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

Question

quant_ds_00000022.jpg In the figure above, ST=3. What is the length of RS? (1) PS = 3\sqrt{3} (2) PT = 6

mikemcgarry · Answer

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 :-)

EMPOWERgmatRichC · Answer

Hi Awli,

Mike is correct. For the given answer to be correct, we would need to KNOW that Angle P is a 90-degree angle (and by extension, that triangle RPT is a right triangle). We cannot deduce that it's a 90-degree angle from the drawing, so we need some type of "proof" that it's a 90 (a text description or the 90-degree "box" symbol drawn into the picture).

GMAT assassins aren't born, they're made,
Rich

Lucky2783 · Answer

God knows how the answer is 'D' for this question . option A can be derived from option B and option B can be derived from option A . 
this is a wrong question or the OA answer is wrong. with current question stem and the 2 option answer should be 'E' rather than D (Surely not 'D' !!) .

KarishmaB · Answer

Actually, this is exactly what indicates that the answer is either (D) or (E) but not (A), (B) or (C). When both statements give you essentially the same info, then either that info is sufficient to answer the question (so answer is (D)) or it is insufficient to answer the question (so answer is (E)). 
As Mike pointed out above, if we know that angle P is 90, then answer is (D). I assume that the original poster forgot the right angle mark on angle P while making the diagram.

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

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