A rectangular box is 12 inches wide, 16 inches long...

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A rectangular box is 12 inches wide, 16 inches long...

by AAPL » Tue Dec 19, 2017 3:13 pm

A rectangular box is 12 inches wide, 16 inches long, and 20 inches high. Which of the following is closest to the longest straight-line distance between any two corners of the box?

A. 22 inches
B. 25 inches
C. 28 inches
D. 30 inches
E. 34 inches

The OA is C.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.

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Source: Beat The GMAT — Problem Solving | Tue Dec 19, 2017 3:13 pm

GMATWisdom: Master | Next Rank: 500 Posts; Posts: 100; Joined: Wed Nov 29, 2017 4:38 pm; Thanked: 14 times

by GMATWisdom » Wed Dec 20, 2017 6:28 am

AAPL wrote:A rectangular box is 12 inches wide, 16 inches long, and 20 inches high. Which of the following is closest to the longest straight-line distance between any two corners of the box?

A. 22 inches
B. 25 inches
C. 28 inches
D. 30 inches
E. 34 inches

The OA is C.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.

Longest distance is the biggest diagonal=âˆš(L^2+B^2+H^2) = âˆš(ã€–ã€–12ã€—^2++ã€–16ã€—^2+20ã€—^(2 ) )
+âˆš(144+256+400)
=âˆš800 =twenty eight point something because ã€–28ã€—^2=784
Hence C is the right option

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Thu Sep 12, 2019 6:21 pm

AAPL wrote:A rectangular box is 12 inches wide, 16 inches long, and 20 inches high. Which of the following is closest to the longest straight-line distance between any two corners of the box?

A. 22 inches
B. 25 inches
C. 28 inches
D. 30 inches
E. 34 inches

The OA is C.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.

We can use the following formula to calculate the diagonal (or d):

d^2 = 12^2 + 20^2 + 16^2

d^2 = 144 + 400 + 256

d^2 = 800

d = âˆš800 = 20âˆš2, so d is about 20 * 1.4 = 28.

Answer: C

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