Question

To decide whether an $n$-digit number is divisible by 7, a process is defined by using weights of powers of 3 from the right: i.e., for number $abc$, compute $a \cdot 3^2 + b \cdot 3^1 + c \cdot 3^0$ Given: $259 \Rightarrow 2 \cdot 9 + 5 \cdot 3 + 9 = 18 + 15 + 9 = 42$ Now for number 203, how many such stages are needed to reduce it to 7?

• A. 2
• B. 3
• C. 4
• D. 1

Hint:

For special divisibility tests, follow the weighted transformation rules exactly and repeat until desired form appears.

Answer 1

The Correct Option is A

Apply weighted sum process: Stage 1: \[ 203 \Rightarrow 2 \cdot 9 + 0 \cdot 3 + 3 = 18 + 0 + 3 = 21 \] Stage 2: \[ 21 \Rightarrow 2 \cdot 3 + 1 = 6 + 1 = \boxed{7} \] So, 2 stages needed.