If r > 0 and s…
We are given that r and s are both greater than zero. We need to determine:
Is r/s < s/r ?
We can simplify by cross multiplying. We can only cross multiply because we know that neither r nor s is equal to 0 and that they are both positive.
Is r^2 < s^2 ?
Is √(r^2) < √(s^2) ?
Is |r|< |s| ?
Since we know r and s are both positive we can ask:
Is r < s ?
Statement One Alone:
r/(3s) = 1/4
We can start by cross multiplying the given equation in statement one.
4r = 3s
r = ¾(s)
Because r = 3/4(s), we know that s must be greater than r. To illustrate this, let’s use some convenient numbers for r and s.
If s = 4, we know that r = 4(3/4) = 3. Thus, we see that s is greater than r.
Let’s double-check that the relationship still holds when s is a proper fraction. Letting s = ½, we have:
r = (3/4)(1/2) = 3/8
We see that, again, s is greater than r.
Statement one is sufficient to answer the question. We can eliminate answer choices B, C, and E.
Statement Two Alone:
s = r + 4
Since s = r + 4, we know that s must be greater than r. To illustrate this, let’s use some convenient numbers for r and s.
If r = 4, we know that s = 4 + 4 = 8. Thus, we see that s is greater than r. Statement two is also sufficient to answer the question.