Problem Solving Question - Geometry - The Beat The GMAT Forum - Expert GMAT Help & MBA Admissions Advice

Problem Solving Question - Geometry

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Smriti Shashikumar: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Sat Feb 16, 2013 9:29 am

by Smriti Shashikumar » Sun Mar 10, 2013 1:14 am

A straight inflexible metal rod with negligible diameter has to be imported through shipping, which should be packed in a rectangular box with dimensions 6 meters by 8 meters by 24 meters respectively. What is the maximum length of the rod that can be fit in the box?

A. 24
B. 25.2
C. 26
D. 34
E. 38

Thanks for the help!

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Source: Beat The GMAT — Problem Solving | Sun Mar 10, 2013 1:14 am

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Anju@Gurome: GMAT Instructor; Posts: 511; Joined: Wed Aug 11, 2010 9:47 amFollowed by: 86 members; Location: Delhi, India; Thanked: 344 times

by Anju@Gurome » Sun Mar 10, 2013 1:24 am

Smriti Shashikumar wrote:A straight inflexible metal rod with negligible diameter has to be imported through shipping, which should be packed in a rectangular box with dimensions 6 meters by 8 meters by 24 meters respectively. What is the maximum length of the rod that can be fit in the box?

Maximum length of the rod = Length of the principal diagonal of the box = âˆš(6Â² + 8Â² + 24Â²) = âˆš(36 + 64 + 576) = âˆš676 = 26

The correct answer is C.

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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 » Sun Mar 10, 2013 3:21 am

Smriti Shashikumar wrote:A straight inflexible metal rod with negligible diameter has to be imported through shipping, which should be packed in a rectangular box with dimensions 6 meters by 8 meters by 24 meters respectively. What is the maximum length of the rod that can be fit in the box?

A. 24
B. 25.2
C. 26
D. 34
E. 38

Thanks for the help!

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:
dÂ² = lÂ² + wÂ² + hÂ².

In the problem above:
dÂ² = 6Â² + 8Â² + 24Â²

dÂ² = 2Â²3Â² + 2Â²4Â² + 2Â²12Â²

dÂ² = 4(9 + 16 + 144)

dÂ² = 4*169

d = 2*13

d = 26.

The correct answer is C.

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