Question
In a certain examination paper, there are n questions. For j = 1,2 ...n, there are 2n−j students who answered j or more questions wrongly. If the total number of wrong answers is 4095, then the value of n is:
Answer: Option A
:
A
Let us say there are only 3 questions.
Thus there are 23−1=4 students who have answered 1 or more questions wrongly, 23−2=2 students who have answered 2 or more questions wrongly and 23−3=1 student who must have answered all 3 wrongly.
Thus total number of wrong answers =4+2+1=7=23−1=2n−1.
In our question, the total number of wrong answers =4095=212−1. Thus n = 12.
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:
A
Let us say there are only 3 questions.
Thus there are 23−1=4 students who have answered 1 or more questions wrongly, 23−2=2 students who have answered 2 or more questions wrongly and 23−3=1 student who must have answered all 3 wrongly.
Thus total number of wrong answers =4+2+1=7=23−1=2n−1.
In our question, the total number of wrong answers =4095=212−1. Thus n = 12.
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