Square

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bobdylan: Senior | Next Rank: 100 Posts; Posts: 68; Joined: Wed Nov 30, 2011 3:12 pm

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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Source: Beat The GMAT — Problem Solving | Tue Jun 12, 2012 4:05 am

Ashujain: Master | Next Rank: 500 Posts; Posts: 123; Joined: Fri Apr 20, 2012 4:36 amFollowed by: 1 member; Thanked: 29 times

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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raunekk: Legendary Member; Posts: 1159; Joined: Wed Apr 16, 2008 10:35 pm; Thanked: 56 times

by raunekk » Tue Jun 12, 2012 5:28 am

IMO: A

17-13/13 = 30

What's the answer?

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bobdylan: Senior | Next Rank: 100 Posts; Posts: 68; Joined: Wed Nov 30, 2011 3:12 pm

by bobdylan » Tue Jun 12, 2012 6:25 am

It is A.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

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 = âˆš2s.

Let s=5.
Distance from A to C along the perimeter = AB+BC = 5+5 = 10.
Diagonal AC = 5âˆš2 â‰ˆ 5(1.4) = 7.
Percent decrease â‰ˆ (10-7)/10 = 3/10 = 30%.

The correct answer is A.

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