in a certain examination paper there are n questions. For j=1,2,3,.....n, there are 2^(n-1) students who answered j or more question wronlgy. if the total number of wrong answers is 4096 then the value of n is
a)12
b)11
c)10
d)9

• According to the question 2^(n-j) students who answered j or more question wrongly...what does its mean???
  Let see--
  Its mean
  2^(n-1) students answered 1 question wrongly (I am taking j as 1)
  2^(n-2) students answered 2 question wrongly (I am taking j as 2)
  2^(n-3) students answered 1 question wrongly (I am taking j as 3)
  ......
  ......
  ......
  i.e. 2^(n-n)=1 student who answered all n question wrongly...
  Now total no. of wrong questions
  1 + 2 + 2^2 + 2^3 + .....2^(n-1)= 2^(n)-1 (which is total no. of wrong answered questions)
  And acccording to question
  Total No. of wrong answered question is 4095
  i.e.
  2^(n)-1=4095
  2^(n)=4095+1===>>4096
  and n= 12. which is required solution....
• 10 years agoHelpfull: Yes(30) No(9)
• If the statement
  there are 2^(n-1) students who answered j or more question wronlgy.
  
  is to be read as
  there are 2^(n-j) students who answered j or more question wronlgy.
  and
  total number of wrong answers is 4095
  Then
  n=12
• 12 years agoHelpfull: Yes(16) No(11)
• there seems to be some mistake in qn.
  pls check.
  
• 12 years agoHelpfull: Yes(15) No(5)
• 2^(n-1)=4096=2^12
  i.e)n-1=12
  ==> n=13
• 12 years agoHelpfull: Yes(15) No(15)
• http://www.youtube.com/watch?v=GmLWoJxdBnk
• 9 years agoHelpfull: Yes(14) No(0)
• If it is
  It is 2^(n-j)
  
  then n=12
• 12 years agoHelpfull: Yes(4) No(5)
• I think this is how we can do it..
  
  According to the question 2^(n-1) students got 1 or more questions wrong.
  
  2^(n-2) students got 2 or more questions wrong.
  
  2^(n-3) students got 3 or more questions wrong.. and so on...
  
  So we can tell that 2^(n-1) – 2^(n-2) students got exactly one question wrong.
  
  2^(n-2) – 2^(n-3) students got exactly two question wrong.
  
  2^(n-3) – 2^(n-4) students got exactly three question wrong and so on..
  
  Now to compute the total number of wrong answers equation would be:
  
  1 * [2^(n-1) – 2^(n-2)] + 2 * [2^(n-2) – 2^(n-3)] + 3 * [2^(n-3) – 2^(n-4)] +…… + (n-1)[2 - n^0] + n
  
  = 2^(n-1) + 2^(n-2) + 2^(n-3) + 2^(n-4) + ........ + 2 - n + 1 + n
  
  Now clearly 2^(n-1) + 2^(n-2) + 2^(n-3) + 2^(n-4) + ........ + 2 + 1 is a GP where a = 1, r = 2
  
  So, 1(2^n – 1) / (2 – 1)
  = 2^n - 1, which is the total number of wrong answers.
  
  Acc. to question, Total No. of wrong answered question is 4095.
  Therefore,
  2^n - 1 = 4095
  =>n = 12. Ans
• 6 years agoHelpfull: Yes(4) No(0)
• 2^n-1 = 4096 =>2^12 so n-1 = 12 =>n-1=12, n=13
• 11 years agoHelpfull: Yes(3) No(8)
• Please explain the answer ie. 12
• 10 years agoHelpfull: Yes(1) No(2)
• n=12
  as in question saying about value of wrong questions is j or more than j, and j is from 1 to n.
  if we take value which is greater than j, i.e. if we take j= n+1, and put this in place of n
  so,
  2^(n-1) = 2^(n+1-1)= 4096
  then, 2^(n) = 4096
  n=12 .
• 10 years agoHelpfull: Yes(1) No(5)
• Right question is ............
  
  
  2^(n-j)
  j=1,2,3.......n
• 8 years agoHelpfull: Yes(1) No(2)
• It is 2^(n-j)
  n number of wrong answer is 4095
• 12 years agoHelpfull: Yes(0) No(6)
• 2^(12-1)=4095....given 2^(n-1). equate for n you get........
  
  (12-1)=(n-1)
  11=n-1
  
  n=12.
• 10 years agoHelpfull: Yes(0) No(6)
• see first convert 4096 into powers of 2 i.e 2^12.
  now from ques (2^n-1)*j=2^12 where j=1,2,3,.....n
  now 1st case: j=1 den n=13 no options
  2nd case: j=2 den n=12 option a matches
  3rd case: j=3 den n will not be perfect square
  so case 2 is valid ans
  
• 10 years agoHelpfull: Yes(0) No(4)
• correct answer is a
  direct formulla of such type of question is
  2^n -1=4096
  bt actually in place of 4096 it is 4095
• 7 years agoHelpfull: Yes(0) No(2)