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M19-22

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M19-22 [#permalink]

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New post 16 Sep 2014, 01:06
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A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

20% (00:31) correct 80% (00:49) wrong based on 168 sessions

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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.
Image

Answer: E
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M19-22 [#permalink]

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New post 01 Apr 2015, 10:06
WOW !

This problem is a really smartly designed !

Got it wrong though :|

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Re: M19-22 [#permalink]

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New post 15 Aug 2015, 20:28
Hello,

I thing I am missing something.

Why not 12?

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

Could you please assist.

Thank you.

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Re: M19-22 [#permalink]

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New post 25 Sep 2015, 13:20
Hello Bunuel

Could you please help me with this one - I didn't understand the explanation.
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Re: M19-22 [#permalink]

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aimtoteach wrote:
Hello Bunuel

Could you please help me with this one - I didn't understand the explanation.


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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Re: M19-22 [#permalink]

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New post 04 Feb 2016, 04:49
I doubt one can get this type of question on exam
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Re: M19-22 [#permalink]

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New post 22 Aug 2016, 09:47
Nice question/solution Bunuel, got it by drawing the figure though :p

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Re M19-22 [#permalink]

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New post 23 Aug 2016, 05:33
I think this is a high-quality question and I agree with explanation.

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Re: M19-22 [#permalink]

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New post 05 Sep 2016, 11:01
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?

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Re: M19-22 [#permalink]

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New post 08 Dec 2016, 12:33
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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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Re: M19-22 [#permalink]

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New post 22 Aug 2017, 06:16
+1 for E. Got it by trial and error.
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Re: M19-22 [#permalink]

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New post 22 Aug 2017, 08:57
shasadou wrote:
I doubt one can get this type of question on exam

Absolutely

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Re: M19-22   [#permalink] 22 Aug 2017, 08:57
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