BTGmoderatorDC wrote:A certain floor of an office building has 1,200 square feet of floor area allocated to 2 equally sized conference rooms and 6 rectangular offices. If no office can be larger than a conference room, does each conference room have a floor area of less than 200 square feet?
(1) Each conference room must have a smaller area than the combined areas of any three offices and a larger area than the combined areas of any two offices.
(2) The four walls of each office have a combined length of less than 46 feet.
Say the area of a conference room is x sq ft and the area of an office is y sq ft.
Thus, 2x + 6y = 1200
=> x + 3y = 600
Given that x > y.
We need to determine whether x < 200 sq ft.
Let's take each statement one by one.
(1) Each conference room must have a smaller area than the combined areas of any three offices and a larger area than the combined areas of any two offices.
=> 2y < x < 3y
From x < 3y and x + 3y = 600, we get that x < 300 and 3y > 300 => y > 100.
=> 2y = 2*100 = 200
Thus, 2y < x < 3y => 200 < x < 300. Sufficient. The answer is no, each conference room does not have a floor area of less than 200 square feet.
(2) The four walls of each office have a combined length of less than 46 feet.
Say length and the width of an office are l and w, respectively.
Thus, 2(l + b) < 46
l + b < 23
We know that the area of a rectangle = l*b
Needless to state that if the area of the offices is minimum, the area of the conference room is going to be maximum as it is governed by x + 3y = 600; thus x >> 200.
It is interesting to see when y, i.e., area of an office, is maximum, what is the minimum value of the area of a conference room?
Given l + b < 23, if we want to maximize, l*b, we must take l = b = (<23/2); or l = b = ~11.5
Thus, the area of an office = l*b < 11.5*11.5
It is time-consuming to calculate 11.5*11.5; we can better calculate 11*12, which is 132; thus, 11.5*11.5 = a little greater than 132
With x + 3y = 600, we see than x = 600 - 3*132 = 600 - 396 = 204 > 200. Sufficient. The answer is no, each conference room does not have a floor area of less than 200 square feet.
The correct answer:
D
Hope this helps!
-Jay
_________________
Manhattan Review
Locations:
Manhattan Review Chennai |
GMAT Prep Himayatnagar |
GRE Prep Hyderabad |
Bangalore GRE Coaching | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor!
Click here.
