RK007 wrote:

jedit wrote:

Bunuel wrote:

In the diagram below, what is the length of RS?

(1) PQ = 28 and TU = 21.

(2) PQ, RS and TU are parallel lines.

Attachment:

2017-07-18_1022.png

It appears to be C.

Statement 1: Insufficient.

We do not know the actual height from the base.

Statement 2: Insufficient.

We do not know lengths.

Combining, if the lines are parallel, their intersection should be the half of the average of the two lengths.

Is this a theorem? Do u have any explaination?

I'm not going to worry about whether this is a theorem or not, since approaching this problem from basic principles will be more relevant for the GMAT anyway.

I would start by re-drawing the diagram, and labeling the lengths of segments with variables as I have done below:

Note that we are solving for c in the above diagram. Now, based on statement 2, if we see that triangle RSU is similar to triangle PQR, and triangle RSQ is similar to triangle TUQ, we can write the ratios of sides as the following equations:

\(\frac{c}{e} = \frac{a}{d+e}\) and \(\frac{c}{d} = \frac{b}{d+e}\)

If we cross-multiply these equation we get:

\(c(d+e) = ae\) and \(c(d+e) = bd\)

This tells us that:

\(ae=bd\)

Now, statement 1 tells us that a = 28 and b = 21, which turns the equation above into:

\(28e = 21d\)

Thus, we have the ratio of e to d, which means that we also can calculate the ratio of e to d+e. We can rearrange the equation \(c(d+e) = ae\) to be:

\(c = a*\frac{e}{d+e}\)

Finally, since we know a = 28 and we can calculate the ratio \(\frac{e}{d+e}\), this is sufficient to calculate c, and thus answer the question.

Please let me know if you have any questions!

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