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In an auditorium, 360 chairs are to be set up in a rectangular arrange

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In an auditorium, 360 chairs are to be set up in a rectangular arrange  [#permalink]

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New post 21 Sep 2019, 14:51
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Question Stats:

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In an auditorium, 360 chairs are to be set up in a rectangular arrangement with x rows of exactly y chairs each. If the only other restriction is that 10 < x < 25, how many different rectangular arrangements are possible?

A. Four
B. Five
C. Six
D. Eight
E. Nine

PS66602.01
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Re: In an auditorium, 360 chairs are to be set up in a rectangular arrange  [#permalink]

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New post 22 Sep 2019, 01:12
360 will have ; 2^3*3^2*5^1 ; 24 factors
possible integers for array x*y where x has restrictions 10<x<25 ; 12,15,18,20,24 ;
5 options
IMO B


gmatt1476 wrote:
In an auditorium, 360 chairs are to be set up in a rectangular arrangement with x rows of exactly y chairs each. If the only other restriction is that 10 < x < 25, how many different rectangular arrangements are possible?

A. Four
B. Five
C. Six
D. Eight
E. Nine

PS66602.01
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Re: In an auditorium, 360 chairs are to be set up in a rectangular arrange  [#permalink]

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New post 22 Sep 2019, 01:21
1
gmatt1476 wrote:
In an auditorium, 360 chairs are to be set up in a rectangular arrangement with x rows of exactly y chairs each. If the only other restriction is that 10 < x < 25, how many different rectangular arrangements are possible?

A. Four
B. Five
C. Six
D. Eight
E. Nine

PS66602.01


x and y are positive integers such that 360 = xy.

The rephrased question: How many factors does 360 have between 10 and 25, exclusive?

Since \(360=2^3\cdot 3^2\cdot 5\), we can quickly list the suitable factors.

\(3\cdot5=15\)
\(2^2\cdot5=20\)
\(2\cdot3^2=18\)
\(2^2\cdot3=12\)
\(2^3\cdot3=24\)

Answer: B
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Re: In an auditorium, 360 chairs are to be set up in a rectangular arrange   [#permalink] 22 Sep 2019, 01:21
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