Latest Elitmus Aptitude Question SOLUTION: In a certain examination paper, there are n questions. For j=1,2,.......n there are 2^n-1 will answered j or more questions wrongly. If the total number of wrong answers are 4095,

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In a certain examination paper, there are n questions. For j=1,2,.......n there are 2^n-1 will answered j or more questions wrongly. If the total number of wrong answers are 4095, then the value of n is

a.12
b.11
c.10
d.9

Asked In Elitmus Shashank Saha (7 years ago)

Unsolved Read Solution (4)

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Manisha Choudhary  (7 years ago)

Ans is 12.
2^n - 1 = 2^12 - 1
=> 4095
therefore, n =12

Is this solution Helpfull? Yes (8) | No (1)  

Soumya Priyadarsini  (7 years ago)

(2^n)-1=4095
=>2^n=4096
=>2^n=2^12
=>n=12

Is this solution Helpfull? Yes (2) | No   

Rajeev kumar  (7 years ago)

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

Is this solution Helpfull? Yes | No   

ramakant  (7 years ago)

2^n-1=4095
=>2^n=4094=2^12
=>n=12.

Is this solution Helpfull? Yes | No (1)  

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