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Bunuel
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Bunuel

If in the figure above OR = 5, what is the length of QR?


(1) The measure of angle QOR = 60.

(2) The area of the triangle POR is 25.
Attachment:
image002.jpg

Question stem:- what is the length of QR?

St1:- The measure of angle QOR = 60.

So, OQR is an equilateral triangle with QR=QO=OR=5 (In triangle OQR, Angle Q=Angle O=60, so Angle R=180-60-60=60. All angles are equal , hence all sides are equal)
Sufficient.

St2:- The area of the triangle POR is 25.
One angle, one side and area of triangle is given. We need one more criteria to determine area.
Insufficient.

Ans. (A)
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Bunuel

If in the figure above OR = 5, what is the length of QR?


(1) The measure of angle QOR = 60.

(2) The area of the triangle POR is 25.


Attachment:
image002.jpg
St1) triangle OQR is equilateral.
So each side is equal in this triangle.
Sufficient

St2) you are given area with OR as fixed length. Now the angle ORQ is not fixed. One can tilt it at a different angle.
We have

area = base * perpendicular height

Area is fixed. So we can keep changing the perpendicular height by changing the tilt of the line QR and hence base value will keep on changing to give a fixed area.

This requires a bit of imagination but that's the beauty of geometry DS questions

Answer is A



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