Question

In a test there were n questions. In the test $2^{n-i}$ students gave wrong answers to i questions where $i=1,2,\mathrm{3...},n$. If the total number of wrong answers given is 2047 then n is

• A. 12
• B. 11
• C. 10
• D. none of these

Answer 1

The correct option is B 11

Total number of wrong answers $=2^{n-1}+2^{n-2}+...+2^2+2+1$
$=2^{n-1}+2^{n-2}+...+2^4+2^3+2^2+2+1$
$\Rightarrow 2^n-1=2043$ [Using formula for sum of G.P]
$\Rightarrow 2^n=2048$
$\Rightarrow 2^n=2^{11}$
$\Rightarrow n=11$
Hence, option 'B' is correct.