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805+ (Hard)|   Combinations|   Geometry|      
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marcodonzelli
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What is the maximum number of pieces that a circular pie can Updated on: 14 Nov 2013, 12:53
Originally posted by marcodonzelli on 15 Mar 2008, 11:52.
Last edited by Bunuel on 14 Nov 2013, 12:53, edited 1 time in total.
Added the OA.
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E
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Difficulty:

95% (hard)

Question Stats:

30% (01:25) correct 70% (01:15) wrong based on 630 sessions

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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
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E
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Bunuel
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What is the maximum number of pieces that a circular pie can 25 Feb 2012, 03:59
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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?
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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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What is the maximum number of pieces that a circular pie can 16 Mar 2008, 01:43
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1. 1st line can divide a circular pie by maximum 2 pieces
2. 2nd line gives us maximum 4 pieces
3. 3rd line can cross 3 pieces (to cross 4 piece is impossible) and we obtain 1+3*2=7 pieces
4. 4th line can cross maximum 4 pieces and we obtain 3+4*2=11

It can be solve less than 1min by means of the consecutive steps
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What is the maximum number of pieces that a circular pie can 15 Mar 2008, 12:14
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Getting 11

Below is the picture
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walker
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What is the maximum number of pieces that a circular pie can 30 May 2008, 03:24
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11.

1 line: 2*1=1
2 lines: 2*2=4
3 lines: 4+3=7
4 lines: 7+4=11
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bsd_lover
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What is the maximum number of pieces that a circular pie can 30 May 2008, 03:32
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EUREKA !!!!! - although I dont know how to do it mathematically .... walker any explanations ??
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walker
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What is the maximum number of pieces that a circular pie can 30 May 2008, 03:39
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It is more tasteful :wink:
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nsp007
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What is the maximum number of pieces that a circular pie can 22 May 2010, 16:15
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Attachment:
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circular pie.JPG [ 9.65 KiB | Viewed 29721 times ]



Hope this helps !
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What is the maximum number of pieces that a circular pie can 17 Nov 2012, 02:22
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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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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...
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File comment: Circular Pie sample soln for 2 and 3 Lines
Circular Pie.docx [46.07 KiB]
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akshaybansal991
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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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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:
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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 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 04 Jul 2026, 08:52
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