Problem Solving

VJesus12 wrote: ↑

Fri Sep 04, 2020 6:18 am

A machine has two flat circular plates of the same diameter both plates have holes of one-inch diameter that are equally placed and are the same from the edges as shown above. one plate is placed on top of the other so that their centers are aligned and two of the holes are perfectly aligned. If one plate remains stationary what is the least number of degrees that the other plate must be rotated so that a different pair of holes is perfectly aligned.

A. 6
B. 12
C. 18
D. 24
E. 36

Answer: C

Solution:

Notice that the centers of the holes in the 4-hole plate are 360/4 = 90 degrees apart and those in the 5-hole plate are 360/5 = 72 degrees apart.

Let’s call the holes of the 4-hole plate A, B, C, D starting from the one at the top and going clockwise. Similarly, let’s call the holes of the 5-hole plate a, b, c, d, and e starting from the one at the top and going clockwise. Now let’s say hole A aligns with hole a. Then we can see that hole B is between holes b and c; hole C is between holes c and d; and lastly, hole D is between d and e.

Holes B and b are 90 - 72 = 18 degrees apart but B and c are 144 - 90 = 54 degrees apart. Holes C and c are 180 - 144 = 36 degrees apart and so are C and d (notice that 216 - 180 = 36). Holes D and e are 288 - 270 = 18 degrees apart but D and d are 270 - 216 = 54 degrees apart. Therefore, we see that the minimum number of degrees to satisfy the required condition is 18 degrees. (For example, we can fix the 4-hole wheel and rotate the 5-hole wheel 18 degrees clockwise so that holes B and b will be aligned together).

Answer: C