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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 ## fractions/ratios/decimal tagged by: BTGmoderatorRO ##### This topic has 2 expert replies and 0 member replies ## fractions/ratios/decimal The value of a precious stone is directly proportional to the cube of its weight. If a big stone broke into three parts in the ratio 1:4:5, what was the percentage drop in the value of the stone? A. 10% B. 40% C. 71% D. 81% E. 93% I have been sweating on this question for hours now, it seems there is no solution. Can any expert help me out on this? i really appreciate. Thank you in advance ### GMAT/MBA Expert Legendary Member Joined 20 Jul 2017 Posted: 503 messages Followed by: 11 members Upvotes: 86 GMAT Score: 770 Let the weight of the original stone be 10 units. The cube of 10 units is 1000. So the value of the original stone is proportional to 1000. To make our lives easier, we'll assume that value is proportional to weight by a factor of 1. This makes the value exactly 1000. The stone is then broken into 3 pieces: 1 unit, 4 units, and 5 units. Cubing those three weights gives 1, 64, and 125. This means that the value of the three new pieces is proportional to 190. Again, assuming that value is proportional to weight by a factor of 1, this gives a value of 190. This means that the value of the stone dropped from 1000 to 190. To find percent change, we use the equation $$\frac{old\ value\ -\ new\ value}{old\ value}=\frac{1000-190}{1000}=\frac{810}{1000}=\frac{81}{100}=81\%$$ So the value of the stone dropped by 81%. _________________ Erika John - Content Manager/Lead Instructor https://gmat.prepscholar.com/gmat/s/ Get tutoring from me or another PrepScholar GMAT expert: https://gmat.prepscholar.com/gmat/s/tutoring/ Learn about our exclusive savings for BTG members (up to 25% off) and our 5 day free trial Check out our PrepScholar GMAT YouTube channel, and read our expert guides on the PrepScholar GMAT blog ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Quote: The value of a precious stone is directly proportional to the cube of its weight. If a big stone broke into three parts in the ratio 1:4:5, what was the percentage drop in the value of the stone? A. 10% B. 40% C. 71% D. 81% E. 93% I have been sweating on this question for hours now, it seems there is no solution. Can any expert help me out on this? i really appreciate. Thank you in advance Hi Roland2rule, Let's take a look at your question. If a big stone broke into three parts in the ratio 1:4:5. Let the weight of the broken stones be 1 unit, 4 unit and 5 unit. Then the weight of the original stone must be 1 + 4 + 5 = 10 units. Since, the value of a precious stone is directly proportional to the cube of its weight, therefore, Value of original stone must be: $$=\ 10^3=1,000$$ Value of the stone with weight 1 unit: $$=\ 1^3=1$$ Value of the stone with weight 4 units: $$=\ 4^3=64$$ Value of the stone with weight 5 units: $$=\ 5^3=125$$ Total value of the 3 broken pieces = 1 + 64 + 125 = 190 Let's now find the percent decrease in the value. $$=\ \frac{1,000-190}{1,000}\times100\%$$ $$=\ \frac{810}{1,000}\times100\%$$ $$=\ \frac{810}{10}\%$$ $$=\ 81\%$$ Hence, there is an 81% drop in the value of the stone. Therefore, Option D is correct. Hope it helps. I am available if you'd like any follow up. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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