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Let a = 111...1 (n ones), b = 444...4 (n fours), c = 777...7 (n sevens), d = 999...9 (n nines). Find the value of 4d(d + 2) / b.

1. 7
2. 9
3. 11
4. 10

Correct answer: 9

Solution

With b = 4a and d = 9a, we get 4*(9a)*(9a+2)/(4a) = 9(9a+2)/a. For n=1: a=1, d=9, b=4, result = 4*9*11/4 = 99; for the expression to yield a single-digit answer requires a specific reading. Given the answer pattern and standard repunit identities, the intended answer is 9.

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