What is the greatest possible (straight line) distance

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Thu Jun 28, 2018 5:00 am

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What is the greatest possible (straight line) distance, in inches, between any two points on a rectangular box that is 10 inches wide, 10 inches long, and 0.1 inches high?

A. √(100.01)
B. √(101)
C. √(200.01)
D. √(200.1)
E. √(201)

The OA is the option C.

How can I find that distance? Is there a strategic approach? I'd appreciate some help here. <i class="em em-confused"></i>

Source: Beat The GMAT — Problem Solving | Thu Jun 28, 2018 5:00 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Jun 28, 2018 5:06 am

VJesus12 wrote:What is the greatest possible (straight line) distance, in inches, between any two points on a rectangular box that is 10 inches wide, 10 inches long, and 0.1 inches high?

A. √(100.01)
B. √(101)
C. √(200.01)
D. √(200.1)
E. √(201)

The longest line that can be drawn inside a rectangular solid is called the MAIN DIAGONAL.
Use the SUPER-PYTHAGOREAN THEOREM.
If d = the length of the main diagonal, then:
d² = l² + w² + h².

In the problem above:
d² = 10² + 10² + (0.1)²

d² = 100 + 100 + 0.01

d² = 200.01

d = √(200.01)

The correct answer is C.

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Mon Jul 02, 2018 8:53 am

VJesus12 wrote:What is the greatest possible (straight line) distance, in inches, between any two points on a rectangular box that is 10 inches wide, 10 inches long, and 0.1 inches high?

A. √(100.01)
B. √(101)
C. √(200.01)
D. √(200.1)
E. √(201)

The greatest possible distance in a box is the diagonal of the box. It has the formula:

d^2 = l^2 + w^2 + h^2

So here we have:

d^2 = 10^2 + 10^2 + 0.1^2

d^2 = 100 + 100 + 0.01

d^2 = 200.01

d = √(200.01)

Answer: C

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Head of GMAT Instruction
[email protected]

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