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.
Answers
Question:
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. 2, 7
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Solution:
Option a)
The password would be 8653513649
8653513649 ÷ 11 = 786683059
8653513649 ÷ 8 = 1081689206 Remainder 1
⇒ Number cannot be divisible by 8
Option b)
The password would be 7653513648
7653513648 ÷ 11 = 695773968
7653513648 ÷ 8 = 956689206
⇒ Number is both divisible by 8 and 11
Option c)
The password would be 3653513644
3653513644 ÷ 11 = 332137604
3653513644 ÷ 8 = 456689205 Remainder 4
⇒ Number cannot be divisible by 8
Option d)
The password would be 2653513647
2653513647 ÷ 11 = 241228513 Remainder 4
2653513647 ÷ 8 = 331689205 Remainder 7
⇒ Number cannot be divisible by 8 and 11
Answer: (b) 7, 8