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# Which of the following best approximates the percent by

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Intern
Joined: 07 Feb 2009
Posts: 13
Which of the following best approximates the percent by  [#permalink]

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10 Oct 2010, 03:58
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45% (medium)

Question Stats:

67% (01:25) correct 33% (01:28) wrong based on 276 sessions

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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%
Math Expert
Joined: 02 Sep 2009
Posts: 48067
Re: Square Diagonal versus Perimeter  [#permalink]

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10 Oct 2010, 04:57
1
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 $$2a-1.4a=0.6a$$ --> $$\frac{0.6a}{2a}=0.3=30%$$.

_________________
Intern
Joined: 07 Feb 2009
Posts: 13
Re: Square Diagonal versus Perimeter  [#permalink]

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10 Oct 2010, 14:44
Great! Thank you!!!
Director
Joined: 23 Apr 2010
Posts: 553
Re: Square Diagonal versus Perimeter  [#permalink]

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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.
Manager
Joined: 13 Jul 2010
Posts: 148
Re: Square Diagonal versus Perimeter  [#permalink]

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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.

Manager
Joined: 01 Nov 2010
Posts: 140
Location: Zürich, Switzerland
Re: Square Diagonal versus Perimeter  [#permalink]

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

Veritas Prep GMAT Instructor
Joined: 26 Jul 2010
Posts: 261
Re: Square Diagonal versus Perimeter  [#permalink]

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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/
_________________

Brian

Save $100 on live Veritas Prep GMAT Courses and Admissions Consulting Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options. GMAT self-study has never been more personalized or more fun. Try ORION Free! Veritas Prep Reviews Manager Joined: 17 Sep 2010 Posts: 187 Concentration: General Management, Finance GPA: 3.59 WE: Corporate Finance (Entertainment and Sports) Re: Square Diagonal versus Perimeter [#permalink] ### Show Tags 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 GMAT Instructor Joined: 26 Jul 2010 Posts: 261 Re: Square Diagonal versus Perimeter [#permalink] ### Show Tags 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! _________________ Brian Save$100 on live Veritas Prep GMAT Courses and Admissions Consulting

Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Veritas Prep Reviews

Manager
Joined: 13 Jul 2010
Posts: 148
Re: Square Diagonal versus Perimeter  [#permalink]

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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/
Intern
Joined: 06 Dec 2012
Posts: 25
GMAT 1: 510 Q46 V21
GPA: 3.5
Re: Square Diagonal versus Perimeter  [#permalink]

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

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...
Math Expert
Joined: 02 Sep 2009
Posts: 48067
Re: Square Diagonal versus Perimeter  [#permalink]

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

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.
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Director
Joined: 05 Mar 2015
Posts: 984
Re: Which of the following best approximates the percent by  [#permalink]

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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
Senior Manager
Joined: 14 Dec 2017
Posts: 459
Re: Which of the following best approximates the percent by  [#permalink]

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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%

Thanks,
GyM
Re: Which of the following best approximates the percent by &nbs [#permalink] 03 Aug 2018, 11:51
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