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705-805 (Hard)|   Geometry|      
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cyberjadugar
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An ant crawls from one corner of a room to the diagonally 13 Jun 2012, 05:48
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28% (01:20) correct 72% (01:29) wrong based on 165 sessions

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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. \(9\)
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cyberjadugar
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An ant crawls from one corner of a room to the diagonally 13 Jun 2012, 08:25
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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? :)
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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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gmatsaga
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An ant crawls from one corner of a room to the diagonally 13 Jun 2012, 06:19
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cyberjadugar
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. \(9\)
Show more


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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An ant crawls from one corner of a room to the diagonally 13 Jun 2012, 06:51
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gmatsaga
cyberjadugar
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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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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An ant crawls from one corner of a room to the diagonally 13 Jun 2012, 07:08
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gmatsaga
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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. \(9\)


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,
Show more

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? :)
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An ant crawls from one corner of a room to the diagonally 13 Jun 2012, 17:52
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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,
Show more


Did I tell you you're good?

AMAZING!!!!!
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An ant crawls from one corner of a room to the diagonally 13 Jun 2012, 19:15
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Thanks for the magical explanation cj ...you deserve some kudos for this! :)
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cyberjadugar
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An ant crawls from one corner of a room to the diagonally 14 Jun 2012, 00:07
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Thanks for the magical explanation cj ...you deserve some kudos for this! :)
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gmatsaga

Did I tell you you're good?
AMAZING!!!!!
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Thanks :-D

I appreciate the appreciation. :wink:
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An ant crawls from one corner of a room to the diagonally 28 Nov 2017, 17:19
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This will help
https://math.stackexchange.com/question ... ite-corner
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An ant crawls from one corner of a room to the diagonally 28 Nov 2017, 18:08
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cyberjadugar
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. \(9\)
Show more

Hi Bunuel, chetan2u

If the ant has to reach opposite corner of a room diagonally, shouldn't the answer be \(3\sqrt{3}\). can you please let me know where I am wrong in the below approach.

First the ant will crawl along the diagonal of one plane i.e. \(3\sqrt{2}\) and the then along the edge to the opposite corner = 3

So the total diagonal length will be \(d^2 = 3^2 + (3\sqrt{2})^2\) = \(27\)
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An ant crawls from one corner of a room to the diagonally 28 Nov 2017, 20:09
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cyberjadugar
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. \(9\)

Hi Bunuel, chetan2u

If the ant has to reach opposite corner of a room diagonally, shouldn't the answer be \(3\sqrt{3}\). can you please let me know where I am wrong in the below approach.

First the ant will crawl along the diagonal of one plane i.e. \(3\sqrt{2}\) and the then along the edge to the opposite corner = 3

So the total diagonal length will be \(d^2 = 3^2 + (3\sqrt{2})^2\) = \(27\)
Show more


Hi..
I'll attach a figure in sometime, but just try to understand..
Take any two adjacent sides which are perpendicular to each other and sides of each are 3*3...ABCD and BDEF are two sides
Now open it ...
A.....B......E
C.....D......F
The ant has to move from C to E..
By opening the two sides you have a rectangle ACFE..
The diagonal CE will be the shortest route..
CE=√(3^2+6^2)=√45=3√5

Hope you could visualise
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An ant crawls from one corner of a room to the diagonally 28 Nov 2017, 20:44
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chetan2u
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cyberjadugar
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. \(9\)

Hi Bunuel, chetan2u

If the ant has to reach opposite corner of a room diagonally, shouldn't the answer be \(3\sqrt{3}\). can you please let me know where I am wrong in the below approach.

First the ant will crawl along the diagonal of one plane i.e. \(3\sqrt{2}\) and the then along the edge to the opposite corner = 3

So the total diagonal length will be \(d^2 = 3^2 + (3\sqrt{2})^2\) = \(27\)


Hi..
I'll attach a figure in sometime, but just try to understand..
Take any two adjacent sides which are perpendicular to each other and sides of each are 3*3...ABCD and BDEF are two sides
Now open it ...
A.....B......E
C.....D......F
The ant has to move from C to E..
By opening the two sides you have a rectangle ACFE..
The diagonal CE will be the shortest route..
CE=√(3^2+6^2)=√45=3√5

Hope you could visualise
Show more

Hi chetan2u.. Thanks for the explanation.. Yes I could visualize it. However, the question never mentions that ant can walk only along the plane. It can take the edge path also. For Ex - it will move from one of Diagonal of ABCD and then the adjoining edge - In this case 3root(2) + 3.
Please correct if I am missing something.
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An ant crawls from one corner of a room to the diagonally 28 Nov 2017, 20:49
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cyberjadugar
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. \(9\)

Hi Bunuel, chetan2u

If the ant has to reach opposite corner of a room diagonally, shouldn't the answer be \(3\sqrt{3}\). can you please let me know where I am wrong in the below approach.

First the ant will crawl along the diagonal of one plane i.e. \(3\sqrt{2}\) and the then along the edge to the opposite corner = 3

So the total diagonal length will be \(d^2 = 3^2 + (3\sqrt{2})^2\) = \(27\)


Hi..
I'll attach a figure in sometime, but just try to understand..
Take any two adjacent sides which are perpendicular to each other and sides of each are 3*3...ABCD and BDEF are two sides
Now open it ...
A.....B......E
C.....D......F
The ant has to move from C to E..
By opening the two sides you have a rectangle ACFE..
The diagonal CE will be the shortest route..
CE=√(3^2+6^2)=√45=3√5

Hope you could visualise

Hi chetan2u.. Thanks for the explanation.. Yes I could visualize it. However, the question never mentions that ant can walk only along the plane. It can take the edge path also. For Ex - it will move from one of Diagonal of ABCD and then the adjoining edge - In this case 3root(2) + 3.
Please correct if I am missing something.
Show more

What you are missing is word SHORTEST..
Check the two answers, diagonal will always be the Shortest
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An ant crawls from one corner of a room to the diagonally 08 Nov 2022, 10:27
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