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

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by BTGModeratorVI » Tue Jul 07, 2020 6:25 am

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B

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D

E

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Difficulty—

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

Answer: B
Source: Official guide
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Re: In an auditorium, 360 chairs are to be set up in a rectangular arrangement

by Brent@GMATPrepNow » Fri Jul 10, 2020 8:19 am
BTGModeratorVI wrote: ↑
Tue Jul 07, 2020 6:25 am
 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

Answer: B
Source: Official guide
From the given information, the TOTAL number of chairs = xy
This means: xy = 360

Since x and y must be POSITIVE INTEGERS, there is a finite number of possibilities.
To help us list the pairs of values with a product of 360, let's find the prime factorization of 360
360 = (2)(2)(2)(3)(3)(5)

When we consider the fact that 10 < x < 25, the possibilities are:
x = 12 & y = 30
x = 15 & y = 24
x = 18 & y = 20
x = 20 & y = 18
x = 24 & y = 15

There are five such possibilities

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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