Question

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

• A. $10$
• B. $11$
• C. $12$
• D. $13$

Answer 1

The correct option is B $11$

$2^{n-1}+2^{n-2}+2^{n-3}+\cdots +2^1+2^0=2047\Rightarrow \frac{1(2^n-1)}{2-1}=2047\Rightarrow 2^n-2048\Rightarrow 2^n=2^{11}\Rightarrow n=11$