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The number of integers from 1 to 100 which are neither divisible by 3 nor by 5 nor by 7 is a)67. b)55. c)45. d)33? correct answer 45 can u explain?
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The number of integers from 1 to 100 which are neither divisible by 3 ...
Solution:
To find the number of integers from 1 to 100 which are neither divisible by 3 nor by 5 nor by 7, we use the principle of inclusion and exclusion.
Step 1: Find the number of integers divisible by 3, 5 and 7 separately.
The number of integers divisible by 3 from 1 to 100 is 33. (Divide 100 by 3 and take the floor value).
The number of integers divisible by 5 from 1 to 100 is 20. (Divide 100 by 5 and take the floor value).
The number of integers divisible by 7 from 1 to 100 is 14. (Divide 100 by 7 and take the floor value).
Step 2: Find the number of integers divisible by 3 and 5, 5 and 7, 3 and 7 separately.
The number of integers divisible by both 3 and 5 from 1 to 100 is 6. (Divide 100 by 15 and take the floor value).
The number of integers divisible by both 5 and 7 from 1 to 100 is 2. (Divide 100 by 35 and take the floor value).
The number of integers divisible by both 3 and 7 from 1 to 100 is 4. (Divide 100 by 21 and take the floor value).
Step 3: Find the number of integers divisible by 3, 5 and 7.
The number of integers divisible by 3, 5 and 7 is 0.
Step 4: Apply the principle of inclusion and exclusion.
The number of integers from 1 to 100 which are neither divisible by 3 nor by 5 nor by 7 is:
= Total number of integers - (Number of integers divisible by 3 + Number of integers divisible by 5 + Number of integers divisible by 7)
+ (Number of integers divisible by both 3 and 5 + Number of integers divisible by both 5 and 7 + Number of integers divisible by both 3 and 7)
- Number of integers divisible by 3, 5 and 7
= 100 - (33 + 20 + 14) + (6 + 2 + 4) - 0
= 45
Therefore, the correct answer is option (c) 45.
To find the number of integers from 1 to 100 which are neither divisible by 3 nor by 5 nor by 7, we use the principle of inclusion and exclusion.
Step 1: Find the number of integers divisible by 3, 5 and 7 separately.
The number of integers divisible by 3 from 1 to 100 is 33. (Divide 100 by 3 and take the floor value).
The number of integers divisible by 5 from 1 to 100 is 20. (Divide 100 by 5 and take the floor value).
The number of integers divisible by 7 from 1 to 100 is 14. (Divide 100 by 7 and take the floor value).
Step 2: Find the number of integers divisible by 3 and 5, 5 and 7, 3 and 7 separately.
The number of integers divisible by both 3 and 5 from 1 to 100 is 6. (Divide 100 by 15 and take the floor value).
The number of integers divisible by both 5 and 7 from 1 to 100 is 2. (Divide 100 by 35 and take the floor value).
The number of integers divisible by both 3 and 7 from 1 to 100 is 4. (Divide 100 by 21 and take the floor value).
Step 3: Find the number of integers divisible by 3, 5 and 7.
The number of integers divisible by 3, 5 and 7 is 0.
Step 4: Apply the principle of inclusion and exclusion.
The number of integers from 1 to 100 which are neither divisible by 3 nor by 5 nor by 7 is:
= Total number of integers - (Number of integers divisible by 3 + Number of integers divisible by 5 + Number of integers divisible by 7)
+ (Number of integers divisible by both 3 and 5 + Number of integers divisible by both 5 and 7 + Number of integers divisible by both 3 and 7)
- Number of integers divisible by 3, 5 and 7
= 100 - (33 + 20 + 14) + (6 + 2 + 4) - 0
= 45
Therefore, the correct answer is option (c) 45.
Community Answer
The number of integers from 1 to 100 which are neither divisible by 3 ...
I think ans is 67
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The number of integers from 1 to 100 which are neither divisible by 3 nor by 5 nor by 7 is a)67. b)55. c)45. d)33? correct answer 45 can u explain?
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The number of integers from 1 to 100 which are neither divisible by 3 nor by 5 nor by 7 is a)67. b)55. c)45. d)33? correct answer 45 can u explain? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The number of integers from 1 to 100 which are neither divisible by 3 nor by 5 nor by 7 is a)67. b)55. c)45. d)33? correct answer 45 can u explain? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of integers from 1 to 100 which are neither divisible by 3 nor by 5 nor by 7 is a)67. b)55. c)45. d)33? correct answer 45 can u explain?.
The number of integers from 1 to 100 which are neither divisible by 3 nor by 5 nor by 7 is a)67. b)55. c)45. d)33? correct answer 45 can u explain? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The number of integers from 1 to 100 which are neither divisible by 3 nor by 5 nor by 7 is a)67. b)55. c)45. d)33? correct answer 45 can u explain? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of integers from 1 to 100 which are neither divisible by 3 nor by 5 nor by 7 is a)67. b)55. c)45. d)33? correct answer 45 can u explain?.
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