Which of the following best approximates the percent by

Question

Which of the following best approximates the percent by which the distance from A to C along a 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%

Bunuel · Answer

Le the side of a square be  a .

Route from A to C along a diagonal AC is  \sqrt{2}a\approx{1.4a} ;
Route from A to C around the edge ABC is  2a ;

Difference is  2a-1.4a=0.6a  -->  \frac{0.6a}{2a}=0.3=30% .

Answer: A.

vivaslluis · Answer

Great! Thank you!!! :-D

nonameee · Answer

Could someone please explain to me the wording of the problem? I thought that the phrase:

means 1.4a/2a = 70%

I am a little bit confused here. Thank you.

gettinit · Answer

Please read the question carefully, the question says - "..the percent by which the distance from A to C along a diagonal of square ABCD reduces the distance from A to C around the edge of square ABCD?"

So its not asking what percent the diagonal is of the distance around the edge but rather the percent of the difference between the two distances.

Hope this was helpful.

Sarang · Answer

Using formula for 45-45-90 triangle, diagonal = sqrt(2) of the each side.

Answer:- A

VeritasPrepBrian · Answer

Great discussion, everyone - I just want to point out that (fittingly), gettinit gets it! One of the easiest things for the GMAT to do to make a pretty hard problem very hard is to bait you toward answering the wrong question. I've seen them do this a lot with Geometry problems that involve percents - there's a significant but subtle difference between:

Percent OF
and Percent GREATER THAN or LESS THAN

When you see a percentage problem, make sure you pause to answer the right question because pretty much any percent problem could be asked in either way.

For another example that also includes squares and diagonals, you may want to check out:  https://www.veritasprep.com/blog/2010/11/gmat-challenge-question-the-squared-circle/

USCTrojan2006 · Answer

You could use pythagorean theorem to solve this.

x^2+x^2=y^2

All sides of a square are equal, hence the two x^2. Plug in any number and solve.

VeritasPrepBrian · Answer

Hey Trojan,

Great call on that - even if you have the x-x-x*sqrt 2 ratio memorized, I think it's important to know where it comes from. In the a^2 + b^2 = c^2 Pythagorean Theorem, if we know that a = b then it's really 2a^2 = c^2.

And deriving that for yourself once or twice means there's very little chance you ever forget it (and you know you can always go back and prove it if you do forget).

Thanks for bringing that up - I'm a huge fan of knowledge over memorization!

gettinit · Answer

Brian great challenge question post -it fits this question perfectly!

sunny3011 · Answer

Hi ,
 i am confused about the denominator in the equation.

if the equation is (2a-1.4a) then the denominator should be 1.4a ???
how it is 2a??? not geeting...

Bunuel · Answer

We are comparing to the route from A to C around the edge, which is 2a, so 2a must be in the denominator.

rohit8865 · Answer

let the sides be 2 units.
original distance=2+2=4units
changed distance=2sq.root2
%change=change dist.-original dist./original dist.
=(2sq.root2-4)/4==-.2955
reduced by ~30%
Ans A

GyMrAT · Answer

Let  a  be the length of the side of the square, hence the diagonal is  \sqrt{2}a  =  1.4 a

Length along the edge of the square =  2a

Hence the % by which the distance is reduced along the diagonal =  \frac{(2a - 1.4a)}{2a}  =  \frac{0.7}{2}  =~  0.3  = 30%

Answer A.

Thanks,
GyM

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Which of the following best approximates the percent by

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Which of the following best approximates the percent by

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