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Square

by bobdylan » Tue Jun 12, 2012 4:05 am
Which of the following best approximates the percent by which the distance from A to C along the diagonal of square ABCD reduces the distance from A to C around the edge of square ABCD?
a.30%
b.43%
c. 45%
d. 50 %
e.70%
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by Ashujain » Tue Jun 12, 2012 5:24 am
bobdylan wrote:Which of the following best approximates the percent by which the distance from A to C along the diagonal of square ABCD reduces the distance from A to C around the edge of square ABCD?
a.30%
b.43%
c. 45%
d. 50 %
e.70%
Let the side of square = x
Then Diagonal AC = 2^1/2 * x = 1.44x
And AC around the edge = AB+BC = AD+DC = 2x
Therefore, decrease in distance = 2x-1.44x = 0.56x
Therefore, % decrease = .56x/2x * 100 = 28%
Hence, [spoiler]A) 30%[/spoiler]
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by raunekk » Tue Jun 12, 2012 5:28 am
IMO: A

17-13/13 = 30

What's the answer?
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by bobdylan » Tue Jun 12, 2012 6:25 am
It is A.
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by GMATGuruNY » Tue Jun 12, 2012 6:27 am
bobdylan wrote:Which of the following best approximates the percent by which the distance from A to C along the diagonal of square ABCD reduces the distance from A to C around the edge of square ABCD?
a.30%
b.43%
c. 45%
d. 50 %
e.70%
The diagonal of a square = √2s.

Let s=5.
Distance from A to C along the perimeter = AB+BC = 5+5 = 10.
Diagonal AC = 5√2 ≈ 5(1.4) = 7.
Percent decrease ≈ (10-7)/10 = 3/10 = 30%.

The correct answer is A.
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