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

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BrentGMATPrepNow
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Each edge of the above cube has length 1. If an ant [#permalink] New post  17 Jun 2018, 08:29
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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

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EgmatQuantExpert
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Re: Each edge of the above cube has length 1. If an ant [#permalink] New post  18 Jun 2018, 04:23
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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.

Answer: C
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chetan2u
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Each edge of the above cube has length 1. If an ant [#permalink] New post  17 Jun 2018, 10:01
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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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Screenshot_2018-06-17-22-39-56-037_com.picsart.studio.png [ 44.85 KiB | Viewed 9423 times ]


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gmatzpractice
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Each edge of the above cube has length 1. If an ant [#permalink] New post  17 Jun 2018, 10:35
Is it the path on the right cube?
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Antreev
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Re: Each edge of the above cube has length 1. If an ant [#permalink] New post  18 Jun 2018, 02:23
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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
H^2=5 so H=\sqrt{5} answer C
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BrentGMATPrepNow
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Re: Each edge of the above cube has length 1. If an ant [#permalink] New post  20 Jun 2018, 06:35
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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

Answer: C

Cheers,
Brent
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Re: Each edge of the above cube has length 1. If an ant [#permalink] New post  13 Oct 2020, 07:34
The question explicitly says from the outside of the cube, then how can we use the longest diagonal of the cube as shortest path, as longest diagonal will be inside cube
So I feel shortest path will be √2 i.e diagonal of front face +1 to B
Ans should be √6

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chetan2u
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Re: Each edge of the above cube has length 1. If an ant [#permalink] New post  13 Oct 2020, 09:18
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Manishg2 wrote:
The question explicitly says from the outside of the cube, then how can we use the longest diagonal of the cube as shortest path, as longest diagonal will be inside cube
So I feel shortest path will be √2 i.e diagonal of front face +1 to B
Ans should be √6

Posted from my mobile device


The path has been taken outside itself, that is the ant moves along the outside surface itself. All the above solutions have calculated the same route.
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Re: Each edge of the above cube has length 1. If an ant [#permalink] New post  01 Feb 2023, 19:35
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