To decide whether a n digit 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).
i1 i2 ……. in ⇒ i1 . 3n-1 + i2 . 3n-2 + ……… + in . 30.
e.g. 259 ⇒ 2.32 + 5.31 + 9.30 = 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?
Explanation:
203 = 2.32 + 0.31 + 3.30 = 18 + 0 + 1 = 21
21 = 2.31 + 1.30 = 6 + 1 = 7.
Therefore we can reduce 203 to 7 in 2 steps.
Hence, option (a).
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