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
This topic has expert replies
- Ashujain
- Master | Next Rank: 500 Posts
- Posts: 123
- Joined: Fri Apr 20, 2012 4:36 am
- 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: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
The diagonal of a square = √2s.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 = 5√2 ≈ 5(1.4) = 7.
Percent decrease ≈ (10-7)/10 = 3/10 = 30%.
The correct answer is A.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3