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

Question

https://i.imgur.com/pCPvPai.png 
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

EgmatQuantExpert · Accepted Answer

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:

https://e-gmat.com/blogs/wp-content/uploads/2018/06/ant_cube.png

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{ } = \sqrt{5}

Hence, the correct answer is option C.

Answer: C

chetan2u · Answer

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

gmatzpractice · Answer

Is it the path on the right cube?

Antreev · Answer

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

BrentGMATPrepNow · Answer

If we open up the cube, we get something like this....
 https://i.imgur.com/9LRJhWQ.png

Let x = the distance from A to B
 https://i.imgur.com/xuj615V.png 
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

Manishg2 · Answer

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

chetan2u · Answer

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.

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

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

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