P,Q,R, and S are integers.?

Question

p,q,r and s are integers.s is greater than q.p is the opposite of s.r is the opposite of q.r is to the right of 0 on the number line .q is less than p .which represents the greatest integer ?

F. p
G. q
H.r
J. s

Answer 1

Let's work this out logically.

For integers p, q, r, and s, we have the following facts:

s > q (s is greater than q)
-p = s (p is the opposite of s)
-r = q (r is the opposite of q)
r > 0 (r is to the right of 0 on the number line)
q < p (q is less than p)

We can combine change (s > q) into (q < s). That means we have these two facts:
(q < s) and (q < p)

We can throw away q as a possibility.

It is given that -r = q (which also means r = -q). Therefore

(-r < s) and (-r < p). We can multiply both inequalities by -1 to flip the sign. We would get

(r > s) and (r > p)

This means r is greater than s and p. We can throw away s as a possibility.

That leaves us with r and p.

s > q and -p = s, so
-p > q. This means p < q, so we throw away p as a possibility.

That leaves r, because nothing is greater than it.
So the answer is H.

Answer 2

The first guy got the right answer, but it is amazing due to the major algegraic error of not carrying the neg sign through when doing -1*(-r < s) => (r > s) which should be (r > -s). This later leads them to concluding that (p < q) even though (p > q) is given. The initial statements are good so we can start there.

given (q < p) => (-r < p) => (r > -p) => (r > s)

given (-p = s) => ( |p| = |s| )

so we now have
(r > s), (r > p), (s > q), (p > q) so r is the greatest integer.

Answer 3

The correct way to solve this problem is with linear algegra, a program such as 'lindo', or 'lingo' will solve a problem of this sort without breaking a sweat (Because of the methods used)

Answer 4

the answer is H.r

this is why
take this situation you need not have numbers just positions
| | | | |
q s 0 p r
you will find that q and s are negative and all of the conditions fit

Answer 5

R is the greatest integer

Answer 6

H. r