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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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A natural number is selected from the set of all natural numbers betwe...
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.
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.
Most Upvoted Answer
A natural number is selected from the set of all natural numbers betwe...
The set of natural numbers between 61 and 1020 (inclusive) can be represented as {61, 62, 63, ..., 1019, 1020}. We need to find the probability that a number selected from this set is a multiple of 3 or 4 or 5.
To solve this, we can find the number of multiples of 3, 4, and 5 separately, and then subtract the overlaps to avoid double counting.
Finding the number of multiples of 3:
The first multiple of 3 in this set is 63, and the last multiple is 1020. To find the number of multiples, we can use the formula:
Number of multiples = (last multiple - first multiple) / common difference + 1
Using this formula, we get:
Number of multiples of 3 = (1020 - 63) / 3 + 1 = 319
Finding the number of multiples of 4:
The first multiple of 4 in this set is 64, and the last multiple is 1020. Using the same formula as above, we get:
Number of multiples of 4 = (1020 - 64) / 4 + 1 = 239
Finding the number of multiples of 5:
The first multiple of 5 in this set is 65, and the last multiple is 1020. Using the same formula, we get:
Number of multiples of 5 = (1020 - 65) / 5 + 1 = 191
Finding the number of overlaps:
To avoid double counting, we need to find the number of multiples that are common to two or more of the numbers 3, 4, and 5.
Number of multiples of 3 and 4:
The first multiple that is common to both 3 and 4 is 12, and the last multiple is 1020. Using the formula, we get:
Number of multiples of 3 and 4 = (1020 - 12) / (3 * 4) + 1 = 84
Number of multiples of 3 and 5:
The first multiple that is common to both 3 and 5 is 15, and the last multiple is 1020. Using the formula, we get:
Number of multiples of 3 and 5 = (1020 - 15) / (3 * 5) + 1 = 68
Number of multiples of 4 and 5:
The first multiple that is common to both 4 and 5 is 20, and the last multiple is 1020. Using the formula, we get:
Number of multiples of 4 and 5 = (1020 - 20) / (4 * 5) + 1 = 50
Number of multiples of 3, 4, and 5:
The first multiple that is common to all 3 numbers is 60, and the last multiple is 1020. Using the formula, we get:
Number of multiples of 3, 4, and 5 = (1020 - 60) / (3 * 4 * 5) + 1 = 17
Calculating the probability:
To solve this, we can find the number of multiples of 3, 4, and 5 separately, and then subtract the overlaps to avoid double counting.
Finding the number of multiples of 3:
The first multiple of 3 in this set is 63, and the last multiple is 1020. To find the number of multiples, we can use the formula:
Number of multiples = (last multiple - first multiple) / common difference + 1
Using this formula, we get:
Number of multiples of 3 = (1020 - 63) / 3 + 1 = 319
Finding the number of multiples of 4:
The first multiple of 4 in this set is 64, and the last multiple is 1020. Using the same formula as above, we get:
Number of multiples of 4 = (1020 - 64) / 4 + 1 = 239
Finding the number of multiples of 5:
The first multiple of 5 in this set is 65, and the last multiple is 1020. Using the same formula, we get:
Number of multiples of 5 = (1020 - 65) / 5 + 1 = 191
Finding the number of overlaps:
To avoid double counting, we need to find the number of multiples that are common to two or more of the numbers 3, 4, and 5.
Number of multiples of 3 and 4:
The first multiple that is common to both 3 and 4 is 12, and the last multiple is 1020. Using the formula, we get:
Number of multiples of 3 and 4 = (1020 - 12) / (3 * 4) + 1 = 84
Number of multiples of 3 and 5:
The first multiple that is common to both 3 and 5 is 15, and the last multiple is 1020. Using the formula, we get:
Number of multiples of 3 and 5 = (1020 - 15) / (3 * 5) + 1 = 68
Number of multiples of 4 and 5:
The first multiple that is common to both 4 and 5 is 20, and the last multiple is 1020. Using the formula, we get:
Number of multiples of 4 and 5 = (1020 - 20) / (4 * 5) + 1 = 50
Number of multiples of 3, 4, and 5:
The first multiple that is common to all 3 numbers is 60, and the last multiple is 1020. Using the formula, we get:
Number of multiples of 3, 4, and 5 = (1020 - 60) / (3 * 4 * 5) + 1 = 17
Calculating the probability:
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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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