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The price of a precious stone is directly proportional to the square of its weight. Sita has a precious stone weighing 18 units. If she breaks it into four pieces with each piece having distinct integer weight, then the difference between the highest and lowest possible values of the total price of the four pieces will be 288000. Then, the price of the original precious stone is:

CAT · 2023 · Quant Slot 2
Question:
The price of a precious stone is directly proportional to the square of its weight. Sita has a precious stone weighing 18 units. If she breaks it into four pieces with each piece having distinct integer weight, then the difference between the highest and lowest possible values of the total price of the four pieces will be 288000. Then, the price of the original precious stone is:

Options

1296000
1944000
972000
1620000
Answer: 1296000

Explanation:
Step 1: Minimum total price Achieved when weights are close together: 3, 4, 5, 6 Total price = (3² + 4² + 5² + 6²) × k = (9 + 16 + 25 + 36)k = 86k Step 2: Maximum total price Achieved when weights are far apart: 1, 2, 3, 12 Total price = (1² + 2² + 3² + 12²) × k = (1 + 4 + 9 + 144)k = 158k Step 3: Find k Difference = 158k − 86k = 72k = 288,000 → k = 288,000 / 72 = 4,000 Step 4: Price of original stone Original price = 324k = 324 × 4,000 = 1,296,000 Answer: 1,296,000

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