GMATPREP QP1 - A machine has two flat circular plates of the

[saswata4s]

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

OA: C.

[GMATGuruNY]

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.

[Jay@ManhattanReview]

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

OA: C.

Great explanation by Mitch.

Upon seeing the diagram a clock clicked me and I solved this one keeping the clock as a reference.

Let's do that way.

For the first plate, the hour hand will move from the first hole position to the 2nd hole in 15 minutes; to the 3rd hole in 30 minutes; to the 4th hole in 45 minutes.

For the second plate, the hour hand will move from the first hole position to the 2nd hole in 12 minutes; to the 3rd hole in 24 minutes; to the 4th hole in 36 minutes; to the 5th hole in 48 minutes.

The smallest time gap is (15 - 12 =) 3 minutes or (48 - 45 =) 3 minutes

3 minutes in degrees = 3*(360/60) = 18 degrees.

The correct answer: C

Hope this helps!

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-Jay
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[Matt@VeritasPrep]

Another trick, since the images are to scale, is to look at the points that seem closest (but not equal).

Looking at the plates, it's clear that the top hole is equal. The holes immediately to the right of the top hole on each plate are remarkably close: visually the closest.

On the first plate, the first hole to the right of the top = 0 + (360/4)°, or 90°.

On the second plate, the first hole to the right of the top = 0 + (360/5)°, or 72°.

That difference is 90 - 72, or 18°, so that's our answer.

[Scott@TargetTestPrep]

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

OA: C.

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