is x -y > r - s?

1) x > r and y < s

I understand you can add the inequalities, but can you subtract them as well?

so:

x > r
s > y

x-s > r-y? (is this true???)
also
s-x > y - r? (is this true???)

If you can subtract the inequalities, I think 1) is insufficient.

for example
x-s > r-y? (is this true???)
x= 10 r = 3 s= 9 y = 1
1 > 2 (DEFINITIVE NO)

x=7 r=1 s=2 y=1
5 > 0 (DEFINITIVE YES)

So - insufficient.

Am I missing something. (I know adding the inequalities produces a sufficient answer, but i want to know why subtracting them does not...)

I don't recommend adding/subtracting inequalities in this way.

Here is a better way to think about statement (1):

we are starting off with x larger than r

we are subtracting something smaller (y) from x and something larger (s) from r

So, we start with x > r and when we do the above we make the right side smaller still

x - y vs. r - s

-Veritas Help