I think there's nothing wrong with the question other than a typo and it's 3,690°. Which I didn't even realize at first because I'm from Brazil, and here works the opposite way. The decimal "point" is "," and the "," is the decimal point.
So, the present position of the sweeping beam it's the one in the figure. "The figure above shows the present position
on a radar screen of a sweeping beam"
Every 90° the sweeping beam will change quadrants, and every 4 times it will come back to the starting point. If we divide 3690 by 90 we get 41. So, that means it will rotate and go back to the starting point 10 times (10*4 = 40) and one more time (10*4+1=41) So. the answer would be A. It will be in the 4th quadrant.
Hope it helps.