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

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by BTGmoderatorDC » Sun Dec 29, 2019 6:10 pm
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




OA B

Source: Official Guide
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correction

by SampathKp » Sun Dec 29, 2019 7:46 pm
BTGmoderatorDC 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




OA B

Source: Official Guide
Factors of 360 in between 10 and 25 are 12, 15, 20 and 24

So we cn form 4 rows with each row containing equal chairs

1. 12 *30 =360
2. 15*24 = 360
3. 20*18=360
4.18*20 = 360
5. 24*15 = 360

5 different rectangular combinations possible.

Answer is B

PS - Edited to correct the error .
Last edited by SampathKp on Mon Dec 30, 2019 7:13 am, edited 1 time in total.
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by Brent@GMATPrepNow » Mon Dec 30, 2019 6:51 am
BTGmoderatorDC 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
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
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by Scott@TargetTestPrep » Sun Jan 05, 2020 8:06 pm
BTGmoderatorDC 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




OA B

Source: Official Guide
We need to find integers x and y such that xy = 360 and 10 < x < 25. Since

360 = 12 * 30 = 15 * 24 = 18 * 20 = 20 * 18 = 24 * 15

We see that x can be 12, 15, 18, 20, or 24. Therefore, there are 5 different arrangements.

Answer: B

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