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 21m divisible by 56? 3. When a whole number is divided by 5, the quotient is 16 and the remainder is 1. What is the whole number? 4. P and Q are positive integers. When P is divided by 10, the remainder is 5. When Q is divided by 10, the remainder is 7. What is the remainder when P + Q is divided by 10? 5. D is a positive integer. When D is divided by 6, the remainder is 5. What is the remainder when 5D is divided by 6? 6. Some roses are put into vases. If each vase holds 6 roses, 6 roses are left. If each vase holds 7 roses, 7 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. 165 has a remainder of 5 when it is divided by a certain number K, 230 has a remainder of 6 when it is divided by the same number K, and 359 has a remainder of 7 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 221 and the quotient is 16. What is the dividend? |