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

This topic has expert replies

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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

Answer: C
Difficulty level: 700+
Source: www.gmatprepnow.com

*I'll post a full solution in 2 days
Brent Hanneson - Creator of GMATPrepNow.com
Image

Master | Next Rank: 500 Posts
Posts: 415
Joined: Thu Oct 15, 2009 11:52 am
Thanked: 27 times

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]

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

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
Brent Hanneson - Creator of GMATPrepNow.com
Image