Discussion
If the 5-digit number 898xy is divisible by 3, 7 and 11, then what is the value of (5x - 2y)?
Answer: B
The value is 7. A number divisible by 3, 7 and 11 is divisible by their product 231. Look for a multiple of 231 between 89800 and 89899. Since 231 x 389 = 89859, the number is 89859, so x = 5 and y = 9. Check: the digit sum 8 + 9 + 8 + 5 + 9 = 39 is divisible by 3, and 231 x 389 is divisible by 7 and 11 by construction. Then \(5x - 2y = 25 - 18 = 7\). The nearby multiples 231 x 388 = 89628 and 231 x 390 = 90090 fall outside the range 898xy, so 89859 is the only number.
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