If 97215*6 is divisible by 11, find the smallest digit that can replace .

Given data

• Number: 9 7 2 1 5 * 6 must be divisible by 11.

Concept / Approach

• Divisibility by 11: (sum of digits in odd positions) − (sum in even positions) ≡ 0 (mod 11).
• Positions from left: 1:9, 2:7, 3:2, 4:1, 5:5, 6:, 7:6.

Step-by-step calculation

Odd sum = 9 + 2 + 5 + 6 = 22Even sum = 7 + 1 + * = 8 + *Difference = 22 − (8 + *) = 14 − *Set ≡ 0 (mod 11) ⇒ 14 − * ≡ 0 ⇒ * ≡ 14 ≡ 3 (mod 11)Smallest digit solution is 3.

Verification

With * = 3: difference = 14 − 3 = 11 ⇒ divisible by 11.

Common pitfalls

• Summing positions incorrectly (ensure consistent left-to-right odd/even indexing).

Final Answer

3