shashank.ism wrote:In a certain examination paper, there are n questions. For j = 1, 2 ...n, there are 2^(n-j) students who answered j or more questions wrongly. If the total number of wrong answers is 4095, then the value of n is

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Let us say there are only 3 questions. Thus there are 23-1 = 4 students who have done 1 or more
questions wrongly, 23-2 = 2 students who have done 2 or more questions wrongly and 23-3 = 1 student who
must have done 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 [spoiler]n = 12.A is the ans.[/spoiler]

Let us say there are only 3 questions. Thus there are 23-1 = 4 students who have done 1 or more
questions wrongly, 23-2 = 2 students who have done 2 or more questions wrongly and 23-3 = 1 student who
must have done 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.A is the ans.
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I'm having trouble understanding this "Thus there are 23-1 = 4 students who have done 1 or more
questions wrongly"

Where is the 23-1=4 coming from?

odod wrote:Let us say there are only 3 questions. Thus there are 23-1 = 4 students who have done 1 or more
questions wrongly, 23-2 = 2 students who have done 2 or more questions wrongly and 23-3 = 1 student who
must have done 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.A is the ans.
_________________

I'm having trouble understanding this "Thus there are 23-1 = 4 students who have done 1 or more
questions wrongly"

Where is the 23-1=4 coming from?

2^(3-1) is what the author means which is indeed 2^2 = 4. Probably the answer was copied from somewhere and the power sign was missed

ajith wrote:

odod wrote:Let us say there are only 3 questions. Thus there are 23-1 = 4 students who have done 1 or more
questions wrongly, 23-2 = 2 students who have done 2 or more questions wrongly and 23-3 = 1 student who
must have done 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.A is the ans.
_________________

I'm having trouble understanding this "Thus there are 23-1 = 4 students who have done 1 or more
questions wrongly"

Where is the 23-1=4 coming from?

2^(3-1) is what the author means which is indeed 2^2 = 4. Probably the answer was copied from somewhere and the power sign was missed

yes, it was copied from www.complore.com

That is their scam, they just copy and paste questions and then the other copies and paste the solution.