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805+ (Hard)|   Combinations|   Geometry|      
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shanmugamgsn
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What is the maximum number of pieces that a circular pie can 11 Jan 2013, 07:10
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Marcab
Hii Bunuel.
Can you please explain the pattern. Though I understood the pattern, I am not able to visualize the pattern.
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Hi Marcab,

Guess u would have found this soln by this time..
I faced this problem in GC test and got it wrong :cry:
So when i searched i found soln in BTG .. here it is...


We start off with 1 piece of pie.

Draw the 1st line, you add 1 more piece to the pie for a total of 2 pieces.
Draw the 2nd line, you add 2 more pieces to the pie for a total of 4 pieces.
Draw the 3rd line, you add 3 more pieces to the pie for a total of 7 pieces.
Draw the 4th line, you add 4 more pieces to the pie for a total of 11 pieces.

So the nth line will always add n more pieces to the pie.

A 5th line would give us 11 + 5 = 16 pieces.
A 6th line would give us 16 + 6 = 22 pieces.


I never knew one Pizza can be sliced into these many pieces :P

Also i drew Soln for 2 n 3 lines ... PFA...
I guess it ll help u...
Attachments

File comment: Circular Pie sample soln for 2 and 3 Lines
Circular Pie.docx [46.07 KiB]
Downloaded 289 times

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Sachin9
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What is the maximum number of pieces that a circular pie can 12 Feb 2013, 03:44
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marcodonzelli
What is the maximum number of pieces that a circular pie can be divided into by four linear cuts?

A. 6
B. 8
C. 9
D. 10
E. 11

Can someone show this to me with a picture?

Such kind of combinations problems are always about a pattern recognition.

Maximum pieces:
0 line gives 1 whole piece;
1 line will gives 2 pieces: 1+1=2;
2 lines will give 4 pieces: 2+2=4;
3 lines will give 7 pieces: 4+3=7;
4 lines will give 7+4=11 pieces.

Similarly:
5 lines will give 11+5=16 pieces;
6 lines will give 16+6=22 pieces;
7 lines will give 22+7=29 pieces.

So, generally kth line will add k new pieces.

Answer: E.

P.S. Though I agree, it doesn't seem to be GMAT type of question.
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but I got this in the GC CAT.. you just said , it aint a GMAT type of Question :shock:
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What is the maximum number of pieces that a circular pie can 29 Jul 2014, 22:57
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[quote="Sachin9"][quote="Bunuel"][quote="marcodonzelli"]What is the maximum number of pieces that a circular pie can be divided into by four linear cuts?

A. 6
B. 8
C. 9
D. 10
E. 11



How does the 3rd line give us 7 pieces. Each time we add one more line we get 2 more pieces So shouldn't 3 lines give us 6 pieces.
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Bunuel
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What is the maximum number of pieces that a circular pie can 30 Jul 2014, 03:57
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akshaybansal991
How does the 3rd line give us 7 pieces. Each time we add one more line we get 2 more pieces So shouldn't 3 lines give us 6 pieces.
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Check below:
Attachment:
Untitled.png
Untitled.png [ 6.5 KiB | Viewed 9179 times ]
0 line gives 1 whole piece;
1 line will gives 2 pieces: 1+1=2;
2 lines will give 4 pieces: 2+2=4;
3 lines will give 7 pieces: 4+3=7;
4 lines will give 7+4=11 pieces.
5 lines will give 11+5=16 pieces;
6 lines will give 16+6=22 pieces;
7 lines will give 22+7=29 pieces.

Generally kth line will add k new pieces.
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What is the maximum number of pieces that a circular pie can 29 Oct 2015, 15:27
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thanks makes a lot of sense with the pattern recognition, hope i get this question now :D
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What is the maximum number of pieces that a circular pie can 27 Nov 2015, 10:11
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In my opinion Max Pieces could be 14.
3 Cuts will Give you 7 Pieces and if you halve the cake from side going through all the pieces , this will double it i.e 7*2=14
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What is the maximum number of pieces that a circular pie can 12 Jan 2022, 09:41
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marcodonzelli
What is the maximum number of pieces that a circular pie can be divided into by four linear cuts?

A. 6
B. 8
C. 9
D. 10
E. 11
Show more

Best way to do this questions is to make each subsequent cut such that-
1. All preceding line are cut by the subsequent line.
2. No two lines are concurrent.

You get the required answer i.e. 11.
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What is the maximum number of pieces that a circular pie can 13 Jan 2022, 00:45
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There is a generalized formula to solve these type of questions

Number of parts divided into = n(n+1)/2 + 1

Here, n = number of linear cuts.

Likewise in this question, n = 4

On solving, we get 11 parts.
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What is the maximum number of pieces that a circular pie can 17 Feb 2025, 06:52
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