Question: The cost of diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ratio 1:2:3:4. When the pieces were sold, the merchant got $70,000 less. What was the original price of the diamond?
- $100,000
- $120,000
- $140,000
- $200,000
- $250,000
Correct Answer: A
Solution and Explanation
Approach Solution 1:
This question has only 1 approach to model answer
The given case of the problem is that the cost of diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ratio 1:2:3:4. It is given that when the pieces were sold, the merchant got $70,000 less.
To find the original cost of the diamond, it is important to consider that the cost of the diamond varies directly to the square of its weight. It can be first therefore that the original weight of the diamond was 10a.
Cost of the original diamond hence would be \((10a)^2\) \(= 100 *a^2\)
Considering that the diamond broke into four pieces with weights in the ratio 1:2:3:4
=> Weights of smaller diamonds = {a,2a,3a,4a}
=> Cost of all small diamonds combined = \(a^2 + (2a)^2+(2a)^2 +(3a)^2 +(4a)^2\)
=> cost of all the small diamonds combined = 30 * \(a^2\)
The given difference in the cost of the diamonds when the merchant sold them was $70,000.
Accordingly, the original cost of the diamond can be found from this aspect-
Cost of the original diamond - cost of the small diamonds combined = Cost different of diamond when sold
= 100 * a - 30 * a = 70,000
= 70 * \(a^2\) = 70,000
=\(a^2\) = 70,000/70
= \(a^2\) = 1000
Thus, from the first equation that stated the original cost of the diamond being 100 * \(a^2\) can be evaluated as
100 * 1000 = $100,000
“The cost of diamond varies directly as the square of its weight.”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.
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