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36 identical chairs must be arranged in rows with the same

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antoxavier
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36 identical chairs must be arranged in rows with the same [#permalink] New post   Updated on: 31 Jan 2013, 04:36
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36 identical chairs must be arranged in rows with the same number of chairs in each row. Each row must contain at least three chairs and there must be at least three rows. A row is parallel to the front of the room. How many different arrangements are possible?

A. 2
B. 4
C. 5
D. 6
E. 10
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C

Originally posted by antoxavier on 30 Jan 2013, 23:41.
Last edited by Bunuel on 31 Jan 2013, 04:36, edited 2 times in total.
Renamed the topic and edited the question.
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Bunuel
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Re: 36 identical chairs must be arranged in rows with the same [#permalink] New post   31 Jan 2013, 04:38
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antoxavier wrote:
36 identical chairs must be arranged in rows with the same number of chairs in each row. Each row must contain at least three chairs and there must be at least three rows. A row is parallel to the front of the room. How many different arrangements are possible?

A. 2
B. 4
C. 5
D. 6
E. 10


We should have at least 3 rows and at least 3 chairs in a row:

# OF ROWS --- # OF CHAIRS IN A ROW
3 --------------------------------- 12
4 ---------------------------------- 9
6 ---------------------------------- 6
9 ---------------------------------- 4
12 -------------------------------- 3

Total of 5 ways.

Answer: C.


Hope it's clear.

P.S. P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to the rule #3 (the name of a topic MUST be the first 40 characters (~the first two sentences) of the question).
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Luckisnoexcuse
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Re: Thirty-six identical chairs must be arranged in rows with the same num [#permalink] New post   02 Nov 2017, 23:34
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Bunuel wrote:
Thirty-six identical chairs must be arranged in rows with the same number of chairs in each row. Each row must contain at least 3 chairs, and there must be at least 3 rows. A row is parallel to the front of the room. How many different arrangements are possible?

(A) 2
(B) 4
(C) 5
(D) 6
(E) 10

r>=3, c>=3
(r,c) = (3,12), (4,9), (6,6), (9,4), (12,3)

C
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Re: Thirty-six identical chairs must be arranged in rows with the same num [#permalink] New post   03 Nov 2017, 04:23
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36 chairs.. so what we are looking for is number of factors of 36 = 9. Out of this we need to remove cases in which one of the factor is less than 3 i.e (36,1) (18,2) so 9-4 = 5

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Shubhashri10
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Re: Thirty-six identical chairs must be arranged in rows with the same num [#permalink] New post   04 Nov 2017, 09:46
The solution can be analysed as m*n type of arrangements which are
12*3
3*12
6*6
4*9
9*4
given the total type of arrangement
The Answer is C- 5
Please correct me if i am wrong
Also Suggest any shortcut method to reduce time

Thanks
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chetan2u
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Thirty-six identical chairs must be arranged in rows with the same num [#permalink] New post   04 Nov 2017, 10:17
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Bunuel wrote:
Thirty-six identical chairs must be arranged in rows with the same number of chairs in each row. Each row must contain at least 3 chairs, and there must be at least 3 rows. A row is parallel to the front of the room. How many different arrangements are possible?

(A) 2
(B) 4
(C) 5
(D) 6
(E) 10


hi..
Shubhashri10, you are looking for a shortcut, then here is a method if you analyze what the Q is all about..

the rows and columns are nothing but factors of 36.
\(36=2^2*3^2\)... so number of factors are 3*3=9

but the rows and columns are ATLEAST 3..
so take out factors which are less than 3 ;- 1 and 2, so TWO
but these 2 can take value of rows or columns so TWO ways
total 2*2=4

ans = 9-4=5
C
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Re: Thirty-six identical chairs must be arranged in rows with the same num [#permalink] New post   06 Nov 2017, 17:32
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Bunuel wrote:
Thirty-six identical chairs must be arranged in rows with the same number of chairs in each row. Each row must contain at least 3 chairs, and there must be at least 3 rows. A row is parallel to the front of the room. How many different arrangements are possible?

(A) 2
(B) 4
(C) 5
(D) 6
(E) 10


We could have the following arrangements:

3 rows of 12 chairs per row

4 rows of 9 chairs per row

6 rows of 6 chairs per row

9 rows of 4 chairs per row

12 rows of 3 chairs per row

We see that the number of arrangements is 5.

Answer: C
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Re: 36 identical chairs must be arranged in rows with the same [#permalink] New post   15 Aug 2022, 08:37
Given: 36 identical chairs must be arranged in rows with the same number of chairs in each row. Each row must contain at least three chairs and there must be at least three rows. A row is parallel to the front of the room.

Asked: How many different arrangements are possible?

36 = 2^2*3^2 = 3*12 = 12*3 = 6*6 = 4*9 = 9*4

IMO C
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Re: 36 identical chairs must be arranged in rows with the same [#permalink] New post   12 Oct 2023, 02:43
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Re: 36 identical chairs must be arranged in rows with the same [#permalink]
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