InterviewSolution
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InterviewSolution
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N a certain test, there are `n`question. In the test, `2^(n-i)`studentsgave wrong answers to at least `i`questions,where `i=1,,2ddot,ndot`if thetotal number of wring answers given is 2047, then `n`is equal toa. `10`b. `11`c. `12`d. `13`A. 10B. 11C. 12D. 13 |
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Answer» The number of studnets answering exactly `k(1leklen-1)` questions wrongly is `2^(n-k)-2^(n-k-1)`. The number of studnets answering all questions wrongly is `2^(0)`. Thus, the total number of wrong answers `=1.(2^(n-1)-2^(n-2))+2.(2^(n-2)-2^(n-3))+......+(n-1)(2^(1)-2^(0))+n.2^(0)` `=2^(n-1)+2^(n-2)+2^(n-3)+......+2^(0)=2^(n)-`1 Thus, `2^(n)-1=2047implies2^(n)=2048implies2^(n)=2^(11)impliesn=11` |
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