A three-digit non-zero number (abc)5 when converted to base 7 becomes (cba)7. What is b?
Explanation:
Given, (abc)5 = (cba)7
∴ 25a + 5b + c = 49c + 7b + a
⇒ 24a – 48c = 2b
⇒ b = 12(a – 2c)
Since b has to be a single digits number (a – 2c) has to be 0.
∴ b = 12 × 0 = 0
Hence, 0.
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