Problem Solving

BTGmoderatorDC wrote:

The dial shown above is divided into equal-sized intervals. At which of the following letters will the pointer stop if it is rotated clockwise from S through 1,174 intervals?

(A) A
(B) B
(C) C
(D) D
(E) E

We are given a diagram with 8 intervals of equal length. Let's start by sketching the diagram.



Notice we have assigned a number to each letter marking between the intervals. Beginning with S = 0 and moving clockwise, we have A = 2, B = 3, C = 4, D = 5 and E = 6.

Let's first study the pattern of the spinner's movement. If the spinner were to go through just 8 intervals, it would stop where it started, at letter S. If, instead, it were to go through 10 intervals, it would go all the way around the circle one time (8 intervals) plus 2 more, stopping at letter A. One more example: if it were to go through 35 intervals it would make four complete revolutions, plus 3 more intervals, stopping at letter B. We can see that if we divide the total number of intervals it travels by 8, the whole number part of the quotient will be the number of revolutions it has made, and the remainder will tell us how many "extra" intervals it has gone past S before stopping.

Therefore, to determine at which letter the pointer will stop when it is rotated clockwise 1,174 intervals, we need to divide 1,174 by 8.

1,174/8 = 146 R 6.

The 146 indicates that the spinner has gone through 146 complete revolutions. The remainder 6 indicates that the spinner has stopped 6 intervals past S, which is location E.

Answer: E