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I found this book on my desk when I came to class. It (leave) by one of the students in the earlier class.

Correct answer is 'must have been left'. Can you explain this answer?
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I found this book on my desk when I came to class. It (leave) by one o...
I found this book on my desk when I came to class. It must have been left by one of the students in the earlier class.


In this context, finding a book on your desk that wasn't there before suggests that it was left there by someone else, presumably during a time you were not present, such as an earlier class. "Must" is a modal verb that indicates a high degree of certainty about a past action, especially when direct evidence or firsthand knowledge is lacking but the circumstances strongly point to a specific conclusion.
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I found this book on my desk when I came to class. It (leave) by one o...
Explanation:

  • The correct answer is "must have been left".

  • This is because the sentence is in the past tense and the speaker is uncertain about who left the book on the desk.

  • "Must have been left" is a modal verb construction in the past tense that expresses probability or certainty about an event in the past.

  • The use of "must" indicates that the speaker believes it is highly likely that the book was left by someone in the earlier class.

  • The use of "have been" is the past participle form of "be", which is used to show that an action was completed in the past.

  • The word "left" is the past participle form of the verb "leave", which means to go away from a place or to abandon something.

  • Therefore, "must have been left" means that it is highly likely that someone left the book on the desk in an earlier class and the action of leaving the book was completed in the past.
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After grading the examination papers of a class of 18 students, a teacher noticed that when arranged in ascending or descending order, the scores formed an arithmetic progression. When the teacher was done recording the marks of the students, calculating average score of the class and finalizing individual ranks of the students (rank 1 being awarded to the student with highest marks), she noticed that the number of papers that had been graded was one more than the number of her students. It was then found that the paper of a student of another class was present in the l o t . Due to this mix up, the teacher had to rearrange the scores and calculate the average marks of her class. To her surprise, the average remained the same as before. What was the rank of the student of the other class in the initial arrangement?

Directions:Read the information carefully to answer the question that follows.Dr. Ravi Patel teaches financial markets course at Indian Management Institute, which is being taught in two parts - one part in first trimester and the other part in second trimester. Initially, the professor divides the students randomly in five classes in first trimester and based on the performance of students in first trimester, he further divides the students of each class into two parts as below average and above average performers. It is observed that in each class, the ratio of below average and above average performers is at least 13/10.Initially, the classes were named as classes P, Q, R, S and T and after further division, the classes were renamed as classes 1, 2, 3, 4 ,....,10 and the classes in trimester 2 are named randomly i.e. it is not necessary that two parts of class A are numbered one after the other.It is also given that 1/5 of total students in first trimester were in class R, 23% of total students were in class Q and 17% of total students were in class T. The ratio of students in classes P and S was 11 : 9. In the second trimester, there were 20 students in class 1. The number of students in classes 3, 10 and 9 were twice, thrice and four times the number of students in class 1. The number of students in classes 4 and 5 are in ratio 1 : 3. The number of students in class 2 were 5 more than the number of students in class 9. The number of students in class 8 was 40% more than the number of students in class 4. The number of students in classes 6 and 7 is 50 and 30 and the total number of students in classes 4, 5 and 8 is 125% more than the number of students in class 10. Each student in first trimester was classified as either below average or above average performer.Q.What was the minimum difference between number of students who performed below average and number of students who performed above average in any class?

Directions:Read the information carefully to answer the question that follows.Dr. Ravi Patel teaches financial markets course at Indian Management Institute, which is being taught in two parts - one part in first trimester and the other part in second trimester. Initially, the professor divides the students randomly in five classes in first trimester and based on the performance of students in first trimester, he further divides the students of each class into two parts as below average and above average performers. It is observed that in each class, the ratio of below average and above average performers is at least 13/10.Initially, the classes were named as classes P, Q, R, S and T and after further division, the classes were renamed as classes 1, 2, 3, 4 ,....,10 and the classes in trimester 2 are named randomly i.e. it is not necessary that two parts of class A are numbered one after the other.It is also given that 1/5 of total students in first trimester were in class R, 23% of total students were in class Q and 17% of total students were in class T. The ratio of students in classes P and S was 11 : 9. In the second trimester, there were 20 students in class 1. The number of students in classes 3, 10 and 9 were twice, thrice and four times the number of students in class 1. The number of students in classes 4 and 5 are in ratio 1 : 3. The number of students in class 2 were 5 more than the number of students in class 9. The number of students in class 8 was 40% more than the number of students in class 4. The number of students in classes 6 and 7 is 50 and 30 and the total number of students in classes 4, 5 and 8 is 125% more than the number of students in class 10. Each student in first trimester was classified as either below average or above average performer.Q.Out of total students in class S, what percent performed below average?

Directions:Read the information carefully to answer the question that follows.Dr. Ravi Patel teaches financial markets course at Indian Management Institute, which is being taught in two parts - one part in first trimester and the other part in second trimester. Initially, the professor divides the students randomly in five classes in first trimester and based on the performance of students in first trimester, he further divides the students of each class into two parts as below average and above average performers. It is observed that in each class, the ratio of below average and above average performers is at least 13/10.Initially, the classes were named as classes P, Q, R, S and T and after further division, the classes were renamed as classes 1, 2, 3, 4 ,....,10 and the classes in trimester 2 are named randomly i.e. it is not necessary that two parts of class A are numbered one after the other.It is also given that 1/5 of total students in first trimester were in class R, 23% of total students were in class Q and 17% of total students were in class T. The ratio of students in classes P and S was 11 : 9. In the second trimester, there were 20 students in class 1. The number of students in classes 3, 10 and 9 were twice, thrice and four times the number of students in class 1. The number of students in classes 4 and 5 are in ratio 1 : 3. The number of students in class 2 were 5 more than the number of students in class 9. The number of students in class 8 was 40% more than the number of students in class 4. The number of students in classes 6 and 7 is 50 and 30 and the total number of students in classes 4, 5 and 8 is 125% more than the number of students in class 10. Each student in first trimester was classified as either below average or above average performer.Q.In how many classes was the number of students who performed below average at least 90% more than the number of students who performed above average?

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I found this book on my desk when I came to class. It (leave) by one of the students in the earlier class.Correct answer is 'must have been left'. Can you explain this answer?
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