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Pls explain this geometry problem

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by [email protected] » Sat Nov 23, 2013 9:12 pm
Hi shibsriz,

This question comes with some odd wording, but here is the "intent" of what it's asking:

The two circles have "holes" drilled at different spots (4 on one circle; 5 on the other). The prompt tells us to line up 2 holes (1 from each circle), then asks what the LEAST number of degrees you'd have to spin either of the circles so that two DIFFERENT holes would line up.

This question is based on the number of degrees in a circle:

In the "Circle with 4 holes", the holes are at 0, 90, 180 and 270
In the "Circle with 5 holes", the holes are at 0, 72, 144, 216 and 288

If we line up the "0 holes", then we have to look for the LEAST difference between any OTHER pair of holes.

You can find the least difference is two different sets: (90 and 72) and (270 and 288). Each has a difference of 18 degrees.

Final Answer: C

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by GMATGuruNY » Sun Nov 24, 2013 5:06 am
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The figure above represents BOTH plates, one on top of the other.

5-holed plate:
The ring of PINK circles represents the 5-holed plate.
Since 360/5 = 72, the pink circles are spaced 72° apart.
A=0°, B=72°, D=144°, F=216°, H=288°.

4-holed plate:
The ring of BLUE circles represents the 4-holed plate.
Since 360/4 = 90, the blue circles are spaced 90° apart:
A=0°, C=90°, E=180°, G=270°.

The least distance between any two circles -- 18° -- occurs between B and C and between G and H.
If the pink ring rotates 18° clockwise, B will move on top of C and G will move on top of H.
If the blue ring rotates 18° counter-clockwise, C will move on top of B and H will move on top of G.
Thus, for one hole to land on top of another, the least number of degrees that one of the plates must rotate is 18°.

The correct answer is C.
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