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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

Sent from my Moto G (5) Plus using GMAT Club Forum mobile app
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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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Bunuel
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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Bunuel
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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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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Don't make it harder than it looks:

Simply start with what will get you at least three rows (12 chairs per row)

Then go down from 12 chairs until you get under three rows

Ignore any number that doesn't leave an integer of chairs per row

Answer 5:)
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