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16 Sep 2014, 01:06
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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
A. 6
B. 8
C. 9
D. 10
E. 11
16 Sep 2014, 01:06
Kudos
Bookmarks
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.
Answer: E
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.
Answer: E
General Discussion
01 Apr 2015, 10:06
Kudos
Bookmarks
WOW !
This problem is a really smartly designed !
Got it wrong though
This problem is a really smartly designed !
Got it wrong though
this question ..... is just too much of a trap 
