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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?

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02 Nov 2017, 22:34

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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?

Re: Thirty-six identical chairs must be arranged in rows with the same num [#permalink]

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03 Nov 2017, 03:23

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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04 Nov 2017, 08:46

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

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

Re: Thirty-six identical chairs must be arranged in rows with the same num [#permalink]

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04 Nov 2017, 10:25

chetan2u wrote:

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 383=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

Hi, Would you please explain the green-colored part of your post above.

Thank you
_________________

------------------------------ "Trust the timing of your life" Hit Kudus if this has helped you get closer to your goal, and also to assist others save time. Tq

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
_________________

Scott Woodbury-Stewart Founder and CEO

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

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 383=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

Hi, Would you please explain the green-colored part of your post above.

Thank you

hi.. sorry for the error.. it is 3*3=9 basically (2+1)(2+1)
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