Problem Solving

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

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