GMATPREP HARD PS QUESTION!!

[owodee]

Here is a problem from a GMAT prep test I took earlier today. The answer I picked is wrong. ANY HELP WILL BE APPRECIATED.

OA after a few replies.

[givemeanid]

s = 1. Answer is B.

[owodee]

thanks givemeanid, but could you please tell me how you solved the question? Im quite lost here

[givemeanid]

Draw a line segment PR where R is on the X axis and PR is perpendicular to X axis.

Now, PRO is a right triangle with PR = 1 and OR = sqrt(3)
OP = sqrt(PR^2 + OR^2) = sqrt(1+3) = 2.
This is a 30-69-90 triangle (its a right triangle with ratios of sides as 1:sqrt3:2)

Angle POR = 30 (since it's opposite to side of length 1 in the above mentioned triangle).

Now, draw a line segment QT where T is on the X axis and QT is perpendicular to X axis.
POR + POQ + QOT = 180 (they form a straight line)
30 + 90 + QOT = 180
QOT = 60
In triangle OQT, QOT = 60, QTO = 90. So, OQT = 30

Also, OP = OQ = 2 (radius of the circle)
So, again from the 30-60-90 triangle property, since OQ = 2, OT = 1 and TQ = sqrt(3).

Hence s = 1.

[owodee]

wow, that makes a lot of sense now, thanks a lot for your help!