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 8m divisible by 28? 3. When a whole number is divided by 6, the quotient is 19 and the remainder is 1. What is the whole number? 4. P and Q are positive integers. When P is divided by 5, the remainder is 3. When Q is divided by 5, the remainder is 4. What is the remainder when P + Q is divided by 5? 5. D is a positive integer. When D is divided by 7, the remainder is 3. What is the remainder when 5D is divided by 7? 6. Some roses are put into vases. If each vase holds 6 roses, 5 roses are left. If each vase holds 7 roses, 3 more roses are needed. How many vases are there? 7. There are numbers that divide 127 with a remainder of 4. Find the largest two-digit number that has this property. 8. 148 has a remainder of 4 when it is divided by a certain number K, 221 has a remainder of 5 when it is divided by the same number K, and 438 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 252 and the quotient is 13. What is the dividend? |