Question : If the nine-digit number 3422213AB is divisible by 99, then what is the value of 2A + B?
Option 1: 11
Option 2: 12
Option 3: 10
Option 4: 13
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Correct Answer: 11
Solution :
To determine if the nine-digit number 3422213AB is divisible by 99, we can use the divisibility rule for 99. According to the rule, a number is divisible by 99 if the sum of its digits is divisible by 9 and the difference between the sum of its odd-positioned digits and the sum of its even-positioned digits is divisible by 11.
Let's calculate the sum of the digits:
For the number to be divisible by 99, the sum of the digits must be divisible by 9.
Therefore, 17+ A + B be divisible by 9.
So, A + B = 1 or A + B = 10
Now, let's calculate the difference between the sum of the odd-positioned digits and the sum of the even-positioned digits:
For the number to be divisible by 99, the difference (3 + B - A) must be divisible by 11.
From the above two conditions,
A = 1 and B = 9
The value of 2A + B = 2 × 1 + 9 = 11
Hence, the correct answer is 11.
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