What is the maximum number of pieces that a circular pie can

Question

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

Bunuel · Accepted Answer

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

Maximum pieces:
0 line gives 1 whole piece;
 1  line will gives 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 kth line will add k new pieces.

Answer: E.

P.S. Though I agree, it doesn't seem to be GMAT type of question.

walker · Answer

1. 1st line can divide a circular pie by maximum 2 pieces
2. 2nd line gives us maximum 4 pieces
3. 3rd line can cross 3 pieces (to cross 4 piece is impossible) and we obtain 1+3*2=7 pieces
4. 4th line can cross maximum 4 pieces and we obtain 3+4*2=11

It can be solve less than 1min by means of the consecutive steps

sreehari · Answer

Getting 11

Below is the picture

sreehari · Answer

Look to maximize the intersections for each line, shouldn't take long.

courant · Answer

the key of this problem is the next line must be intersect all the previous line.so the answer is 2+2+3+4=11.Paint a chart is a directly and simply method.
sorry ,my english is so poor and I can't clearly express my viewpoint.

bsd_lover · Answer

9 is the best I can do.

walker · Answer

11.

1 line: 2*1=1
2 lines: 2*2=4
3 lines: 4+3=7
4 lines: 7+4=11

bsd_lover · Answer

EUREKA !!!!! - although I dont know how to do it mathematically .... walker any explanations ??

walker · Answer

It is more tasteful :wink:

walker · Answer

I guess it is better to go step by step, from 1 line to 4 lines

bsd_lover · Answer

walker the big piece is for u - when u nail 750 ....

walker · Answer

Agree, and I will cut it by 10000 pieces for all GMATclubbers who help me

buffdaddy · Answer

typo walker,

for those who were perplexed by walker's method,

he is saying for  P_n = P_{n-1} + n 
which in plain english mean, every new line n will will create n new pieces

sondenso · Answer

Wow, Wow, beautiful cake! Walker! I follow the 50-50 rule, so I cut the cake maximum 8 peices. Now I understand how the rule 20-80 works!

Thanks every body! If I see this question in real Gmat, I must bring with me a cake! :lol:

bsd_lover · Answer

If I see this in real gmat I'll never eat a cake again ...

wizardofwashington · Answer

hahahaha.. that's really funny. In my case, I'll be only focused on food after that point and not the quants. GMAT will be creaming me with such a question as my brain would immediately start thinking about food..

nsp007 · Answer

circular pie.JPG Hope this helps !

v1rgi3 · Answer

I personally don't like this question because it resembles too much of those brainteasers and I ended up with 14 pieces... 3 cuts would equal 7 pieces and then one linear straight slice horizontally would give me 14 pieces...

Marcab · Answer

Hii Bunuel.
Can you please explain the pattern. Though I understood the pattern, I am not able to visualize the pattern.

What is the maximum number of pieces that a circular pie can

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

What is the maximum number of pieces that a circular pie can

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards