A machine has two flat circular plates of the same diameter both plate

The question might be a bit complicated to understand but the solution is very simple and straight forward:


Let's look at how the holes are placed with respect to each other. The plate which has 4 holes has holes which are 90 degrees away from each other. The plate which has 5 holes has holes which are 360/5 = 72 degrees away from each other. Assume that the holes at the top are aligned.

This is how the rest of the holes are placed on the two plates:
5 hole plate - 72 degrees, 144 degrees, 216 degrees, 288 degrees
4 hole plate - 90 degrees, 180 degrees, 270 degrees

To align the first holes with each other, we can move the 5 hole plate clockwise 18 degrees. Or the second hole of 5 hole plate 36 degrees clockwise. The minimum movement required to align any two holes is 18 degrees (the difference between any two angles of the two plates)

Answer (C)

As the holes are equidistant on both the plates, they form pentagon and square on their respective plate (as shown in the figure)

Lets consider two circular plates as below:
Plate1: Consider holes A & B are on Pentagon in plate1
Plate2: Consider holes P & Q are on square in plate2

Its given that two plates are kept over other and two of their holes are coinciding. Lets assume holes A & P are coinciding.
From the diagram you can see, holes B & Q can be aligned with minimum rotation. i.e. we need to find out <BOQ = x =?

Central angle formed by two vertices of pentagon i.e. \(<AOB = y = \frac{360}{5} = 72\)
Central angle formed by two vertices of square i.e. \(<POQ = \frac{360}{4} = 90\)

\(<AOB + <BOQ = <AOQ\)
i.e. \(y + x = 90\)
i.e. \(72 + x = 90\)
Resolve to \(x = 18\)

Hence choice (C) is the answer

The four equidistant circular rings on the first circular plate divides it into four equal parts; so each part is 1/4
The five equidistant rings on the second cirular plate divides it into five equal parts; each part is 1/5


If one of the circular plate is overlaid on the other with a pair of circular holes aligned, the holes will be 1/4 minus 1/5 = 1/20 apart from each other. If we have to align a different pair of circles, we have to move the circular plate on the top 1/20 * 360 degrees.
1/20*360 = 18 degrees.

Further explanation: I interpreted this as a form of a circle and its sector problem. Area covered by a sector is given by A = angle/360 * area of the circle
If we take area of the circular plate as 1, the area covered by each sector will be 1/20. We are asked to find out the angle subtended by the sector between the holes.

1/20 = angle/360 *1

angle = 360/20


So C is the answer.

Hope this approach helps.

Refer screenshot below:

I just believe that it takes more time to read the problem than to solve it

"Align a pair of circles..."

When I read this question, in my mind, I understood it as two circle from each plate have to be aligned. I spent 10 minutes tryin to figure out how the f@#$, you align two sets of holes on a plate with 4 90* seprated circle on top of 5 holed plate with 72* seperation. What they meant was a pair of holes from the TWO DIFFERENT PLATES.

Is this really math exam or an english exam. Honest to christ, I dont know.

Posted from my mobile device

Can some one please explain to me what does this mean:
"one plate is placed on top of the other so that their centers are aligned and two of the holes are perfectly aligned. "

How can two holes be aligned in this scenario ... I am not able to figure this out.

Look at the original diagram given. If you just put one plate perfectly on top of the other, in their current position, their top holes will be aligned.

one hole from each plate is coinciding that is how two holes are aligned in this scenario

Hi All,

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:

GMAT assassins aren't born, they're made,
Rich

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
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Let's call the 4-holed plate ABCD, with holes A, B, C and D.
Since \(\frac{360}{4} = 90\), 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 \(\frac{360}{5} = 72\), 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°.

.
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This should be at the top lol. Lots of people are going to get stuck because of the wording. I wasted about 10 minutes too thinking about it.

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