In the IT department of backrub, the administrator password is changed every…
2025
In the IT department of backrub, the administrator password is changed every month. The team of administrators, spread across the globe, receive an 8 digit number via email. This number is to be prefixed with a single digit number and suffixed with a single digit number to get the actual password. The password is divisible by 11 and 8. If the team received 65351364 this month, then which of the following pairs give prefix and suffix respectively.
- A.
8,9
- B.
7,8
- C.
3,4
- D.
Cannot be determined / Data Insufficient
Attempted by 533 students.
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Correct answer: B
Key insight: Use divisibility rules. A number is divisible by 8 if its last three digits form a number divisible by 8. A number is divisible by 11 if the alternating sum of its digits (sum of digits in odd positions minus sum of digits in even positions) is a multiple of 11.
Prefix 8 and suffix 9 → number formed: 8653513649. Last three digits 649: 649 ÷ 8 leaves remainder 1, so not divisible by 8. Reject.
Prefix 7 and suffix 8 → number formed: 7653513648. Last three digits 648: 648 ÷ 8 = 81, so divisible by 8. Alternating sum check for 11: (7+5+5+3+4) − (6+3+1+6+8) = 24 − 24 = 0, which is a multiple of 11. The number is divisible by both 8 and 11. Accept.
Prefix 3 and suffix 4 → number formed: 3653513644. Last three digits 644: 644 ÷ 8 leaves remainder 4, so not divisible by 8. Reject.
Answer: Prefix 7 and suffix 8.