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How many positive integers less than 1000 (1) are divisible by 7? (2) are divisible by 7 but not by 11? (3) are divisible by both 7 and 11? (4) are divisible by either 7 or 11?

How many positive integers less than 1000 (1) are divisible by 7? (2) are divisible by 7 but not by 11? (3) are divisible by both 7 and 11? (4) are divisible by either 7 or 11?

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter11: Rational And Irrational Numbers
Section11.8: Adding And Subtracting Radicals
Problem 5E
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How many positive integers less than 1000 (1) are divisible by 7? (2) are divisible by 7 but not by 11? (3) are divisible by both 7 and 11? (4) are divisible by either 7 or 11? (5) are divisible by exactly one of 7 and 11? (6) are divisible by neither 7 nor 11? (7) have distinct digits? (Numbers are written without leading Os. For example, it is 23, not 023.) (8) have distinct digits and are even? (Numbers are written without leading Os. For example, it is 23, not 023.) Note: (a) Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. (b) "divisible": for example, 6 is divisible by 3. (c) "Having distinct digits" means every digit is different, i.e., no two digits are the same.
Transcribed Image Text:How many positive integers less than 1000 (1) are divisible by 7? (2) are divisible by 7 but not by 11? (3) are divisible by both 7 and 11? (4) are divisible by either 7 or 11? (5) are divisible by exactly one of 7 and 11? (6) are divisible by neither 7 nor 11? (7) have distinct digits? (Numbers are written without leading Os. For example, it is 23, not 023.) (8) have distinct digits and are even? (Numbers are written without leading Os. For example, it is 23, not 023.) Note: (a) Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. (b) "divisible": for example, 6 is divisible by 3. (c) "Having distinct digits" means every digit is different, i.e., no two digits are the same.
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