A teacher noticed a strange distribution of marks in the exam. There were only three distinct scores: 6, 8 and 20. The mode of the distribution was 8. The sum of the scores of all the students was 504. The number of students in the in most populated ?->(Show Answer!)

1. A teacher noticed a strange distribution of marks in the exam. There were only three distinct scores: 6, 8 and 20. The mode of the distribution was 8. The sum of the scores of all the students was 504. The number of students in the in most populated category was equal to the sum of the number of students with lowest score and twice the number of students with the highest score. The total number of students in the class was:

Write Comment

Comments

By: anil on 05 May 2019 02.37 am

Let $$x, y, z$$ be the number of students getting 6, 8 and 20 marks respectively. => $$6x + 8y + 20z = 504$$ -------------Eqn(I) Since, the mode is 8, => Most populated category = $$y$$ => $$y = x + 2z$$ => $$x = y - 2z$$ -------------Eqn(II) Substituting it in eqn(I), we get : => $$(6y - 12z) + 8y + 20z = 504$$ => $$14y + 8z = 504$$ By hit and trial, since $$x,y,z$$ are integers, we get : $$y = 32$$ and $$z = 7$$ Putting it in Eqn(II), => $$x = 32 - 2 imes 7 = 18$$ $$ herefore$$ Total students = $$x + y + z = 18 + 32 + 7 = 57$$

Tags

Show Similar Question And Answers

QA->There are 50 students in a class. In a class test 22 students get 25 marks each, 18 students get 30 marks each. Each of the remaining gets 16 marks. The average mark of the whole class is :....

QA->In a class of 20 students the average age is 16 years.If the age of the class teacher is added to that of students,the average age of the class becomes 17 years.What is the age of the teacher?....

QA->In a class of 50 students, 32 students passed in English and 38 students passed in Mathematics. If 20 students passed in both the subjects, the number of students who passed neither English nor Mathematics is :....

QA->A school has only three classes comprised of 40, 50 and 60 students respectively. In these classes, 10%, 20% and 10% students respectively passed in the examinations. What is the percentage of students passed in the examination from the entire school?....

QA->In a class of 60 students, 55% are boys. The number of girls in the class is :....

MCQ->A teacher noticed a strange distribution of marks in the exam. There were only three distinct scores: 6, 8 and 20. The mode of the distribution was 8. The sum of the scores of all the students was 504. The number of students in the in most populated category was equal to the sum of the number of students with lowest score and twice the number of students with the highest score. The total number of students in the class was:....

MCQ-> Directions: Read the following information carefully and answer the given questions:Despite repeated announcements that mobile phones were not allowed in the examination hall, three students were caught with their mobile phones. (A) Mobile phones nowadays have a lot of features and it is easy to cheat with their help. (B) The invigilator must immediately confiscate the mobile phones and ask the students to leave the exam hall immediately. (C) Mobile phones are very expensive and leaving them in bags outside the exam hall is not safe. (D) There have been incidents where students who left the exam hall early stole the mobile phones kept in the bags of the students who were writing the exam. (E) The school authorities must ask the students to leave their phones in the custody of the invigilator before the exam in order to avoid thefts of mobile phones. (F) None of the other students were carrying their phones in the exam hall.Which of the following among (A), (B), (C) and (D) may be a strong argument in favour of the three students who were caught with their mobile phones?
....

MCQ->A, B, C and D are four students in a class. A's total score is 20% less than B's total score, C's total score is 25% more than A's total score, D's total score is 20% more than A's total score. If the least total score among the scores is 240, then the ratio of the scores of the four students in the decreasing order is....

MCQ-> Study the following information carefully and answer the questions given below. Six friends— A ,B, C, D, E and F are going for entrance exam during a period of starting from Monday to Saturday. Only one exam will be held on each day. • C gives exam atleast before three exams. • F gives exam on Tuesday. • Both B and E does, not give 100. exam on even day. • D is going for exam immediately after the exam on which C given. • Atleast four persons are going for exam after E.On which day E gives entrance exam ?
....

MCQ-> Study the following information carefully and answer the question given below: Following are the conditions for selecting Senior Manager General Banking in a bank: (i) have secured at least 60 percent marks in Std XII. (ii) have secured at least 55 percent marks in Graduation in any discipline (iii) have secured at least 60 percent marks in Post-graduate degree/diploma in Management/Economics/Statistics. (iv) be at least 25 years and not be more than 35 years as on 01.03.2010. (v) have post qualification work experience of at least 2 years as General Banking Officer in a bank. (vi) have secured at least 50 percent marks in written examination. (vii) have secured at least 40 percent marks in Personal Interview. In the case of a candidate who satisfies all the above conditions Except----- (a) at (iii) above but has secured at least 60 percent marks in CA or ICWA the case is to be referred to VP-Recruitment. (b) at (vii) above but have secured at least 65 percent marks in the written examination and at least 35 percent marks in the personal interview the case is to be referred to President Recruitment. In each question below are given details of one candidate You have to take one of the following courses of actions based on the information provided and the conditions and sub-conditions given above and mark the number of that course of action as your answer You are not to assume anything other than the information provided in each question All these cases are given to you as on 01.03.2010. Mark answer (a) if the data provided are inadequate to take a decision Mark answer (b) if the case is to be referred to VP- Recruitment Mark answer (c) if the case is to be referred to President Recruitment Mark answer (d) if the candidate is to be selected Mark answer (e) if the candidate is not to be selected.Kesav vora was born on 8th November 1978 He has secured 65 per cent marks in Std. XII and 60 per cent marks in Graduation He has secured 58 percent marks in M.A. Economics and 60 per cent marks in ICWA He has been working in a bank as generalist officer for the past two years after completing his education He has also secured 50 per cent marks in the written examination and 45 percent marks in personal interview.
....