GMAT OFFICIAL GUIDE DS – If r > 0 and s…

Solution:

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.