pieces of a circular pie

Expert replies

arora007: Community Manager; Posts: 1048; Joined: Mon Aug 17, 2009 3:26 amFollowed by: 27 members; Location: India; Thanked: 51 times; GMAT Score:670

by arora007 » Wed Jul 07, 2010 12:44 am

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

a) 6
b) 8
c) 9
d) 10
e) 11

[spoiler]OA is E and i cannot believe it... oh boy!! what a problem to get as the 2nd problem of a test?
i could not visualize till i saw the figure though...
https://gmatclub.com/forum/maximum-numbe ... 79-20.html
[/spoiler]

gmatclub test problem

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gmatmachoman: Legendary Member; Posts: 2326; Joined: Mon Jul 28, 2008 3:54 amFollowed by: 2 members; Thanked: 173 times; GMAT Score:710

by gmatmachoman » Wed Jul 07, 2010 1:01 am

yeah... look at my ameatur mspaint dwg..

Is there any mathematical logic?

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kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members; Thanked: 215 times

by kvcpk » Wed Jul 07, 2010 1:16 am

Here is the answer.. With great difficulty I was able to put it on paint

arora007: Community Manager; Posts: 1048; Joined: Mon Aug 17, 2009 3:26 amFollowed by: 27 members; Location: India; Thanked: 51 times; GMAT Score:670

by arora007 » Wed Jul 07, 2010 10:47 am

even i would like to know if there is some mathematical logic...there must be!

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Jul 07, 2010 3:31 pm

arora007 wrote:What is the maximum number of pieces that a circular pie can be divided into using four linear cuts?

a) 6
b) 8
c) 9
d) 10
e) 11

[spoiler]OA is E and i cannot believe it... oh boy!! what a problem to get as the 2nd problem of a test?
i could not visualize till i saw the figure though...
https://gmatclub.com/forum/maximum-numbe ... 79-20.html
[/spoiler]

gmatclub test problem

There is a pattern:

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.

Pretty neat!

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kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members; Thanked: 215 times

by kvcpk » Wed Jul 07, 2010 8:19 pm

GMATGuruNY wrote:
arora007 wrote:What is the maximum number of pieces that a circular pie can be divided into using four linear cuts?

a) 6
b) 8
c) 9
d) 10
e) 11

[spoiler]OA is E and i cannot believe it... oh boy!! what a problem to get as the 2nd problem of a test?
i could not visualize till i saw the figure though...
https://gmatclub.com/forum/maximum-numbe ... 79-20.html
[/spoiler]

gmatclub test problem
There is a pattern:

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.

Pretty neat!

Wow!! Thats Awesome!!

diebeatsthegmat: Legendary Member; Posts: 1119; Joined: Fri May 07, 2010 8:50 amFollowed by: 3 members; Thanked: 29 times

by diebeatsthegmat » Sun Jul 18, 2010 11:47 am

gmatmachoman wrote:yeah... look at my ameatur mspaint dwg..

Is there any mathematical logic?

ohh man, i dawned the same as you did and didnt understand i just counted it 10 triangles
lol

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