1. How can one tell if an integer is divisible by 6? The last digit is even and the sum of digits is divisible by 3 The sum of digits is divisible by 6 The last digit is even and the sum of digits is divisible by 9 The multiple of digits is even

2. Which of the following is a rule for divisibility by 4? The tens digit is even and the last digit is 0,4 or 8 The number formed by the last two digits is divisible by 4 The tens digit is odd and the last digit is 2 or 6 All three are valid

3. 999999 is evenly divisible by 7. True False

4. Which of the following integers is evenly divisible by 11? 855513 855533 855523 855503

5. Do you know these ultra-superstitious people? I knew someone who refused to have anything to do with the number 13, or any of its multiples. He once rejected 3 phone numbers offered by his cellphone operator on this very ground. Which number was he willing to accept eventually? 8910720 6815705 4826808 4592224

6. Fill in the blank digit in order for the resultant number to be divisible by 45: 5_1_5_1_5 (the same number goes in all the blanks.) Answer: (one digit, think prime factorization)

7. Which of the following statements about the integer 9699690 is correct? It is divisible by all prime numbers up to 29 (inclusive) It is divisible by all prime numbers up to 23 (inclusive) It is divisible by all prime numbers up to 19 (inclusive) It is divisible by all prime numbers up to 969 (inclusive)

8. How many of the first 1000 prime integers have divisibility rules? 959 997 All of them 920

9. Let's move on from the specific decimal realm to generic bases. For this question, our base is B. Complete the following rule: "If the sum of digits of an integer is divisible by ___ then the integer is divisible by ___." Answer: (Same expression in both blanks - a simple function of B)

10. If k is a prime factor of the base B, then a number is divisible by k^n if and only if the last n digits of the number are divisible by k^n. True False