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27 May 2022, 01:30
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Difficulty:
25%
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Question Stats:
74% (01:28) correct
26%
(02:25)
wrong
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For a set of five True or False questions , no student has marked all correct answer , and no two students have given the same sequence of answer. What is the maximum number of students in class for this to be possible?
(A) 21
(B) 31
(C) 32
(D) 33
(E) 35
Are You Up For the Challenge: 700 Level Questions
(A) 21
(B) 31
(C) 32
(D) 33
(E) 35
Are You Up For the Challenge: 700 Level Questions
27 May 2022, 01:55
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As all five of the questions have two possible answer choices (true or false), there are \(2^5 = 32\) possible ways in which the questions can be answered. However, we are told that no one scored 100% on the questions, which means that one needs to subtract 1 from the total to find the answer: \(32-1=31\)
Answer B
Answer B
27 May 2022, 02:23
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Given : 5 True or False questions, no student has marked all correct answer and no 2 with same sequence of answers
To Find : Maximum number of students in class for this to be possible
Solution : From our given statement, it is evident that maximum possible number of correct answers = 4
Therefore, Max number of students = Students with 0 correct answer + 1 correct answer + 2 correct answers + 3 correct answers + 4 correct answers
Since no 2 repeat sequence of correct answers, we need a unique sequence for each student.
0 correct answer --> Only 1 possibility (All Wrong) = Max 1 student (since sequence cannot repeat)
1 correct answer --> This can be chosen in 5C1 sequences = 5 students (one student per sequence)
2 correct answers --> This can be chosen in 5C2 sequences = 10 students (one student per sequence)
3 correct answers --> This can be chosen in 5C3 sequences = 10 students (one student per sequence)
4 correct answers --> This can be chosen in 5C4 sequences = 5 students (one student per sequence)
=> Max number of students = 1+5+10+10+5 = 31 students
Hence Option (B) is the right answer
To Find : Maximum number of students in class for this to be possible
Solution : From our given statement, it is evident that maximum possible number of correct answers = 4
Therefore, Max number of students = Students with 0 correct answer + 1 correct answer + 2 correct answers + 3 correct answers + 4 correct answers
Since no 2 repeat sequence of correct answers, we need a unique sequence for each student.
0 correct answer --> Only 1 possibility (All Wrong) = Max 1 student (since sequence cannot repeat)
1 correct answer --> This can be chosen in 5C1 sequences = 5 students (one student per sequence)
2 correct answers --> This can be chosen in 5C2 sequences = 10 students (one student per sequence)
3 correct answers --> This can be chosen in 5C3 sequences = 10 students (one student per sequence)
4 correct answers --> This can be chosen in 5C4 sequences = 5 students (one student per sequence)
=> Max number of students = 1+5+10+10+5 = 31 students
Hence Option (B) is the right answer
