To decide whether a n digit number is divisible by 7, we can define a process by which its magnitude is reduced as follows: (i 1 , i 2 , i 3 , … , are the digits of the number, starting from the most significant digit). i 1 i 2 ……. i n ⇒ i 1 . 3 n-1 + i 2 . 3 n-2 + …

Question

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).

i₁i₂ ……. i_n ⇒ i₁. 3^n-1 + i₂ . 3^n-2 + ……… + i_n . 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?

Accepted Answer

2 — 203 = 2.3 2 + 0.3 1 + 3.3 0 = 18 + 0 + 1 = 21 21 = 2.3 1 + 1.3 0 = 6 + 1 = 7. Therefore we can reduce 203 to 7 in 2 steps. Hence, option (a).

CAT 1991 — QA Question 47

Answer & solution

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