Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 25 May 2015, 05:41

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A machine has two flat circular plates of the same diameter

 Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Director
Joined: 29 Nov 2012
Posts: 926
Followers: 12

Kudos [?]: 456 [4] , given: 543

A machine has two flat circular plates of the same diameter [#permalink]  08 Jan 2013, 20:16
4
This post received
KUDOS
3
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

74% (02:07) correct 26% (01:55) wrong based on 95 sessions
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
[Reveal] Spoiler: OA

Attachments

Question.png [ 51.23 KiB | Viewed 3437 times ]

_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios gmat-prep-software-analysis-and-what-if-scenarios-146146.html

Last edited by fozzzy on 09 Jan 2013, 02:54, edited 2 times in total.
Current Student
Joined: 27 Jun 2012
Posts: 418
Concentration: Strategy, Finance
Followers: 56

Kudos [?]: 455 [11] , given: 182

Re: A machine has 2 flat [#permalink]  08 Jan 2013, 21:20
11
This post received
KUDOS
2
This post was
BOOKMARKED
Attachment:

Circular Plates.jpg [ 118.78 KiB | Viewed 3427 times ]

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
_________________

Thanks,
PraPon

Tough 700+ Level RCs: Passage1 | Passage2 | Passage3 | Passage4 | Passage5 | Passage6 | Passage7
Reading Comprehension notes: Click here
VOTE: vote-best-gmat-practice-tests-excluding-gmatprep-144859.html
PowerScore CR Bible - Official Guide 13 Questions Set Mapped: Click here

Intern
Joined: 08 Jan 2013
Posts: 4
Followers: 0

Kudos [?]: 3 [1] , given: 1

Re: A machine has 2 flat [#permalink]  09 Jan 2013, 15:30
1
This post received
KUDOS
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.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 5548
Location: Pune, India
Followers: 1372

Kudos [?]: 6973 [1] , given: 178

Re: A machine has two flat circular plates of the same diameter [#permalink]  16 Jun 2014, 21:03
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
fozzzy 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

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

Ques3.jpg [ 5.38 KiB | Viewed 1339 times ]

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)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for 199 Veritas Prep Reviews Current Student Joined: 27 Jun 2012 Posts: 418 Concentration: Strategy, Finance Followers: 56 Kudos [?]: 455 [0], given: 182 Re: A machine has 2 flat [#permalink] 08 Jan 2013, 20:18 Where is the screenshot! _________________ Thanks, PraPon Tough 700+ Level RCs: Passage1 | Passage2 | Passage3 | Passage4 | Passage5 | Passage6 | Passage7 Reading Comprehension notes: Click here VOTE: vote-best-gmat-practice-tests-excluding-gmatprep-144859.html PowerScore CR Bible - Official Guide 13 Questions Set Mapped: Click here Director Joined: 29 Nov 2012 Posts: 926 Followers: 12 Kudos [?]: 456 [0], given: 543 Re: A machine has 2 flat [#permalink] 08 Jan 2013, 20:19 PraPon wrote: Where is the screenshot! sorry it was a bit blurry tried changing it doesn't look any better _________________ Click +1 Kudos if my post helped... Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/ GMAT Prep software What if scenarios gmat-prep-software-analysis-and-what-if-scenarios-146146.html Director Joined: 29 Nov 2012 Posts: 926 Followers: 12 Kudos [?]: 456 [0], given: 543 Re: A machine has 2 flat [#permalink] 09 Jan 2013, 01:29 PraPon wrote: Attachment: Circular Plates.jpg 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 Great explanation! I didn't realize they were testing the concepts of polygon! kudos to you! _________________ Click +1 Kudos if my post helped... Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/ GMAT Prep software What if scenarios gmat-prep-software-analysis-and-what-if-scenarios-146146.html Moderator Joined: 01 Sep 2010 Posts: 2601 Followers: 439 Kudos [?]: 3438 [0], given: 720 Re: A machine has 2 flat [#permalink] 09 Jan 2013, 08:12 Expert's post fozzzy wrote: PraPon wrote: Attachment: Circular Plates.jpg 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 Great explanation! I didn't realize they were testing the concepts of polygon! kudos to you! see the new Gmatclub math book. is well explained inside _________________ Manager Joined: 04 Oct 2011 Posts: 224 Location: India Concentration: Entrepreneurship, International Business GMAT 1: 440 Q33 V13 GMAT 2: 0 Q0 V0 GPA: 3 Followers: 0 Kudos [?]: 31 [0], given: 44 Re: A machine has 2 flat [#permalink] 09 Jan 2013, 18:19 fozzzy 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. 6 12 18 24 36 First plate (4 holes) = 360/4 = 90 Second Plate (5 holes) = 360/5 = 72 So least degree to get a hole aligned with other = 90 - 72 =18 Guys Please validate this! Will this method be useful for similar type problems ? Or did i go wrong anywhere? _________________ GMAT - Practice, Patience, Persistence Kudos if u like Director Joined: 29 Nov 2012 Posts: 926 Followers: 12 Kudos [?]: 456 [0], given: 543 Re: A machine has 2 flat [#permalink] 09 Jan 2013, 20:57 chvrmohan4 wrote: 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. Really nice solution! very well thought! kudos to you _________________ Click +1 Kudos if my post helped... Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/ GMAT Prep software What if scenarios gmat-prep-software-analysis-and-what-if-scenarios-146146.html Manager Joined: 29 Oct 2013 Posts: 172 Concentration: Finance GMAT 1: 750 Q48 V46 GMAT 2: Q V0 GRE 1: 327 Q161 V166 GPA: 3.7 WE: Corporate Finance (Retail Banking) Followers: 7 Kudos [?]: 177 [0], given: 116 Re: A machine has 2 flat [#permalink] 03 Jun 2014, 21:50 carcass wrote: fozzzy wrote: PraPon wrote: Attachment: Circular Plates.jpg 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 Great explanation! I didn't realize they were testing the concepts of polygon! kudos to you! see the new Gmatclub math book. is well explained inside There is a potential pitfall in this approach. We cannot rely on visual inspection that <BOQ is the least. In fact there are two different pairs of holes which are the least distance apart here and hence two least degree angles though both are 18 degrees. And hence your answer happens to be correct. Here is a different approach which I believe is more water tight. Let plate A have 4 holes and B 5. So holes on plate will divide the circle in the following fractions: 1/4, 2/4, 3/4 and 4/4 Similarly holes on B will divide the circle in the following fractions: 1/5, 2/5, 3/5, 4/5 and 5/5 Lets multiply all values by the LCM of 4 & 5: Holes on A: 5/20, 10/20, 15/20, 20/20 and holes on B: 4/20, 8/20, 12/20, 16/20, 20/20 4/4(20/20) from and 5/5(20/20) are already coinciding. So the next closet pairs are : 1) 5/20 & 4/20 2) 15/20 & 16/20 Both these pairs are 1/20 fraction apart. On a circle this means 360*1/20 = 18 degrees apart Ans: C Hope it is clear! _________________ Please consider giving 'kudos' if you like my post and want to thank Read about my journey to 750 here - a-non-native-speakers-journey-to-99-le-on-verbal-750overall-171722.html#p1367876 SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1858 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Followers: 22 Kudos [?]: 896 [0], given: 193 Re: A machine has two flat circular plates of the same diameter [#permalink] 04 Jun 2014, 22:52 Refer screenshot below: I just believe that it takes more time to read the problem than to solve it Attachments cir.jpg [ 40.46 KiB | Viewed 1477 times ] _________________ Kindly press "+1 Kudos" to appreciate Manager Joined: 12 Feb 2012 Posts: 109 Followers: 1 Kudos [?]: 14 [0], given: 28 Re: A machine has two flat circular plates of the same diameter [#permalink] 16 Jun 2014, 19:24 "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
Re: A machine has two flat circular plates of the same diameter   [#permalink] 16 Jun 2014, 19:24
Similar topics Replies Last post
Similar
Topics:
29 A circular rim 28 inches in diameter rotates the same number 20 08 Jun 2008, 11:01
A circular rim 28 inches in diameter rotates the same number 9 09 Dec 2007, 10:21
10 A circular rim 28 inches in diameter rotates the same number 6 08 Nov 2006, 15:15
A circular rim 28 inches in diameter rotates the same number 4 07 Nov 2006, 07:29
A circular rim 28 inches in diameter rotates the same number 2 15 Apr 2006, 19:59
Display posts from previous: Sort by

# A machine has two flat circular plates of the same diameter

 Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.