Number Thinking (2)( Week 28 Evaluation) 1. What is the largest possible integer n to satisfy 0 < < 1? 2. If 29 ≤ X ≤ 32, 12 ≤ Y ≤ 18, and 60 ≤ Z ≤ 63 with X, Y, and Z all being integers, what is the smallest value of ? 4. 35's factorial is the product of all natural numbers from 1 through 35. Let M = 1 × 2 × 3... × 35. How many continuous zeroes will M have at its end? 5. A symmetrical number is a number that reads the same from either direction, e.g. 11, 121, 1221 are symmetrical numbers. How many 6-digit symmetrical numbers are divisible by 11? 7. If the digits of a natural number are reversed to form a new number, the two numbers are palimage each other. 123 and 321, 1234 and 4321 are examples of palimages. If a number ends with 0, its palimage assumes a leading 0, which has no effect to its value. For example, the palimage of 1230 will be 0321, which is equal to 321. Now add 144 and its palimage to get the sum A. Add A and its palimage to get the sum B. Add B and its palimage to get the sum C. What will be the value for C? 8. What is the sum of all two-digit whole numbers in which one digit is of the other digit? 9. If p is a negative integer and q is a positive integer, which of the following statements must be true?
I. pq > 0 II. pq > 0 III. < 0 10. How many two-digit whole numbers that are of another two-digit whole number? |