Maths · Simple applications
In a test there were questions. In the test students gave wrong answers to at le
In a test there were \( n \) questions. In the test \( 2^{n-i} \) students gave wrong answers to at least \( i \) questions \( i=1,2,3 \dots . n . \) If the total number of wrong answers given is \( 2047, \) then \( n \) is
- A. 12
- B. 11
- C. 10
- D. 13
Step-by-step solution
Let a_i be number of students with exactly i wrong answers. Given sum_{j=i}^n a_j = 2^{n-i}. Then a_i = 2^{n-i} - 2^{n-i-1} for i=1..n-1, and a_n = 1. Total wrong answers = sum i a_i = 2^n - 1 = 2047, so n=11.
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