In the figure above, ST=3. What is the length of RS?

Dear Awli,
My friend, something seems amiss with this problem.

In its current form, we are given no information about angle RPT. You see, a very typical trick on the real GMAT is for the test maker to draw an angle in a DS diagram that appears right, and tempts us into believing that it is in fact a right angle, despite any evidence.

If we were explicitly guaranteed that angle RPT = 90 degrees, then we would have a diagram with three similar triangles and a host of interrelationship:
(triangle RPT) ~ (triangle RSP) ~ (triangle PST)
That would give us a ton of ratios, and having any two lengths in the diagram would be enough to find every other length. That would lead to the answer of (D), which you cite here.

By contrast, the version you give here, we know zilch about the angle at P, so even with both statements, we can find everything about the triangle on the right, right triangle PST, but we could slide point R in and out, adjusting the lengths of RS & RP to whatever we like --- there would be nothing at all determining that side of the triangle. Technically, in the form you have stated the problem here, the answer would be (E).

Now, it may be in copying the diagram, that you left out the "perpendicular square" at the top of the triangle. That's an absolute crucial piece of information, and without it, the problem is very different. I would suggest looking again at the source. BTW, please let us know the source of this question.

Does all this make sense?
Mike