What least value must be assigned to * so that the number 197*5462 is…
2025
What least value must be assigned to * so that the number 197*5462 is divisible by 9?
Answer: A. 2 — Concept A number is divisible by 9 exactly when the sum of all its digits is a multiple of 9 — this follows because 10 leaves remainder 1 when divided by 9,…
- A.
2
- B.
5
- C.
4
- D.
9
Attempted by 3 students.
Show answer & explanation
Correct answer: A
Concept
A number is divisible by 9 exactly when the sum of all its digits is a multiple of 9 — this follows because 10 leaves remainder 1 when divided by 9, so every digit contributes its own face value to the total remainder.
Application
Let the missing digit * be x.
Sum of the known digits of 197*5462 = 1+9+7+5+4+6+2 = 34.
Total digit sum = 34 + x.
For divisibility by 9, 34+x must be a multiple of 9. The nearest multiples are 27 (needs x negative, invalid) and 36 (needs x = 2); the next multiple 45 would need x = 11, which is outside the single-digit range 0-9.
So the least valid single digit is x = 2, giving a digit sum of 36.
Cross-check
36 ÷ 9 = 4 exactly, confirming divisibility. Re-adding the full digit string 1+9+7+2+5+4+6+2 also gives 36.