Q15
A king has distributed all his rare jewels in three boxes. The first box contains 1/3 of the rare jewels, while the second box contains k/5 of the rare jewels, for some positive integer value of k. The third box contains 66 rare jewels. How many rare jewels does the king have?
Answer: A
Fraction in box 3: \( 1 - \frac{1}{3} - \frac{k}{5} = \frac{10 - 3k}{15} \), which must be positive, so k = 1, 2 or 3.
- k = 1: box 3 = 7/15 of the total, so total = 66 × 15/7, not an integer.
- k = 2: box 3 = 4/15, so total = 66 × 15/4 = 247.5, not an integer.
- k = 3: box 3 = 1/15, so total = 66 × 15 = 990.
Check: 990/3 = 330, 3 × 990/5 = 594, and 330 + 594 + 66 = 990.
The value is unique, so "cannot be determined" is out.
Answer: 990 (Option 1)