Latest Elitmus Aptitude Question SOLUTION: 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 i

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(#M40008866) ELITMUS Numerical Ability question Keep an EYE

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

Asked In Elitmus amrit bhagat (12 years ago)

Unsolved Read Solution (15)

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Read Solution (15) :

prayas goel  (10 years ago)

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....

Is this solution Helpfull? Yes (30) | No (9)  

Pargat Pal Singh  (12 years ago)

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

Is this solution Helpfull? Yes (16) | No (11)  

Pargat Pal Singh  (12 years ago)

there seems to be some mistake in qn.
pls check.

Is this solution Helpfull? Yes (15) | No (5)  

Balakrishnan M  (12 years ago)

2^(n-1)=4096=2^12
i.e)n-1=12
==> n=13

Is this solution Helpfull? Yes (15) | No (15)  

Smita Bambode  (9 years ago)

http://www.youtube.com/watch?v=GmLWoJxdBnk

Is this solution Helpfull? Yes (14) | No   

Ashu  (12 years ago)

If it is
It is 2^(n-j)

then n=12

Is this solution Helpfull? Yes (4) | No (5)  

Neha Dushyani  (6 years ago)

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

Is this solution Helpfull? Yes (4) | No   

cracker  (11 years ago)

2^n-1 = 4096 =>2^12 so n-1 = 12 =>n-1=12, n=13

Is this solution Helpfull? Yes (3) | No (8)  

ranjeet singh chauhan  (10 years ago)

Please explain the answer ie. 12

Is this solution Helpfull? Yes (1) | No (2)  

pradeep singh  (10 years ago)

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 .

Is this solution Helpfull? Yes (1) | No (5)  

mukesh kumar  (8 years ago)

Right question is ............


2^(n-j)
j=1,2,3.......n

Is this solution Helpfull? Yes (1) | No (2)  

amrit bhagat  (12 years ago)

It is 2^(n-j)
n number of wrong answer is 4095

Is this solution Helpfull? Yes | No (6)  

Raghav  (10 years ago)

2^(12-1)=4095....given 2^(n-1). equate for n you get........

(12-1)=(n-1)
11=n-1

n=12.

Is this solution Helpfull? Yes | No (6)  

MANPREET SINGH  (10 years ago)

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

Is this solution Helpfull? Yes | No (4)  

Vikash kumar  (7 years ago)

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

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