saswata4s wrote:
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
Let's call the 4-holed plate ABCD, with holes A, B, C and D.
Since 360/4 = 90, the holes are spaced 90° apart.
Let A=0°, B=90°, C=180°, and D=270°.
Let's call the 5-holed plate RSTUV, with holes R, S, T, U, and V.
Since 360/5 = 72, the holes are spaced 72° apart.
Let R=0°, S=72°, T=144°, U=216°, and V=288°.
Let the plates be positioned so that A is aligned with R at 0°.
Since S is at 72° and B is at 90° -- a difference of 18° -- S will align with B if plate RSTUV rotates 18° degrees clockwise or if plate ABCD rotates 18° counter-clockwise.
There is no difference smaller than 18°.
Thus, the least number of degrees that one of the plates must rotate is 18°.
The correct answer is
C.
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