dots in the array

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Fri Jul 23, 2010 3:25 am

All the dots in the array are 2 units apart vertically and horizontally. What is the length of the longest line segment that can be drawn joining any two dots in the array without passing through any other dot?
A. 2
B. 2√2
C. 3
D. √10
E. √20

[spoiler]Source: majortests.com[/spoiler]

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Source: Beat The GMAT — Problem Solving | Fri Jul 23, 2010 3:25 am

kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members; Thanked: 215 times

by kvcpk » Fri Jul 23, 2010 3:27 am

Jon the edge dot and the middle dot of the opposite side.

sqrt(4^2 + 2^2) = sqrt(20)

pick E

selango: Legendary Member; Posts: 1460; Joined: Tue Dec 29, 2009 1:28 amFollowed by: 7 members; Thanked: 135 times

by selango » Fri Jul 23, 2010 3:27 am

Pick E

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

Re: dots in the array

by Brent@GMATPrepNow » Sun Sep 27, 2020 6:33 am

sanju09 wrote: ↑
Fri Jul 23, 2010 3:25 am
All the dots in the array are 2 units apart vertically and horizontally. What is the length of the longest line segment that can be drawn joining any two dots in the array without passing through any other dot?
A. 2
B. 2√2
C. 3
D. √10
E. √20

[spoiler]Source: majortests.com[/spoiler]

The longest line segment it's created when we connect points on opposite sides of the diagonal.

HOWEVER, this does not meet the condition that the line cannot pass through any other point

So, the next longest line segment looks something like this:

Since we have a right triangle, we can apply the Pythagorean theorem to write: 2² + 4² = x²
Simplify: 20 = x²
Solve: x = √20

Answer: E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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