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
In an auditorium, 360 chairs are to be set up in a
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Factors of 360 in between 10 and 25 are 12, 15, 20 and 24BTGmoderatorDC 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
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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From the given information, the TOTAL number of chairs = xyBTGmoderatorDC 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
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
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We need to find integers x and y such that xy = 360 and 10 < x < 25. SinceBTGmoderatorDC 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
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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