Oct 16 08:00 PM PDT  09:00 PM PDT EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299) Oct 18 08:00 AM PDT  09:00 AM PDT Learn an intuitive, systematic approach that will maximize your success on Fillintheblank GMAT CR Questions. Oct 19 07:00 AM PDT  09:00 AM PDT Does GMAT RC seem like an uphill battle? eGMAT is conducting a free webinar to help you learn reading strategies that can enable you to solve 700+ level RC questions with at least 90% accuracy in less than 10 days. Sat., Oct 19th at 7 am PDT Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions)
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58381

A rectangular box is 12 inches wide, 16 inches long, and 20 inches hig
[#permalink]
Show Tags
09 Jul 2015, 04:21
Question Stats:
75% (01:40) correct 25% (02:14) wrong based on 110 sessions
HideShow timer Statistics
A rectangular box is 12 inches wide, 16 inches long, and 20 inches high. Which of the following is closest to the longest straightline distance between any two corners of the box? A. 22 inches B. 25 inches C. 28 inches D. 30 inches E. 34 inches Kudos for a correct solution.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________



Manager
Joined: 26 Dec 2011
Posts: 115

Re: A rectangular box is 12 inches wide, 16 inches long, and 20 inches hig
[#permalink]
Show Tags
09 Jul 2015, 04:28
Bunuel wrote: A rectangular box is 12 inches wide, 16 inches long, and 20 inches high. Which of the following is closest to the longest straightline distance between any two corners of the box?
A. 22 inches B. 25 inches C. 28 inches D. 30 inches E. 34 inches
Kudos for a correct solution. Answer  The longest straightline distance between any two corners of the box = √(W^2+L^2+H^2) = √(144+256+400) = √800 ANS C
_________________



CEO
Joined: 20 Mar 2014
Posts: 2599
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

A rectangular box is 12 inches wide, 16 inches long, and 20 inches hig
[#permalink]
Show Tags
09 Jul 2015, 04:38
Bunuel wrote: A rectangular box is 12 inches wide, 16 inches long, and 20 inches high. Which of the following is closest to the longest straightline distance between any two corners of the box?
A. 22 inches B. 25 inches C. 28 inches D. 30 inches E. 34 inches
Kudos for a correct solution. If L, B and H denote the Length, Breadth and Height of a cube or a cuboid, the longest straight line distance is equal to = \(\sqrt{(L^2+B^2+H^2)}\) Thus, per the questions, as L=16, B=12 and H=20, substituting these values , we get Longets distance = 28 inches \((=20 \sqrt{2})\)



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2977
Location: India
GMAT: INSIGHT
WE: Education (Education)

A rectangular box is 12 inches wide, 16 inches long, and 20 inches hig
[#permalink]
Show Tags
09 Jul 2015, 06:48
Bunuel wrote: A rectangular box is 12 inches wide, 16 inches long, and 20 inches high. Which of the following is closest to the longest straightline distance between any two corners of the box?
A. 22 inches B. 25 inches C. 28 inches D. 30 inches E. 34 inches
Kudos for a correct solution. The longest straightline distance between any two corners of the box = \(\sqrt{L^2+B^2+H^2}\) = \(\sqrt{12^2+16^2+20^2}\) = \(\sqrt{144+256+400}\) = \(\sqrt{800}\) = 28.3 approx. Answer: Option C Please see the Derivation of Longest Diagonal in a Rectangular Solid. Longest diagonal in the figure is S
Attachments
File comment: www.GMATinsight.com
3dtrigincuboid.jpg [ 37.95 KiB  Viewed 3459 times ]
_________________
Prosper!!!GMATinsightBhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhihttp://www.GMATinsight.com/testimonials.htmlACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Retired Moderator
Status: On a mountain of skulls, in the castle of pain, I sit on a throne of blood.
Joined: 30 Jul 2013
Posts: 300

Re: A rectangular box is 12 inches wide, 16 inches long, and 20 inches hig
[#permalink]
Show Tags
09 Jul 2015, 10:58
Bunuel wrote: A rectangular box is 12 inches wide, 16 inches long, and 20 inches high. Which of the following is closest to the longest straightline distance between any two corners of the box?
A. 22 inches B. 25 inches C. 28 inches D. 30 inches E. 34 inches
Kudos for a correct solution. We need the diagonal. Diagonal = \(\sqrt{12^2+16^2+20^2}\) = \(\sqrt{144+256+400}\) =\(\sqrt{800}\) =20\(\sqrt{2}\) =20*1.41 =28.2 Answer: C



Intern
Joined: 30 Jul 2008
Posts: 19

A rectangular box is 12 inches wide, 16 inches long, and 20 inches hig
[#permalink]
Show Tags
10 Jul 2015, 09:03
Bunuel wrote: A rectangular box is 12 inches wide, 16 inches long, and 20 inches high. Which of the following is closest to the longest straightline distance between any two corners of the box?
A. 22 inches B. 25 inches C. 28 inches D. 30 inches E. 34 inches
Kudos for a correct solution. longest diagonal =\(\sqrt{l^2+b^2+h^2} = \sqrt{16^2+12^2+20^2}\) = \(\sqrt{800}\) = \(20 X \sqrt{2}\) = 28 (approx)



Math Expert
Joined: 02 Aug 2009
Posts: 7959

Re: A rectangular box is 12 inches wide, 16 inches long, and 20 inches hig
[#permalink]
Show Tags
10 Jul 2015, 09:14
Bunuel wrote: A rectangular box is 12 inches wide, 16 inches long, and 20 inches high. Which of the following is closest to the longest straightline distance between any two corners of the box?
A. 22 inches B. 25 inches C. 28 inches D. 30 inches E. 34 inches
Kudos for a correct solution. although the answer is straight from formulae \(\sqrt{l^2+b^2+h^2}\)= \(\sqrt{12^2+16^2+20^2}\) the other way to look at is 12, 16 ,hyp is a right angle triange of ratio 3:4:5.. so here hyp =20.. now the sides are 20,20,hyp in a right angle triangle in ratio 1:1:\(\sqrt{2}\).. hyp=20\(\sqrt{2}\)=28 ans C
_________________



Director
Joined: 21 May 2013
Posts: 636

Re: A rectangular box is 12 inches wide, 16 inches long, and 20 inches hig
[#permalink]
Show Tags
11 Jul 2015, 10:35
Bunuel wrote: A rectangular box is 12 inches wide, 16 inches long, and 20 inches high. Which of the following is closest to the longest straightline distance between any two corners of the box?
A. 22 inches B. 25 inches C. 28 inches D. 30 inches E. 34 inches
Kudos for a correct solution. Longest straight line distance between any two corners of the box=\sqrt{L^2+B^2+H^2} =\sqrt{144+256+400} =\sqrt{800} Answer C



Math Expert
Joined: 02 Sep 2009
Posts: 58381

Re: A rectangular box is 12 inches wide, 16 inches long, and 20 inches hig
[#permalink]
Show Tags
13 Jul 2015, 02:49
Bunuel wrote: A rectangular box is 12 inches wide, 16 inches long, and 20 inches high. Which of the following is closest to the longest straightline distance between any two corners of the box?
A. 22 inches B. 25 inches C. 28 inches D. 30 inches E. 34 inches
Kudos for a correct solution. 800score Official Solution:We must first determine which two corners are furthest apart in a rectangular box. To determine the corners that are furthest apart in a rectangular box, pick any corner, and think about drawing a line through the center of the box to the furthest other corner. Let's call corners that have this relationship "opposite corners". The distance D between any two opposite corners in a rectangular solid (whether a perfect cube or not) can be determined very quickly using the Pythagorean Theorem in a 3dimensional manner: D² = a² + b² + c², where a, b, and c represent the dimensions of the solid. Now let's use the formula to determine the distance: D² = 12² + 16² + 20² D² = 144 + 256 + 400 = 800. So D = √800. Rather than trying to approximate √800, let's square the answer choices and determine which is closest to 800. We know that 30² = 900, so the correct answer must be either choice (C) or (D). Now let's square the number in choice (C). 28² = 784. Since 784 is much closer to 800 than 900 is, the correct answer is choice (C).Another way to solve this question is to use 3:4:5 triangles. Since 12:16:20 is a multiple of 3:4:5, the diagonal is 20. To find the answer, find the hypotenuse of a triangle with that diagonal and the third dimension of the box – 20 and 20, which has a hypotenuse of 20√2. √2 equals approximately 1.4, so the answer is about 28.
_________________



Math Expert
Joined: 02 Sep 2009
Posts: 58381

Re: A rectangular box is 12 inches wide, 16 inches long, and 20 inches hig
[#permalink]
Show Tags
13 Jul 2015, 02:50
Bunuel wrote: Bunuel wrote: A rectangular box is 12 inches wide, 16 inches long, and 20 inches high. Which of the following is closest to the longest straightline distance between any two corners of the box?
A. 22 inches B. 25 inches C. 28 inches D. 30 inches E. 34 inches
Kudos for a correct solution. 800score Official Solution:We must first determine which two corners are furthest apart in a rectangular box. To determine the corners that are furthest apart in a rectangular box, pick any corner, and think about drawing a line through the center of the box to the furthest other corner. Let's call corners that have this relationship "opposite corners". The distance D between any two opposite corners in a rectangular solid (whether a perfect cube or not) can be determined very quickly using the Pythagorean Theorem in a 3dimensional manner: D² = a² + b² + c², where a, b, and c represent the dimensions of the solid. Now let's use the formula to determine the distance: D² = 12² + 16² + 20² D² = 144 + 256 + 400 = 800. So D = √800. Rather than trying to approximate √800, let's square the answer choices and determine which is closest to 800. We know that 30² = 900, so the correct answer must be either choice (C) or (D). Now let's square the number in choice (C). 28² = 784. Since 784 is much closer to 800 than 900 is, the correct answer is choice (C).Another way to solve this question is to use 3:4:5 triangles. Since 12:16:20 is a multiple of 3:4:5, the diagonal is 20. To find the answer, find the hypotenuse of a triangle with that diagonal and the third dimension of the box – 20 and 20, which has a hypotenuse of 20√2. √2 equals approximately 1.4, so the answer is about 28. Similar question to practice: acarpenterwantstoshipacopperrodtohisnewconstructionlocatio187870.html
_________________



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8069
Location: United States (CA)

Re: A rectangular box is 12 inches wide, 16 inches long, and 20 inches hig
[#permalink]
Show Tags
18 Sep 2019, 10:02
Bunuel wrote: A rectangular box is 12 inches wide, 16 inches long, and 20 inches high. Which of the following is closest to the longest straightline distance between any two corners of the box?
A. 22 inches B. 25 inches C. 28 inches D. 30 inches E. 34 inches
Kudos for a correct solution. 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 = √800 = 20√2, so d is about 20 * 1.4 = 28. Answer: C
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4782
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

Re: A rectangular box is 12 inches wide, 16 inches long, and 20 inches hig
[#permalink]
Show Tags
18 Sep 2019, 10:54
Bunuel wrote: A rectangular box is 12 inches wide, 16 inches long, and 20 inches high. Which of the following is closest to the longest straightline distance between any two corners of the box?
A. 22 inches B. 25 inches C. 28 inches D. 30 inches E. 34 inches
Kudos for a correct solution. \(\sqrt{12^2 + 16^2 + 20^2}\) = \(\sqrt{144 + 256 + 400}\) = \(\sqrt{800}\) We know \(30^2 = 900\), so our answer must be a bit less than 30 , among the given options only (C) 28 matches, so Answer must be (C)
_________________




Re: A rectangular box is 12 inches wide, 16 inches long, and 20 inches hig
[#permalink]
18 Sep 2019, 10:54






