Question
A two-digit number '8d' is completely divisible by '4'.
When the same number is divided by '3', there is a remainder of '1'. Find the value of 'd'.Solution
Let number = 8d = 80 + d Divisible by 4: 80 + d ≡ 0 (mod 4) 80 ≡ 0 (mod 4) => d ≡ 0 (mod 4) So d ∈ {0, 4, 8} Remainder 1 when divided by 3: 80 + d ≡ 1 (mod 3) 80 ≡ 2 (mod 3) 2 + d ≡ 1 (mod 3) => d ≡ 2 (mod 3) Check {0,4,8}: 0 mod 3 = 0 (no) 4 mod 3 = 1 (no) 8 mod 3 = 2 (yes) Answer: d = 8
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