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A natural number is selected from the set of all natural numbers between 61 and 1020 (both numbers inclusive). What is the probability that the number is a multiple of 3 or 4 or 5?
- a)11/20
- b)12/20
- c)14/20
- d)15/20
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A natural number is selected from the set of all natural numbers betw...
The LCM of 3, 4 and 5 is 60.
Thus checking the remainder of 61 w.r.t. 3/4/5 is the same as checking the remainder of 1 w.r.t. 3/4/5.
Similarly 62 is akin to 2, 63 to 3 and so on.
So let us simply look at the 1st 60 numbers.
Divisible by 3 = |60/3| = 20
Divisible by 4 = |60/4| = 15
Divisible by 5 = |60/5| = 12
Divisible by 3 & 4 = |60/12| = 5
Divisible by 3 & 5 = |60/15| = 4
Divisible by 4 & 5 = |60/20| = 3
Divisible by 3 & 4 & 5 = |60/60| = 1
Thus total number of number divisible by 3 or 4 or 5 = (20 + 15 + 12) - (5 + 4 + 3) + 1
= 47 - 12 + 1
= 36
Thus for every 60 numbers, 36 of them will satisfy, hence probability = 36/60 = 12/20.
Now 61-1020 involves 960 numbers which is 16 sets of 60 numbers, hence Probability = 12/20.
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A natural number is selected from the set of all natural numbers between 61 and 1020 (both numbers inclusive). What is the probability that the number is a multiple of 3 or 4 or 5?a)11/20b)12/20c)14/20d)15/20Correct answer is option 'B'. Can you explain this answer?
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A natural number is selected from the set of all natural numbers between 61 and 1020 (both numbers inclusive). What is the probability that the number is a multiple of 3 or 4 or 5?a)11/20b)12/20c)14/20d)15/20Correct answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A natural number is selected from the set of all natural numbers between 61 and 1020 (both numbers inclusive). What is the probability that the number is a multiple of 3 or 4 or 5?a)11/20b)12/20c)14/20d)15/20Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A natural number is selected from the set of all natural numbers between 61 and 1020 (both numbers inclusive). What is the probability that the number is a multiple of 3 or 4 or 5?a)11/20b)12/20c)14/20d)15/20Correct answer is option 'B'. Can you explain this answer?.
A natural number is selected from the set of all natural numbers between 61 and 1020 (both numbers inclusive). What is the probability that the number is a multiple of 3 or 4 or 5?a)11/20b)12/20c)14/20d)15/20Correct answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A natural number is selected from the set of all natural numbers between 61 and 1020 (both numbers inclusive). What is the probability that the number is a multiple of 3 or 4 or 5?a)11/20b)12/20c)14/20d)15/20Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A natural number is selected from the set of all natural numbers between 61 and 1020 (both numbers inclusive). What is the probability that the number is a multiple of 3 or 4 or 5?a)11/20b)12/20c)14/20d)15/20Correct answer is option 'B'. Can you explain this answer?.
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