Source: Official Guide for the GMAT 12th Ed. Section 6.3 Data Sufficiency; #173

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# If arc PQR above is a semicircle

If arc PQR above is a semicircle, what is the length of diameter PR? (1) a=4 (2) b=1 Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient., Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient., BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient., EACH statement ALONE is sufficient., Statements (1) and (2) TOGETHER are not sufficient.

### 1 Explanation

1 Mike McGarry, Magoosh Tutor

Nov 12, 2012 • Comment

abhishek thakur

can u explain the similarity part in detail?

Carolyn Shasha, Magoosh Tutor

Hi Abhishek!

Happy to help :) If two triangles are similar, that means that they have all the same angles, and their corresponding sides are proportional. So in this case, since we know that triangles PTQ and QTR have the same angles, they must be similar triangles. That means that their corresponding sides will be proportional. So for example, the ratio of the hypotenuses, PQ and QR, will be the same as the ratio of the shortest sides, 2 and b. So we can set up an equation like PQ/QR = 2/b. For more detail on this, I'd recommend watching our lesson on Similar Triangles :)

Hope that helps! :)