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

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Senior Manager
Joined: 04 Sep 2017
Posts: 291
In an auditorium, 360 chairs are to be set up in a rectangular arrange  [#permalink]

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21 Sep 2019, 14:51
4
00:00

Difficulty:

45% (medium)

Question Stats:

60% (02:31) correct 40% (02:28) wrong based on 58 sessions

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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
Manager
Joined: 14 Apr 2017
Posts: 70
Location: Hungary
GMAT 1: 760 Q50 V42
WE: Education (Education)
Re: In an auditorium, 360 chairs are to be set up in a rectangular arrange  [#permalink]

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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.

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

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

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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
Re: In an auditorium, 360 chairs are to be set up in a rectangular arrange   [#permalink] 22 Sep 2019, 01:12
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