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If a marching band has 72 members that always march in fo

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Intern
Joined: 09 Feb 2012
Posts: 47
If a marching band has 72 members that always march in fo  [#permalink]

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Updated on: 20 Aug 2012, 11:42
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57% (00:37) correct 43% (01:24) wrong based on 23 sessions

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If a marching band has 72 members that always march in formations of at least three rows and at least 3 members in each row, how many different formations can they march in?

OA: 8

Many thanks guys!

Originally posted by NYC5648 on 20 Aug 2012, 11:27.
Last edited by Bunuel on 20 Aug 2012, 11:42, edited 1 time in total.
Edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 58340
Re: If a marching band has 72 members that always march in fo  [#permalink]

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20 Aug 2012, 11:34
1
NYC5648 wrote:
If a marching band has 72 members that always march in formations of at least three rows and at least 3 members in each row, how many different formations can they march in?

OA: 8

Many thanks guys!

ROWS - PEOPLE IN EACH ROW
3 ------------- 24 (3*24=72)
4 ------------- 18
6 ------------- 12
8 ------------- 9

9 ------------- 8
12 ----------- 6
18 ----------- 4
24 ----------- 3

Total of 8 different formations.
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Joined: 05 Jul 2012
Posts: 58
Location: India
Concentration: Finance, Strategy
GMAT Date: 09-30-2012
GPA: 3.08
WE: Engineering (Energy and Utilities)
Re: If a marching band has 72 members that always march in fo  [#permalink]

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20 Aug 2012, 18:58
1
Bunuel wrote:
NYC5648 wrote:
If a marching band has 72 members that always march in formations of at least three rows and at least 3 members in each row, how many different formations can they march in?

OA: 8

Many thanks guys!

ROWS - PEOPLE IN EACH ROW
3 ------------- 24 (3*24=72)
4 ------------- 18
6 ------------- 12
8 ------------- 9

9 ------------- 8
12 ----------- 6
18 ----------- 4
24 ----------- 3

Total of 8 different formations.

How did you find out that the number of people in each row is the same ??
Senior Manager
Joined: 13 Oct 2016
Posts: 359
GPA: 3.98
Re: If a marching band has 72 members that always march in fo  [#permalink]

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16 Dec 2016, 05:55
1
NYC5648 wrote:
If a marching band has 72 members that always march in formations of at least three rows and at least 3 members in each row, how many different formations can they march in?

OA: 8

Many thanks guys!

We have $$X$$ rows and $$Y$$ columns (members in each row)

$$X*Y = 72$$

We need to find out the number of ways 72 can be expressed as a product of 2 factors.
$$72 = 2^3*3^2$$

# of ways = $$\frac{(3+1)*(2+1)}{2} = 6$$

But we can’t use this answer because in our question ORDER MATTERS. Rows are different from the columns (number of people in a row). $$3*24$$ here is different from $$24*3$$. Hence we should not divide by 2 and we get 12 total possibilities.

Next step: we need to take into consideration additional restriction: $$X ≥ 3$$, $$Y ≥ 3$$.

We need to deduct following 4 cases from our total set: $$1*72$$, $$2*36$$ and $$72*1$$, $$36*2$$

Final answer: $$12 – 4 = 8$$
Intern
Joined: 12 Feb 2018
Posts: 10
Re: If a marching band has 72 members that always march in fo  [#permalink]

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20 Feb 2019, 16:09
Bunuel wrote:
NYC5648 wrote:
If a marching band has 72 members that always march in formations of at least three rows and at least 3 members in each row, how many different formations can they march in?

OA: 8

Many thanks guys!

ROWS - PEOPLE IN EACH ROW
3 ------------- 24 (3*24=72)
4 ------------- 18
6 ------------- 12
8 ------------- 9

9 ------------- 8
12 ----------- 6
18 ----------- 4
24 ----------- 3

Total of 8 different formations.

Bunuel
The issue with this solution is that it´s assumed that all rows will request the same number of participants. However whether we consider minimum of 3 row within 3 people in each, we will have a significant increase in this number...
Re: If a marching band has 72 members that always march in fo   [#permalink] 20 Feb 2019, 16:09
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