure if it does) that I also must be true (may be I am also missing something- also u,t,r,q does not even have to be intgers if they are not given to be integers)


Is it OG 11 th edition or OG 10th edition?