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Challenge question: Each edge of the above cube has length 1

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Challenge question: Each edge of the above cube has length 1

by Brent@GMATPrepNow » Sun Jun 17, 2018 7:22 am

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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

Answer: C
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*I'll post a full solution in 2 days
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by regor60 » Mon Jun 18, 2018 8:14 am
"Open" the cube up, drawing all 6 sides flat. Visualize that the cube's internal surfaces are flat against the table.

So you will have 4 squares in a column, with a square attached to each side of the square one up from the bottom

Points A and B are diagonally across from each other, with the short leg being 1 unit and the long leg being 2 units. Points A and B are on a straight line, therefore the shortest distance.

Apply hypotenuse of right triangle rule: (1^2 + 2^2 )^1/2 = [spoiler]5^1/2, C[/spoiler]
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by Brent@GMATPrepNow » Wed Jun 20, 2018 5:28 am
Brent@GMATPrepNow wrote:Image
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
If we open up the cube, we get something like this....
Image

Let x = the distance from A to B
Image
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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