36 identical chairs must be arranged in rows with the same

Question

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

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

Bunuel · Answer

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).

Luckisnoexcuse · Answer

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

C

saicharan1191 · Answer

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 · Answer

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

chetan2u · Answer

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

ScottTargetTestPrep · Answer

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

Kinshook · Answer

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

Asked: How many different arrangements are possible?

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

IMO C

Jalmagro · Answer

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:)

36 identical chairs must be arranged in rows with the same

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36 identical chairs must be arranged in rows with the same

Prep Toolkit

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