GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Oct 2018, 17:01

### 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

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

Author Message
TAGS:

### Hide Tags

Current Student
Joined: 29 Mar 2012
Posts: 316
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
An ant crawls from one corner of a room to the diagonally  [#permalink]

### Show Tags

13 Jun 2012, 05:48
3
11
00:00

Difficulty:

95% (hard)

Question Stats:

25% (01:21) correct 75% (01:28) wrong based on 174 sessions

### HideShow timer Statistics

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. $$9$$
Current Student
Joined: 29 Mar 2012
Posts: 316
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]

### Show Tags

13 Jun 2012, 08:25
10
2
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,
Attachments

Path.jpg [ 8.46 KiB | Viewed 17510 times ]

##### General Discussion
Manager
Status: Rising GMAT Star
Joined: 05 Jun 2012
Posts: 122
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]

### Show Tags

13 Jun 2012, 06:19
2
1
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?
_________________

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

Current Student
Joined: 29 Mar 2012
Posts: 316
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]

### Show Tags

13 Jun 2012, 06:51
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
Status: Rising GMAT Star
Joined: 05 Jun 2012
Posts: 122
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]

### Show Tags

13 Jun 2012, 07:08
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?
_________________

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

Manager
Status: Rising GMAT Star
Joined: 05 Jun 2012
Posts: 122
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]

### Show Tags

13 Jun 2012, 17:52
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!!!!!
_________________

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

Intern
Joined: 03 Jun 2012
Posts: 29
Location: United States
WE: Project Management (Computer Software)
Re: An ant crawls from one corner of a room to the diagonally  [#permalink]

### Show Tags

13 Jun 2012, 19:15
Thanks for the magical explanation cj ...you deserve some kudos for this!
Current Student
Joined: 29 Mar 2012
Posts: 316
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]

### Show Tags

14 Jun 2012, 00:07
1
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: 161
Location: India
WE: Sales (Mutual Funds and Brokerage)
Re: An ant crawls from one corner of a room to the diagonally  [#permalink]

### Show Tags

28 Nov 2017, 17:19
Senior Manager
Joined: 31 Jul 2017
Posts: 477
Location: Malaysia
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
An ant crawls from one corner of a room to the diagonally  [#permalink]

### Show Tags

28 Nov 2017, 18:08
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 $$d^2 = 3^2 + (3\sqrt{2})^2$$ = $$27$$
_________________

If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!

Math Expert
Joined: 02 Aug 2009
Posts: 6961
Re: An ant crawls from one corner of a room to the diagonally  [#permalink]

### Show Tags

28 Nov 2017, 20:09
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
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Senior Manager
Joined: 31 Jul 2017
Posts: 477
Location: Malaysia
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
Re: An ant crawls from one corner of a room to the diagonally  [#permalink]

### Show Tags

28 Nov 2017, 20:44
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.
_________________

If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!

Math Expert
Joined: 02 Aug 2009
Posts: 6961
Re: An ant crawls from one corner of a room to the diagonally  [#permalink]

### Show Tags

28 Nov 2017, 20:49
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
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Re: An ant crawls from one corner of a room to the diagonally &nbs [#permalink] 28 Nov 2017, 20:49
Display posts from previous: Sort by