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An ant crawls from one corner of a room to the diagonally

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An ant crawls from one corner of a room to the diagonally [#permalink] New post 13 Jun 2012, 04:48
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An ant crawls from one corner of a room to the diagonally opposite corner along the shortest possible path. If the dimensions of the room are 3 x 3 x 3, what distance does the ant cover?

A. 3\sqrt{2}+3

B. 6\sqrt{2}

C. 3*3^{\frac 13}

D. 3\sqrt{5}

E. 9
[Reveal] Spoiler: OA

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Re: An ant crawls from one corner of a room to the diagonally [#permalink] New post 13 Jun 2012, 05:19
cyberjadugar wrote:
An ant crawls from one corner of a room to the diagonally opposite corner along the shortest possible path. If the dimensions of the room are 3 x 3 x 3, what distance does the ant cover?

A. 3\sqrt{2}+3

B. 6\sqrt{2}

C. 3*3^{\frac 13}

D. 3\sqrt{5}

E. 9



This is a Physics question LOL

Anyway, for any dimension of a room that has dimensions a, b and c, the length of the shortest path is:

minimum among (1) square root[(a+b)^2 + c^2] (2) square root[(b+c)^2 + a^2] (3) square root](a+c)^2 + b^2\

Since we have dimensions 3, 3 and 3 we can try any of the three:

square root [(3+3)^2 + 3^2]= square root [6^2 + 9] = square root [36 +9] = square root [45] = square root [9*5] = 3 square root 5


Now how about some kudos, yes? :)
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Senior Manager
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Joined: 28 Mar 2012
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Concentration: Entrepreneurship
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Re: An ant crawls from one corner of a room to the diagonally [#permalink] New post 13 Jun 2012, 05:51
gmatsaga wrote:
cyberjadugar wrote:
An ant crawls from one corner of a room to the diagonally opposite corner along the shortest possible path. If the dimensions of the room are 3 x 3 x 3, what distance does the ant cover?

A. 3\sqrt{2}+3

B. 6\sqrt{2}

C. 3*3^{\frac 13}

D. 3\sqrt{5}

E. 9



This is a Physics question LOL

Anyway, for any dimension of a room that has dimensions a, b and c, the length of the shortest path is:

minimum among (1) square root[(a+b)^2 + c^2] (2) square root[(b+c)^2 + a^2] (3) square root](a+c)^2 + b^2\

Since we have dimensions 3, 3 and 3 we can try any of the three:

square root [(3+3)^2 + 3^2]= square root [6^2 + 9] = square root [36 +9] = square root [45] = square root [9*5] = 3 square root 5


Now how about some kudos, yes? :)

You are good at googling..!
This indeed is a physics problem, but many variants of this problem are asked in various competitive exams.
If one can do this, then similar concept can be extended to squares, rectangles or even cylinders.

Anyways, it is good problem :wink:

Regards,
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Kudos [?]: 17 [0], given: 16

Re: An ant crawls from one corner of a room to the diagonally [#permalink] New post 13 Jun 2012, 06:08
cyberjadugar wrote:
gmatsaga wrote:
cyberjadugar wrote:
An ant crawls from one corner of a room to the diagonally opposite corner along the shortest possible path. If the dimensions of the room are 3 x 3 x 3, what distance does the ant cover?

A. 3\sqrt{2}+3

B. 6\sqrt{2}

C. 3*3^{\frac 13}

D. 3\sqrt{5}

E. 9



This is a Physics question LOL

Anyway, for any dimension of a room that has dimensions a, b and c, the length of the shortest path is:

minimum among (1) square root[(a+b)^2 + c^2] (2) square root[(b+c)^2 + a^2] (3) square root](a+c)^2 + b^2\

Since we have dimensions 3, 3 and 3 we can try any of the three:

square root [(3+3)^2 + 3^2]= square root [6^2 + 9] = square root [36 +9] = square root [45] = square root [9*5] = 3 square root 5


Now how about some kudos, yes? :)

You are good at googling..!
This indeed is a physics problem, but many variants of this problem are asked in various competitive exams.
If one can do this, then similar concept can be extended to squares, rectangles or even cylinders.

Anyways, it is good problem :wink:

Regards,


Hehe is that a good thing or a bad thing?

Anyway, this is the first time I encountered such type of question. I can only remember the greatest distance (deluxe Pythagorean theorem). If my memory serves me right we could also use Calculus here. Does the topic multi-variable Calculus ring any bell? :)
_________________

Far better is it to dare mighty things, to win glorious triumphs, even though checkered by failure... than to rank with those poor spirits who neither enjoy nor suffer much, because they live in a gray twilight that knows not victory nor defeat.
- T. Roosevelt

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Re: An ant crawls from one corner of a room to the diagonally [#permalink] New post 13 Jun 2012, 07:25
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Quote:
Hehe is that a good thing or a bad thing?

Anyway, this is the first time I encountered such type of question. I can only remember the greatest distance (deluxe Pythagorean theorem). If my memory serves me right we could also use Calculus here. Does the topic multi-variable Calculus ring any bell? :)

Hi gmatsaga,

The concept of this question is to open up the surfaces and consider two adjacent surfaces as a plane. (Check the diagram below)
Thus, using the classical Pythagoras concept, the hypotenuse (or the shortest distance between two points) would be calculated as:
\sqrt{(3+3)^2+3^2} = 3\sqrt{5}

well talking about calculus, I would only say out of scope! :wink:

Regards,
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_________________

My posts: Solving Inequalities, Solving Simultaneous equations, Divisibility Rules

My story: 640 What a blunder!

Vocabulary resource: EdPrep

Facebook page: fb.com/EdPrep

Manager
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User avatar
Status: Rising GMAT Star
Joined: 05 Jun 2012
Posts: 133
Location: Philippines
Concentration: General Management, Finance
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WE: Corporate Finance (Consulting)
Followers: 6

Kudos [?]: 17 [0], given: 16

Re: An ant crawls from one corner of a room to the diagonally [#permalink] New post 13 Jun 2012, 16:52
cyberjadugar wrote:
Quote:
Hehe is that a good thing or a bad thing?

Anyway, this is the first time I encountered such type of question. I can only remember the greatest distance (deluxe Pythagorean theorem). If my memory serves me right we could also use Calculus here. Does the topic multi-variable Calculus ring any bell? :)

Hi gmatsaga,

The concept of this question is to open up the surfaces and consider two adjacent surfaces as a plane. (Check the diagram below)
Thus, using the classical Pythagoras concept, the hypotenuse (or the shortest distance between two points) would be calculated as:
\sqrt{(3+3)^2+3^2} = 3\sqrt{5}

well talking about calculus, I would only say out of scope! :wink:

Regards,



Did I tell you you're good?

AMAZING!!!!!
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Far better is it to dare mighty things, to win glorious triumphs, even though checkered by failure... than to rank with those poor spirits who neither enjoy nor suffer much, because they live in a gray twilight that knows not victory nor defeat.
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Re: An ant crawls from one corner of a room to the diagonally [#permalink] New post 13 Jun 2012, 18:15
Thanks for the magical explanation cj ...you deserve some kudos for this! :)
Senior Manager
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Re: An ant crawls from one corner of a room to the diagonally [#permalink] New post 13 Jun 2012, 23:07
gmatdog wrote:
Thanks for the magical explanation cj ...you deserve some kudos for this! :)


gmatsaga wrote:
Did I tell you you're good?
AMAZING!!!!!


Thanks :-D

I appreciate the appreciation. :wink:
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Re: An ant crawls from one corner of a room to the diagonally [#permalink] New post 19 Jan 2014, 04:19
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Re: An ant crawls from one corner of a room to the diagonally   [#permalink] 19 Jan 2014, 04:19
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