Divisibility and Remainder( Week 14 Evaluation) 1. For how many integer values of i will the expression be evaluated positive? 2. What is the smallest positive integer m that will make 20m divisible by 30? 3. When a whole number is divided by 8, the quotient is 19 and the remainder is 7. What is the whole number? 4. P and Q are positive integers. When P is divided by 6, the remainder is 4. When Q is divided by 6, the remainder is 5. What is the remainder when P + Q is divided by 6? 5. D is a positive integer. When D is divided by 9, the remainder is 3. What is the remainder when 5D is divided by 9? 6. Some roses are put into vases. If each vase holds 4 roses, 6 roses are left. If each vase holds 5 roses, 8 more roses are needed. How many vases are there? 7. There are numbers that divide 131 with a remainder of 8. Find the largest two-digit number that has this property. 8. 174 has a remainder of 4 when it is divided by a certain number K, 243 has a remainder of 5 when it is divided by the same number K, and 414 has a remainder of 6 when it is divided by the same number K. What is the largest possible value for K? 10. A whole number is divisible by another whole number. The sum of the dividend and the divisor is 285 and the quotient is 14. What is the dividend? |