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Each edge of the above cube has length 1. If an ant

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Joined: 11 Sep 2015
Posts: 4331
Each edge of the above cube has length 1. If an ant  [#permalink]

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17 Jun 2018, 07:29
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Difficulty:

75% (hard)

Question Stats:

45% (01:40) correct 55% (01:29) wrong based on 101 sessions

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Each edge of the above cube has length 1. If an ant walks from point A to point B along the OUTSIDE of the cube, what is shortest distance the ant must travel?
A) √3
B) 2
C) √5
D) √6
E) √7

*kudos for all correct solutions

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Posts: 8256
Each edge of the above cube has length 1. If an ant  [#permalink]

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17 Jun 2018, 09:01
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1
GMATPrepNow wrote:

Each edge of the above cube has length 1. If an ant walks from point A to point B along the OUTSIDE of the cube, what is shortest distance the ant must travel?
A) √3
B) 2
C) √5
D) √6
E) √7

*kudos for all correct solutions

There can be two shortest distance..
1) A fly in the centre of box moving from ptA to pt B..
It will be the diagonal of cube
2) an ant that has to move on surface...
It will be a line joining A and B along the surface..

Here we are looking at case 2
So when we join A and B, ut creates a triangle ( imagine that you open two sides that A and B are on same plane..
So the triangle becomes a right angle triangle with base along A as 2 sides of cube so 2 *1=2
The altitude along B is one side so 1
Hypotenuse AB = $$√(2^2+1^1)=√5$$

C
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Each edge of the above cube has length 1. If an ant  [#permalink]

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17 Jun 2018, 09:35
Is it the path on the right cube?
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Re: Each edge of the above cube has length 1. If an ant  [#permalink]

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18 Jun 2018, 01:23
3
GMATPrepNow wrote:

Each edge of the above cube has length 1. If an ant walks from point A to point B along the OUTSIDE of the cube, what is shortest distance the ant must travel?
A) √3
B) 2
C) √5
D) √6
E) √7

*kudos for all correct solutions

Since, ant has to go through the surface thus we just have to imagine that cube is not on a 3d but a 2d plane, ie we open the cube. Now AB will the hypotenuse that we have to find and the base will be 1+1=2 and Perpendicular =1 so H^2=2^2+1^2=4+1=5
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Re: Each edge of the above cube has length 1. If an ant  [#permalink]

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18 Jun 2018, 03:23
4
1

Solution

Given:
• Each edge of the above cube has length 1
• An ant walks from point A to point B along the outside of the cube

To find:
• The shortest distance the ant must travel

Approach and Working:
Although the cube is a 3-D figure, if we unfold the surfaces containing points A and B respectively, we get a figure like this:

As the ant is at point A and needs to go at point B, with shortest possible distance,
• The minimum distance the ant needs to cover = $$\sqrt{[(1+1)^2 + 1^2]} = \sqrt{5}$$

Hence, the correct answer is option C.

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Re: Each edge of the above cube has length 1. If an ant  [#permalink]

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20 Jun 2018, 05:35
3
Top Contributor
1
GMATPrepNow wrote:

Each edge of the above cube has length 1. If an ant walks from point A to point B along the OUTSIDE of the cube, what is shortest distance the ant must travel?
A) √3
B) 2
C) √5
D) √6
E) √7

*kudos for all correct solutions

If we open up the cube, we get something like this....

Let x = the distance from A to B

Since we have a right triangle, we can apply the Pythagorean Theorem to get: 1² + 2² = x²
Simplify to get: 1 + 4 = x²
So, 5 = x², which means x = √5

Cheers,
Brent
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Re: Each edge of the above cube has length 1. If an ant  [#permalink]

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24 Jul 2019, 01:04
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).

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Re: Each edge of the above cube has length 1. If an ant   [#permalink] 24 Jul 2019, 01:04
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