How many positive integers less than 1000 Note: so we consider the integers 1, 2, , 999 (a) are divisible by 7? b999 7 c = 142 (b) are divisible by 7 but not by 11? As shown in (a), 142 integers are divisible by 7 Similarly, b999 77 c = 12 integers are divisible by 77 (equivalently, are divisible by both 7 and 11) Therefore 142 12 = 130
4 a) How many positive six-digit integers are greater than 999 985? b) How many negative six-digit integers are less than ?999 985? How do you know? Answers: a) 999 999 ? 999 985 = 14, b) 14, because the negative six-digit integers that are less than ?999 985 are exactly the opposites of the positive six-digit integers that are greater
Answers:a) 999 999 ? 999 985 = 14; b) 14, because the six-digit negative integers that are less than ?999 985 are exactly the opposites of the six-digit positive integers that are greater than 999 985 5
The integers 1, 2, , 40 are written on a blackboard The following operation is then repeated 39 How many integers, greater than 999 but not greater than 4000
The integers 1, 2, , 40 are written on a blackboard The following operation is then repeated 39 times: How many integers, greater than 999 but not greater
This means the number of integers from 3000 to 5999, inclusive, in which the digit 5 does not occur is 2 9 9 9 = 1458 Therefore, the number of the total number the integers from 300 to 599, inclusive, contain the digit 4 at least once is 3000 - 1458 = 1542 Exercise 4: Consider the integers from 400 to 899, inclusive How many of these
How many positive integers n exist, such that n < 500, will have seed ( n) = 9? 1 39 2 72 3 81 4 108 5 55 10 In a triangle ABC, the lengths of the sides AB and A C equal 17 5 cm and 9 cm respectively Let D be a point on the line segment BC such that AD is perpendicular to BC If AD = 3cm,
How many integers greater than 4000 and less than 5000 are divisible by 4 or 7? 8 9 What is the smallest integer greater than 999 which uses only the digit 9
How many integers, greater than 999 but not greater than 4000, can be formed finger 5, then reversed direction, calling the ring finger 6, middle finger 7, index