M19-22

Question

What is the maximum number of pieces that a circular pie can be divided into by making four linear cuts?

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

Bunuel · Accepted Answer

Official Solution:

What is the maximum number of pieces that a circular pie can be divided into by making four linear cuts?

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

To solve this type of combinatorial problem, pattern recognition is often the key.
 
Maximum pieces:
   
0 cuts result in 1 whole piece;
 
1 cut will produce 2 pieces:  1 + 1 = 2 ;
 
2 cuts will produce 4 pieces:  2 + 2 = 4 ;
 
3 cuts will produce 7 pieces:  4 + 3 = 7 ;
 
4 cuts will produce 11 pieces:  7 + 4 = 11 .
   
Following the same pattern:
   
5 cuts will produce 16 pieces:  11 + 5 = 16 ;
 
6 cuts will produce 22 pieces:  16 + 6 = 22 ;
 
7 cuts will produce 29 pieces:  22 + 7 = 29 .
   
In general, the  k_{th}  cut will add  k  new pieces.
 
Thus, with four linear cuts, a circular pie can be divided into a maximum of 11 pieces.
 
 https://gmatclub.com/gmat-practice-tests/resources/import/img/m19-22.jpg

Answer: E

buddyisraelgmat · Answer

WOW ! This problem is a really smartly designed ! Got it wrong though

aimtoteach · Answer

Hello  Bunuel

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

happyface101 · Answer

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!

sanghar · Answer

Nice question/solution  Bunuel , got it by drawing the figure though :p

Senthil7 · Answer

I think this is a  high-quality  question and I agree with explanation.

manhasnoname · Answer

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?

arvind910619 · Answer

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.

CAMANISHPARMAR · Answer

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.

Mrjack · Answer

this question ..... is just too much of a trap

TBT · Answer

good question

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

Josvit · Answer

Nice question.

If it had been 14 in the answer choices, that would have been the highest number.

Three vertical cuts and one horizontal cut.

Given that we don´t have 14, 11 is the correct one.

Bunuel · Answer

Three vertical cuts and one horizontal cut give 8 pieces, not 14. 11 is the maximum number.

Dooperman · Answer

Nice question. Maximize the intersections when drawing the figure.

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