The figure above shows the present position on a radar screen of a sweeping beam that is rotating at a constant rate in a clockwise direction. In which of the four quadrants will the beam lie 30 seconds from now ?

(1) In each 30-second period, the beam sweeps through 3690°
(2) r = 40

Target question: In which of the four quadrants will the beam lie 30 seconds from now ?

Statement 1: In each 30-second period, the beam sweeps through 3690°
So, the beam will spin clockwise around the screen several times over the 30-second period.

IMPORTANT: Each time the beam spins 360°, the beam stops at the SAME PLACE as its present location.
So, if the beam spins 3600°, it is spinning around 10 times, and stopping at the SAME PLACE as its present location. At the moment, the beam is is Quadrant I.

Statement 1 says that the beam spins 3690°. In other words, it spins 10 complete times PLUS an extra 90°
So, the beam's final resting place will be 90° (in a clockwise direction) from its present location. Since each quadrant spans 90° and since the beam is presently in Quadrant I, we can be certain that the beam will end up in Quadrant IV
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: r = 40
No information about how the beam will move during the next 30 seconds.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent