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%

## Square

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- Ashujain
- Master | Next Rank: 500 Posts
**Posts:**123**Joined:**20 Apr 2012**Thanked**: 29 times**Followed by:**1 members

Let the side of square = xbobdylan 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%

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]

- GMATGuruNY
- GMAT Instructor
**Posts:**15533**Joined:**25 May 2010**Location:**New York, NY**Thanked**: 13060 times**Followed by:**1898 members**GMAT Score:**790

The diagonal of a square = âˆš2s.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 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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