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Which of the following best approximates the percent by [#permalink]

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10 Oct 2010, 02:58

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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?

I've seen the following example that I have doubts to solve:

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%

Thank you

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 \(2a-1.4a=0.6a\) --> \(\frac{0.6a}{2a}=0.3=30%\).

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.

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.

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

vivaslluis wrote:

Hello,

I've seen the following example that I have doubts to solve:

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%

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!
_________________

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

VeritasPrepBrian wrote:

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.

I've seen the following example that I have doubts to solve:

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%

Thank you

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.

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...

I've seen the following example that I have doubts to solve:

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%

Thank you

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.

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...

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

Re: Which of the following best approximates the percent by [#permalink]

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15 Nov 2014, 06:13

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Re: Which of the following best approximates the percent by [#permalink]

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31 May 2016, 20:04

vivaslluis wrote:

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%

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

gmatclubot

Re: Which of the following best approximates the percent by
[#permalink]
31 May 2016, 20:04

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