Inequalities

[JackH825]

If 2s > 8 and 3t < 9, which of the following could be the value of s – t ?

I. -1
II. 0
III. 1

a. None
b. I only
c. II only
d. III only
e. II and III


Answer is A. Looking at the explanation it makes sense. However, please can you give a brief explanation of how one can correctly combine inequalities so I don't make the same mistake next time. (taken from GMAT official Qs)

Thanks

[Sage Pearce-Higgins]

With inequalities, I keep Algebra to a minimum and prefer to test some cases. I would just simplify 2s > 8 to s > 4, and 3t < 9 to t < 3 After that, I would think "well, s could be 5, and t could be 2, so s - t would be 3. That's bigger than any of the numbers they give, so could I make it smaller? I guess they don't have to be integers, so s could be 4.01 and t could be 2.99, that's pretty close, but they're never going to reach a gap of 1 as s can't actually be 4 and s can't actually be 3."

On some problems, you may need to combine inequalities, but be careful! You don't have the same flexibility to manipulate inequalities as you would regular equations. The only real procedure is to line up the inequality signs and add. So we know that s > 4, and 3 > t, so we can deduce that s + 3 > t + 4, so that s - t > 1.