Rectangular area calculation

[vinhaha]

Hi, could anybody help me with below question? Why is is not (10+60)(10+80) = 70 x 90 = 6,300 for the walkway area? Thanks in advance!

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A new exhibit at a zoo is rectangular and measures 60 feet by 80 feet. An observation walkway around the whole exhibit will be added that is 10 feet wide. If it takes 1 ton of concrete to pave 10 square feet of walkway, how many tons of concrete will be needed to pave the entire walkway?
â—‹ 150
â—‹ 240
â—‹ 320
â—‹ 480
â—‹ 2,400

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Solution:

We can find the area of the walkway by subtracting the smaller rectangle, the dimensions of which we are given in the question as 60 by 80, from the area of the big rectangle, the area that will include the proposed walkway.

We can find the area of the walkway by subtracting the smaller rectangle, the dimensions of which we are given in the question as 60 by 80, from the area of the big rectangle, the area that will include the proposed walkway.

Since the 10-foot-wide walkway will completely surround the exhibit, we will have to add 2 x 10 = 20 to both the length and the width given in the question.

The area of the large rectangle is therefore (20+60)(20+80) = 80 x 100 = 8,000.
The area of the small rectangle is 60 x 80 = 4,800.
The area of the walkway = 8,000 - 4,800 = 3,200 square feet.

One ton of concrete is required for every 10 square feet, so 3200 / 10 = 320 tons of concrete.

Answer choice (C) is correct.

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Hi vinhaha,

The explanation that you've attached is correct. If you're having trouble following the logic, then it might help you to draw a picture:

1) Draw a rectangle; label the sides 60 ft and 80 ft.
2) Draw a 'walkway' AROUND the rectangle; label the width of it 10ft.
3) Notice how the length and width of this larger shape is (80+10+10) ft and (60+10+10) ft.

4) To answer the question that's asked, we need the area of JUST the WALKWAY, so we can calculate the area of the larger rectangle (100x80) and subtract the area of the smaller rectangle (80x60)...

8000 - 4800 = 3200 square ft.

We know that it takes 1 ton of concrete to pave 10 square feet of walkway, so... 3200/10 = 320 tons of concrete.

GMAT assassins aren't born, they're made,
Rich

[DavidG@VeritasPrep]

See here for a visual:

[vinhaha]

Thanks guys!

I'm still a bit confused; area is L x W and this has expanded both by 10, so shouldn't it be L is 80 + 10 and W is 60 + 10 if you add the width of the walkway?
The calculation now is 60 + 10 + 10 times 80 + 10 + 10, wouldn't that mean the walkway is 20 in width?

[GMATGuruNY]

Thanks guys!

I'm still a bit confused; area is L x W and this has expanded both by 10, so shouldn't it be L is 80 + 10 and W is 60 + 10 if you add the width of the walkway?
The calculation now is 60 + 10 + 10 times 80 + 10 + 10, wouldn't that mean the walkway is 20 in width?

As illustrated by David's figure above:
The walkway extends beyond the rectangular exhibit 10 feet TO THE LEFT and 10 feet TO THE RIGHT, with the result that the total length is increased by 10+10 = 20 feet.
The walkway extends beyond the rectangular exhibit 10 feet UPWARDS and 10 feet DOWNWARDS, with the result that the total height is increased by 10+10 = 20 feet.

Similar problem:
https://www.beatthegmat.com/border-of-ph ... 54590.html

[vinhaha]

Thanks again; for whoever is confused like me, this really clears it for me:

"The walkway extends beyond the rectangular exhibit 10 feet TO THE LEFT and 10 feet TO THE RIGHT, with the result that the total length is increased by 10+10 = 20 feet."

[Matt@VeritasPrep]

Thanks again; for whoever is confused like me, this really clears it for me:

"The walkway extends beyond the rectangular exhibit 10 feet TO THE LEFT and 10 feet TO THE RIGHT, with the result that the total length is increased by 10+10 = 20 feet."

This is a very easy thing to overlook, so the GMAT (and math teachers everywhere) are very fond of testing it! When in doubt, DRAW IT OUT; you'll catch yourself that way.