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# M19-22

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Math Expert
Joined: 02 Sep 2009
Posts: 53066

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16 Sep 2014, 00:06
1
13
00:00

Difficulty:

95% (hard)

Question Stats:

25% (00:36) correct 75% (00:49) wrong based on 268 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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Math Expert
Joined: 02 Sep 2009
Posts: 53066

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16 Sep 2014, 00:06
6
9
Official Solution:

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

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

Maximum pieces:

0 line gives 1 whole piece;

1 line will give 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 $$k_{th}$$ line will add $$k$$ new pieces.

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Manager
Joined: 14 Jul 2014
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01 Apr 2015, 09:06
WOW !

This problem is a really smartly designed !

Got it wrong though
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15 Aug 2015, 19:28
Hello,

I thing I am missing something.

Why not 12?

A pie could be divided into 12 pieces (maximum) through 03 linear cuts?

Thank you.
Manager
Status: GMAT Date: 10/08/15
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25 Sep 2015, 12:20
Hello Bunuel

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aimtoteach

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Joined: 05 Aug 2015
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18 Jan 2016, 11:34
2
aimtoteach wrote:
Hello Bunuel

Not sure if this is still helpful to you ... it's been a few months since you posted the question, but here is some clarify:

1 line: 1+1 = 2 pieces -- straight forward
2 lines: carry the 2 pieces from the last one + 2 lines = 4 pieces
3 lines: carry the 4 from the last one + 3 lines = 7 pieces
4 lines: carry the 7 from the last one + 4 lines = 11 pieces

Hope this helps you!
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04 Feb 2016, 03:49
I doubt one can get this type of question on exam
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22 Aug 2016, 08:47
Nice question/solution Bunuel, got it by drawing the figure though :p
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23 Aug 2016, 04:33
1
I think this is a high-quality question and I agree with explanation.
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Joined: 21 Apr 2016
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05 Sep 2016, 10:01
Although answered incorrectly, I liked this question after reading the solution. Can someone post such similar questions? Thanks!

I believe this is true for any shape, need not necessarily be a circle? Am I correct?
Intern
Joined: 30 Sep 2016
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08 Dec 2016, 11:33
1
Hi All,

I feel the number of pieces can be even more, 14 to be precise. Here's how - the first three cuts same as described previously = 7. The last cut however will be along the surface of the circular pie ( A cut that maintains the circular shape of the pie, a horizontal cut along the thickness of the pie ) doubling the number of pieces! This cut is also linear as per the question stem.

Not sure where am I going wrong ? Or the question stem needs update?

Thanks!
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22 Aug 2017, 05:16
+1 for E. Got it by trial and error.
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22 Aug 2017, 07:57
I doubt one can get this type of question on exam

Absolutely

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03 Jul 2018, 07:10
wow this problem is really good for maximum pieces we have to divide the pie into unequal parts and make sure that lines do not pass through intersection points. Then we will maximum pieces.
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03 Jul 2018, 09:37
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. (a) this feels slightly unrealistic? It doesn't build or expand on any GMAT theories that I can recognise

(b) if it does, the explanation could be clearer. It's not clear from the pattern you set out how you're supposed to spot this in 2 minutes without basic trial and error
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17 Aug 2018, 04:22
is this an appropriate GMAT question. Also, the explanation is not very good. Can any moderator give a better explanation?
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Joined: 11 Feb 2015
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08 Oct 2018, 21:18
Attachment:
Circle With lines.jpg

There is nothing much one can do when you draw the first line. The circle will be divided intwo two parts.

When you draw the second line then you have a choice, either you can interest the first line or not? Obviously when the second line intersects the first line within the circle then you have more divisions, i.e. 4 in all.

So one can learn from step two to draw the third line which will intersect as many lines as possible within the circle. I.e. third line intersecting the first two lines. Similarly the fourth line intersecting the first three lines, giving us 11 parts.
>> !!!

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M19-22   [#permalink] 08 Oct 2018, 21:18
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# M19-22

Moderators: chetan2u, Bunuel

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