CAT Quant Practice Problems

Question: To decide whether a n digits number is divisible by 7, we can define a process by which its magnitude is reduced as follows: (i1, i2, i3, … , are the digits of the number, starting from the most significant digit).\({i_1}{i_2} \cdots \cdots {i_n} = {i_1}{3^{n - 1}} + {i_2}{3^{n - 2}} + \cdots \cdots + {i_n}{3^0}\)

e.g. \(259 \Rightarrow {2.3^2} + {5.3^1} + {9.3^0} = 18 + 15 + 9 = 42\)

Ultimately the resulting number will be seven after repeating the above process a certain number of times. After how many such stages, does the number 203 reduce to 7?

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