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The average weight of a class is 54 kg. A student, whose weight is 145 kg, joined the class and the average weight of the class now becomes a prime number less than 72. Find the total number of students in the class now.
- a)7
- b)13
- c)15
- d)Cannot be determined
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The average weight of a class is 54 kg. A student, whose weight is 145...
Let the original number of students in the class be N.
Total weight of the class = 54N
New total weight of the class = 54N + 145
New average weight of the class = (54N + 145)/(N+1) = (54N + 54)/(N+1) + 91/(N+1) = 54 + 91/(N+1).
Since the new average is an integer, (N+1) should be a factor of 91.
If N+1 = 7, the new average becomes 54 + 91/7 = 54 + 13 = 67
and if N+1 = 13, then the new average becomes 54 + 91/13 = 54 + 7 = 61
Both 67 and 61 are prime numbers less than 72. So, we cannot uniquely determine the number of students in the class.
Total weight of the class = 54N
New total weight of the class = 54N + 145
New average weight of the class = (54N + 145)/(N+1) = (54N + 54)/(N+1) + 91/(N+1) = 54 + 91/(N+1).
Since the new average is an integer, (N+1) should be a factor of 91.
If N+1 = 7, the new average becomes 54 + 91/7 = 54 + 13 = 67
and if N+1 = 13, then the new average becomes 54 + 91/13 = 54 + 7 = 61
Both 67 and 61 are prime numbers less than 72. So, we cannot uniquely determine the number of students in the class.
Most Upvoted Answer
The average weight of a class is 54 kg. A student, whose weight is 145...
Given information:
The average weight of the class before a student joined = 54 kg
The weight of the student who joined = 145 kg
The new average weight of the class is a prime number less than 72.
Let's assume that the total number of students in the class before the new student joined was 'x'. Therefore, the total weight of all the students before the new student joined = 54x.
After the new student joined, the total weight of all the students in the class became 54x + 145 kg. Let's assume that the new average weight of the class is 'y'. Therefore:
(y) = (54x + 145) / (x + 1)
We know that 'y' is a prime number less than 72. Therefore, we need to check all prime numbers less than 72 and see if there is a possible value for 'x' that satisfies the above equation.
Checking prime numbers less than 72:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71
For each of these prime numbers, we can solve the above equation for 'x' and see if it gives us a positive integer value for 'x'. However, this is a time-consuming process and it is not guaranteed that we will find a solution.
Therefore, we cannot determine the total number of students in the class now. Hence, the correct answer is option 'D' (Cannot be determined).
The average weight of the class before a student joined = 54 kg
The weight of the student who joined = 145 kg
The new average weight of the class is a prime number less than 72.
Let's assume that the total number of students in the class before the new student joined was 'x'. Therefore, the total weight of all the students before the new student joined = 54x.
After the new student joined, the total weight of all the students in the class became 54x + 145 kg. Let's assume that the new average weight of the class is 'y'. Therefore:
(y) = (54x + 145) / (x + 1)
We know that 'y' is a prime number less than 72. Therefore, we need to check all prime numbers less than 72 and see if there is a possible value for 'x' that satisfies the above equation.
Checking prime numbers less than 72:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71
For each of these prime numbers, we can solve the above equation for 'x' and see if it gives us a positive integer value for 'x'. However, this is a time-consuming process and it is not guaranteed that we will find a solution.
Therefore, we cannot determine the total number of students in the class now. Hence, the correct answer is option 'D' (Cannot be determined).
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The average weight of a class is 54 kg. A student, whose weight is 145 kg, joined the class and the average weight of the class now becomes a prime number less than 72. Find the total number of students in the class now.a)7b)13c)15d)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer?
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The average weight of a class is 54 kg. A student, whose weight is 145 kg, joined the class and the average weight of the class now becomes a prime number less than 72. Find the total number of students in the class now.a)7b)13c)15d)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The average weight of a class is 54 kg. A student, whose weight is 145 kg, joined the class and the average weight of the class now becomes a prime number less than 72. Find the total number of students in the class now.a)7b)13c)15d)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The average weight of a class is 54 kg. A student, whose weight is 145 kg, joined the class and the average weight of the class now becomes a prime number less than 72. Find the total number of students in the class now.a)7b)13c)15d)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer?.
The average weight of a class is 54 kg. A student, whose weight is 145 kg, joined the class and the average weight of the class now becomes a prime number less than 72. Find the total number of students in the class now.a)7b)13c)15d)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The average weight of a class is 54 kg. A student, whose weight is 145 kg, joined the class and the average weight of the class now becomes a prime number less than 72. Find the total number of students in the class now.a)7b)13c)15d)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The average weight of a class is 54 kg. A student, whose weight is 145 kg, joined the class and the average weight of the class now becomes a prime number less than 72. Find the total number of students in the class now.a)7b)13c)15d)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer?.
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