A circle has 29 points arranged in a clock wise manner from o to 28. A bug moves clockwise manner from 0 to 28. A bug moves clockwise on the circle according to following rule. If it is at a point i on the circle, it moves clockwise in 1 sec by (1 + r) places, where r is the remainder (possibly 0) when i is divided by 11. If it starts in 23rd position, at what position will it be after 2012 sec. Options.
A) 10th
B) 15th
C) 20th
D) 25th
E) 28th
After 1st second, it moves 1 + (23/11)r = 1 + 1= 
<gadget id="calculator">1 + 1</gadget>
<output>2</output>
2, So 25th position   After 2nd second, it moves 1 + 25/11= 1 + 3= 
<gadget id="calculator">1 + 3</gadget>
<output>4</output>
4, So 29th position= 0   After 3rd second, it moves  1 + 0/11= 
<gadget id="calculator"> 1 + 0/11</gadget>
<output>1</output>
1 + 0= 
<gadget id="calculator">1 + 0</gadget>
<output>1</output>
1, So 1st position   After 4th second, it moves 1 + 1= 3rd position   after 5th, 1 + 3/11 = 4 So 7th   After 6th, 1 + 7/11 = 8 so 15th   After 7th, 1 + 15/11 = 5 so 20th   After 8th, 1 + 20/11 = 10th, So 30th = 1st   So it is on 1st after every 3 + 5n seconds. So it is on 1st position after 2008 seconds (3 + 5 x 401) So on 20th after 2012 position.   ANSWER:20th
<result>C</result>
A circle has 29 points arranged in a clock wise manner from o to 28. A bug moves clockwise manner from 0 to 28. A bug moves clockwise on the circle according to following rule. If it is at a point i on the circle, it moves clockwise in 1 sec by (1 + r) places, where r is the remainder (possibly 0) when i is divided by 11. If it starts in 23rd position, at what position will it be after 2012 sec.