Last visit was: 12 Jul 2024, 19:06 It is currently 12 Jul 2024, 19:06
Toolkit
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

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

SORT BY:
Tags:
Show Tags
Hide Tags
Senior Manager
Joined: 29 Mar 2012
Posts: 266
Own Kudos [?]: 1525 [22]
Given Kudos: 23
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Senior Manager
Joined: 29 Mar 2012
Posts: 266
Own Kudos [?]: 1525 [15]
Given Kudos: 23
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
General Discussion
Manager
Joined: 05 Jun 2012
Status:Rising GMAT Star
Posts: 106
Own Kudos [?]: 278 [3]
Given Kudos: 16
Location: Philippines
Concentration: General Management, Finance
GPA: 3.22
WE:Corporate Finance (Consulting)
Senior Manager
Joined: 29 Mar 2012
Posts: 266
Own Kudos [?]: 1525 [0]
Given Kudos: 23
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Re: An ant crawls from one corner of a room to the diagonally [#permalink]
gmatsaga 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

Regards,
Manager
Joined: 05 Jun 2012
Status:Rising GMAT Star
Posts: 106
Own Kudos [?]: 278 [0]
Given Kudos: 16
Location: Philippines
Concentration: General Management, Finance
GPA: 3.22
WE:Corporate Finance (Consulting)
Re: An ant crawls from one corner of a room to the diagonally [#permalink]
gmatsaga 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

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?
Manager
Joined: 05 Jun 2012
Status:Rising GMAT Star
Posts: 106
Own Kudos [?]: 278 [0]
Given Kudos: 16
Location: Philippines
Concentration: General Management, Finance
GPA: 3.22
WE:Corporate Finance (Consulting)
Re: An ant crawls from one corner of a room to the diagonally [#permalink]
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!

Regards,

Did I tell you you're good?

AMAZING!!!!!
Intern
Joined: 03 Jun 2012
Posts: 22
Own Kudos [?]: 155 [0]
Given Kudos: 2
Location: United States
WE:Project Management (Computer Software)
Re: An ant crawls from one corner of a room to the diagonally [#permalink]
Thanks for the magical explanation cj ...you deserve some kudos for this!
Senior Manager
Joined: 29 Mar 2012
Posts: 266
Own Kudos [?]: 1525 [1]
Given Kudos: 23
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Re: An ant crawls from one corner of a room to the diagonally [#permalink]
1
Kudos
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

I appreciate the appreciation.
Manager
Joined: 04 May 2014
Posts: 111
Own Kudos [?]: 73 [0]
Given Kudos: 126
Location: India
WE:Sales (Mutual Funds and Brokerage)
Re: An ant crawls from one corner of a room to the diagonally [#permalink]
Senior Manager
Joined: 31 Jul 2017
Posts: 434
Own Kudos [?]: 450 [0]
Given Kudos: 752
Location: Malaysia
GPA: 3.95
WE:Consulting (Energy and Utilities)
An ant crawls from one corner of a room to the diagonally [#permalink]
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 $$d^2 = 3^2 + (3\sqrt{2})^2$$ = $$27$$
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11468
Own Kudos [?]: 34263 [0]
Given Kudos: 322
Re: An ant crawls from one corner of a room to the diagonally [#permalink]
rahul16singh28 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. $$9$$

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
Senior Manager
Joined: 31 Jul 2017
Posts: 434
Own Kudos [?]: 450 [0]
Given Kudos: 752
Location: Malaysia
GPA: 3.95
WE:Consulting (Energy and Utilities)
Re: An ant crawls from one corner of a room to the diagonally [#permalink]
chetan2u wrote:
rahul16singh28 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. $$9$$

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.
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11468
Own Kudos [?]: 34263 [0]
Given Kudos: 322
Re: An ant crawls from one corner of a room to the diagonally [#permalink]
rahul16singh28 wrote:
chetan2u 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. $$9$$

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.

What you are missing is word SHORTEST..
Check the two answers, diagonal will always be the Shortest
Non-Human User
Joined: 09 Sep 2013
Posts: 33953
Own Kudos [?]: 851 [0]
Given Kudos: 0
Re: An ant crawls from one corner of a room to the diagonally [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: An ant crawls from one corner of a room to the diagonally [#permalink]
Moderator:
Math Expert
94302 posts