The figure above shows the present position on a radar screen of

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Problem Solving
Figures: All figures accompanying problem solving questions are intended to provide information useful in solving the problems. Figures are drawn as accurately as possible. Exceptions will be clearly noted. Lines shown as straight are straight, and lines that appear jagged are also straight. The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero. All figures lie in a plane unless otherwise indicated.

Data Sufficiency:
Figures:
• Figures conform to the information given in the question, but will not necessarily conform to the additional information given in statements (1) and (2).
• Lines shown as straight are straight, and lines that appear jagged are also straight.
• The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero.
• All figures lie in a plane unless otherwise indicated.

Bunuel
Would you be able to explain "Regardless the value of r, the beam will be in the IV quadrant."

Is this because the angle is currently at about 45 degrees in the first quadrant. Each quadrant is 90 degrees, so 90-45=45, therefore it would be in quadrant four at 90 degrees? Thank you for your help.

The beam is currently in the I quadrant, no matter whether it's 45 degrees or not, anything in I quadrant + 90 degrees will be in the IV quadrant. For example, if the angle were 89 degrees, still + 90 degrees will move the beam to the IV quadrant. If the angle angle were 1 degree, still + 90 degrees will move the beam to the IV quadrant.

Next, if we were told that the beam moved say 60 degrees in 30 seconds, instead of 90 degrees, then the statement would not be sufficient because we cannot assume that the beam is at 45 degrees with x-axis. It could be at 80 degrees and in this case the beam would still be in the I quadrant. So, basically we can answer the question if we are given that in 30 seconds the beam moved:

360k + 0 degrees, in this case the beam will be in the I quadrant (for some integer k).
360k + 90 degrees, in this case the beam will be in the IV quadrant (our case).
360k + 180 degrees, in this case the beam will be in the III quadrant.
360k + 270 degrees, in this case the beam will be in the II quadrant.

The radius of the circle is totally irrelevant. Who cares how large the circle is ? We need the angle the beam is moving in 30 seconds.

Does this make sense ?

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