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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  [#permalink]

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New post 10 Oct 2010, 03:58
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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?

A. 30%
B. 43%
C. 45%
D. 50%
E. 70%
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Re: Square Diagonal versus Perimeter  [#permalink]

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New post 10 Oct 2010, 04:57
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1
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%

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.
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Re: Square Diagonal versus Perimeter  [#permalink]

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New post 10 Oct 2010, 14:44
Great! Thank you!!! :-D
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Re: Square Diagonal versus Perimeter  [#permalink]

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New post 27 Nov 2010, 03:19
Could someone please explain to me the wording of the problem? I thought that the phrase:

Quote:
... by which the distance from A to C along a diagonal of square ABCD reduces ...


means 1.4a/2a = 70%

I am a little bit confused here. Thank you.
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Re: Square Diagonal versus Perimeter  [#permalink]

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New post 28 Nov 2010, 11:16
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.
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Re: Square Diagonal versus Perimeter  [#permalink]

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New post 29 Nov 2010, 16:39
Using formula for 45-45-90 triangle, diagonal = sqrt(2) of the each side.

Answer:- A
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Re: Square Diagonal versus Perimeter  [#permalink]

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New post 30 Nov 2010, 13:07
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: http://www.veritasprep.com/blog/2010/11/gmat-challenge-question-the-squared-circle/
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Re: Square Diagonal versus Perimeter  [#permalink]

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New post 30 Nov 2010, 16:46
1
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.

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%

Thank you
Veritas Prep and Orion Instructor
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Re: Square Diagonal versus Perimeter  [#permalink]

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New post 30 Nov 2010, 21:08
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!
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Re: Square Diagonal versus Perimeter  [#permalink]

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New post 01 Dec 2010, 19:45
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.

For another example that also includes squares and diagonals, you may want to check out: http://www.veritasprep.com/blog/2010/11/gmat-challenge-question-the-squared-circle/
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Re: Square Diagonal versus Perimeter  [#permalink]

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New post 11 Oct 2013, 06:50
Bunuel wrote:
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%

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...
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Re: Square Diagonal versus Perimeter  [#permalink]

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New post 11 Oct 2013, 06:53
sunny3011 wrote:
Bunuel wrote:
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%

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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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New post 31 May 2016, 21:04
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
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Re: Which of the following best approximates the percent by  [#permalink]

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New post 03 Aug 2018, 11:51
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 \(a\) 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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Re: Which of the following best approximates the percent by &nbs [#permalink] 03 Aug 2018, 11:51
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