• NEW! FREE Beat The GMAT Quizzes
Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## The length, width, and height of a rectangular box tagged by: AbeNeedsAnswers ##### This topic has 2 expert replies and 0 member replies ### Top Member ## The length, width, and height of a rectangular box ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult The length, width, and height of a rectangular box, in centimeters, are L, W, and H. If the volume of this box is V cubic centimeters and the total area of the 6 sides of this box is A square centimeters, what is the value of V/A ? (1) At least 2 of L, W, and H are equal to 5. (2) L, W, and H all have the same value. C Source: Official Guide 2020 ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 1946 messages Followed by: 30 members Upvotes: 470 AbeNeedsAnswers wrote: The length, width, and height of a rectangular box, in centimeters, are L, W, and H. If the volume of this box is V cubic centimeters and the total area of the 6 sides of this box is A square centimeters, what is the value of V/A ? (1) At least 2 of L, W, and H are equal to 5. (2) L, W, and H all have the same value. C Source: Official Guide 2020 With the given information, we have Volume of the box = V = LWH; and Area of the box = A = 2(LW + WH + LH) Thus, V/A = LWH / 2(LW + WH + LH) Let's take each statement one by one. (1) At least 2 of L, W, and H are equal to 5. We do not know the value of the third side, we can't get the unique value of V/A. Insufficient. (2) L, W, and H all have the same value. Say L = W = H = x Thus, V/A = LWH / 2(LW + WH + LH) = x^3 / 6x^2 = x/6 Can't get the unique value of V/A. Insufficient. (1) and (2) together Since L, W, and H all have the same value and at least 2 of L, W, and H are equal to 5, we have L = W = H = 5 = x. Thus, V/A = x/6 = 5/6. Sufficient. The correct answer: C Hope this helps! -Jay _________________ Manhattan Review GMAT Prep Locations: GRE Manhattan | ACT Tutoring Tampa | GRE Prep Courses Seattle | Boston IELTS Tutoring | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10184 messages Followed by: 494 members Upvotes: 2867 GMAT Score: 800 Hi All, We're told that the length, width, and height of a rectangular box, in centimeters, are L, W, and H, respectively, the VOLUME of this box is V cubic centimeters and the TOTAL SURFACE AREA of the 6 sides of this box is A square centimeters. We're asked for the value of V/A. This question is based around some standard Geometry formulas for solids and can be solved by TESTing VALUES. To start, Volume of a rectangular solid is V = (L)(W)(H) and Total Surface area is SA = 2(L)(W) + 2(L)(H) + 2(W)(H). (1) At least 2 of L, W, and H are equal to 5. Fact 1 tells us that 2 (or perhaps all 3) of the dimensions are equal to 5, but that still leads to a number of different answers to the question. IF... L = 5, W = 5, H = 5, then the Volume = (5)(5)(5) = 125 and Total Surface Area = (2)(5)(5) + (2)(5)(5) + (2)(5)(5) = 150... so the answer to the question is 125/150 = 5/6. L = 5, W = 5, H = 1, then the Volume = (5)(5)(1) = 25 and Total Surface Area = (2)(5)(5) + (2)(5)(1) + (2)(5)(1) = 70... so the answer to the question is 25/70 = 5/14. Fact 1 is INSUFFICIENT (2) L, W, and H all have the SAME value. Fact 2 tells us that we're actually dealing with a CUBE, but the answer to the question will still vary depending on the side length. IF.... L = 5, W = 5, H = 5, then the Volume = (5)(5)(5) = 125 and Total Surface Area = (2)(5)(5) + (2)(5)(5) + (2)(5)(5) = 150... so the answer to the question is 125/150 = 5/6. L = 1, W = 1, H = 1, then the Volume = (1)(1)(1) = 1 and Total Surface Area = (2)(1)(1) + (2)(1)(1) + (2)(1)(1) = 6... so the answer to the question is 1/6. Fact 2 is INSUFFICIENT Combined, we know... At least 2 of L, W, and H are equal to 5. L, W, and H all have the SAME value. When combining the two Facts, it's clear that we're dealing with a cube with a side length of 5, so the answer to the question is 5/6. Combined, SUFFICIENT Final Answer: C GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to \$200

Available with Beat the GMAT members only code

### Top First Responders*

1 Ian Stewart 59 first replies
2 Brent@GMATPrepNow 59 first replies
3 Jay@ManhattanReview 53 first replies
4 GMATGuruNY 30 first replies
5 ceilidh.erickson 20 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 Scott@TargetTestPrep

Target Test Prep

188 posts
2 Max@Math Revolution

Math Revolution

90 posts
3 Brent@GMATPrepNow

GMAT Prep Now Teacher

88 posts
4 Ian Stewart

GMATiX Teacher

68 posts
5 Jay@ManhattanReview

Manhattan Review

61 posts
See More Top Beat The GMAT Experts