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- But not 9.
- But if the original had and only for 7,8 — but says 7,8,9.
- Alternatively, suppose it’s a typo, and the intended moduli are 5, 7, and 8 — but LCM=280.
- But let’s calculate $ y = \text{LCM}(7,8,9) = 504 $, so $ x = 501 $ — not two-digit.
- Thus, the only logical conclusion is that **no such two-digit number exists**.
- But since olympiad problems usually have positive answers, perhaps the intended modulus was smaller.
