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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 ## A rectangular solid has length, width, and height of L cm tagged by: AbeNeedsAnswers ##### This topic has 1 expert reply and 0 member replies ### Top Member ## A rectangular solid has length, width, and height of L cm ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult A rectangular solid has length, width, and height of L cm, W cm, and H cm, respectively. If these dimensions are increased by x%, y%, and z%, respectively, what is the percentage increase in the total surface area of the solid? (1) L, W, and H are in the ratios of 5:3:4. (2) x = 5, y = 10, z = 20 C Source: Official Guide 2020 ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10196 messages Followed by: 494 members Upvotes: 2867 GMAT Score: 800 Hi All, We're told that a rectangular solid has length, width, and height of L cm, W cm, and H cm, respectively. We're asked if these dimensions are increased by X%, Y%, and Z%, respectively, what would be the PERCENTAGE INCREASE in the total SURFACE AREA of the solid. This question is based around a couple of specific math formulas and can be solved with a mix of Arithmetic and TESTing VALUES. There are clearly a lot of variables in this question, so we'll need a lot of information to define the percentage increase in the total surface area. To start, Total Surface area is SA = 2(L)(W) + 2(L)(H) + 2(W)(H) and the Percentage Change Formula = (New - Old)/(Old) = (Difference)/(Original). (1) L, W, and H are in the ratios of 5:3:4 Fact 1 defines the relationships between the three dimensions (for example, the width is 3/4 of the height), but tells us nothing about the percent increase in any of the 3 dimensions, so there's clearly no way to define the percentage increase in surface area. Fact 1 is INSUFFICIENT (2) X = 5, Y = 10, Z = 20 Fact 2 gives us the exact percent increase in each dimension, but without any information on the original dimensions of the rectangular solid, we have no way to define the 'impact' that each increase would have on the total surface area. Fact 2 is INSUFFICIENT Combined, we know... L, W, and H are in the ratios of 5:3:4 X = 5, Y = 10, Z = 20 With the ratio in Fact 1, we can refer to the three dimensions as Length = 5X, Width = 3X and Height = 4X, so whatever "X" actually is, the increase or decrease in the side lengths will be proportional. This means that the impact on the Original Surface Area and New Surface Area will always be the same in the above calculation and we will ALWAYS end up with the exact same answer (the math would look a bit 'ugly', so I'm going to refrain from presenting it here). Combined, SUFFICIENT Final Answer: C GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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