Question:
In a school of more than 500 students, when the students were standing in a row of 7, 5 students were left out. When these students were standing in a row of 10, again 5 students were left out and when they were standing in a row of 15, 5 students were left out again. If each time, at least one row was formed and the number of students in the school is the least possible, then find the average of the number of rows formed in the above three cases.
In a school of more than 500 students, when the students were standing in a row of 7, 5 students were left out. When these students were standing in a row of 10, again 5 students were left out and when they were standing in a row of 15, 5 students were left out again. If each time, at least one row was formed and the number of students in the school is the least possible, then find the average of the number of rows formed in the above three cases.
Updated On: Sep 10, 2024
- 70
- 68
- 55
- 65
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
The correct option is (D): 65.
From the given question, we can observe that in each case 5 students are being left out.
So, the number of students in the school will be
LCM of (7, 10 and 15) × k + 5 = 210k + 5
Also, it is given that the number of students in the school is more than 500.
So, if k = 1, number of students = 215 (not possible)
If k = 2, number of students = 420 + 5 = 425 (not possible)
If k = 3, number of students = 630 + 5 = 635 (possible)
After simplifying:
average =80.
From the given question, we can observe that in each case 5 students are being left out.
So, the number of students in the school will be
LCM of (7, 10 and 15) × k + 5 = 210k + 5
Also, it is given that the number of students in the school is more than 500.
So, if k = 1, number of students = 215 (not possible)
If k = 2, number of students = 420 + 5 = 425 (not possible)
If k = 3, number of students = 630 + 5 = 635 (possible)
After simplifying:
average =80.
Was this answer helpful?
0
0
Top Questions on Average
- In an office with 8 employees, the average rating of all employees is 30. The average rating of the top five employees is 38, and the average rating of the bottom three employees is 25. Which of the following is not possible?
- The average of the observations 10, 20, 65, 102, 108, 115 is
- The average of 101 consecutive odd numbers is 303. Find the largest number.
- For predicting the straight-line trend in the sales of washing machines (in thousands) on the basis of 8 consecutive years' data, the company calculates 4-year moving averages. If the sales of washing machines for respective years are \( a, b, c, d, e, f, g, \) and \( h \), then which of the following averages will be computed?
(A) \( \frac{a + b + c + d}{4} \)
(B) \( \frac{a + c + d + e}{4} \)
(C) \( \frac{c + d + f + h}{4} \)
(D) \( \frac{b + c + d + e}{4} \)
Choose the correct answer from the options given below: - If the average of p numbers is q2 and that of q numbers is p2, then the average of (p+q) numbers is:
View More Questions
Questions Asked in CAT exam
- For any natural Number 'n', let an be the largest number not exceeding \(\sqrt{n}\) , then a1 + a2 + a3... +a50 =
- CAT - 2024
- Number Systems
- The number of all positive integers up to 500 with non-repeating digits is
- CAT - 2024
- Number Systems
- The sum of all real values of $k$ for which $(\frac{1}{8})^k \times (\frac{1}{32768})^{\frac{4}{3}} = \frac{1}{8} \times (\frac{1}{32768})^{\frac{k}{3}}$ is
- CAT - 2024
- Logarithms
- When $10^{100}$ is divided by 7, the remainder is ?
- CAT - 2024
- Basics of Numbers
- In September, the incomes of \(K\), \(A\), and \(V\) are in the ratio \(8:6:5\). They rent a house, contributing \(15\%\), \(12\%\), and \(18\%\) of their respective incomes. In October, the rent remains the same, but the salaries of \(K\), \(A\), and \(V\) increase by \(10\%\), \(12\%\), and \(15\%\), respectively. What percentage of their total income is paid as house rent in October? (Round to the nearest percentage.)
- CAT - 2024
- Percentages
View More Questions