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09 Nov 2016, 17:03
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Hey - can anyone help me out with the following question?
A department of 20 people is moving into a new office. Each person will have a 4 meter by 4 meter work space. The perimeter of the new office is 85 meters and the ratio of length to width is 3:2. How much space in square meters will be left once the peoples' work spaces are set?
A: 21.68
B: 27.09
C: 113.50
D: 131.50
Thanks for your help!
A department of 20 people is moving into a new office. Each person will have a 4 meter by 4 meter work space. The perimeter of the new office is 85 meters and the ratio of length to width is 3:2. How much space in square meters will be left once the peoples' work spaces are set?
A: 21.68
B: 27.09
C: 113.50
D: 131.50
Thanks for your help!
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09 Nov 2016, 18:23
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Dear coolcoolcool2016,
I'm happy to respond.
Interesting: this is not a GMAT question, because it is a multiple choice with only four answers. What is the source of this question? I would start with ratios & portioning.
The aspect ratio of the space is 3:2, 3 "parts" by 2 "parts," so the perimeter is 10 parts.
10 parts = 85 m
1 part = 8.5 m
This means that
length = 3 parts = 25.5 m
width = 2 part = 17 m
We can fit four of the (4m) x (4 m) spaces across the width, and up to six across the length. We could compute the area of the whole space (25.5. x 17, not a fun product) and subtract the total are of the workspaces (20 x 16). Instead, I think it's easy to consider the leftover spaces. See this diagram:
Attachment:
new office with work spaces.png
Probably the 20 workspaces wouldn't be crammed together like this, but arranging them like this makes it easiest to compute the leftover area, the area in blue. Imagine a line from the lower right corner of the workspaces that goes horizontally to the right wall. This divides the blue into two rectangles.
The first is 25.5 m long and 1 meter high, with an area of A = 25.5 sq m
The second is 16 m tall and 5.5 meters wide.
We can use the doubling and halving trick for this second multiplication:
16 x 5.5 = 8 x 11 = 88
Add the two areas: 25.5 + 88 = 113.5 sq m
Answer = (C)
That's a great problem! Let me know if you have any questions.
Mike
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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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