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dots in the array

by sanju09 » Fri Jul 23, 2010 3:25 am

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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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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
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by selango » Fri Jul 23, 2010 3:27 am
Pick E
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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.
Image
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:
Image

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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