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1. The integer \(A67,83B\) where \(A\) and \(B\) are the first and last digits of the integer\(,\) respectively\(,\) is divisible by \(1515.\) What is the largest possible sum of \(A\) and \(B?\)

 

2. The six-digit integer \(234,ABC\) is divisible by \(11\) and \(13.\) It is also known that \(A, B\) and \(C\) are different non-zero digits\(.\) What is the three-digit integer \(ABC?\)

 

3. How many four digit numbers are divisible by all of the following: \(2, 3, 5, 7\) and \(11?\)

 

4. For how many \(3\)-digit integer \(n,\) the product \((n+1)(n+2)(n+3)\) is divisible by \(7?\)

 

5. The first digit of a string of \(2020\) digits is a \(1.\) Any two-digit number formed by consecutive digits within this string is divisible by either \(19\) or \(31.\) What is the largest possible last digit in this string\(?\)

 Apr 22, 2021
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1. The largest possible sum of A and B is 16.

 Apr 22, 2021

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