In a certain test there are n questions. In this test 2k students gave wrong answers to at least (n – k) questions, where k = 0, 1, 2,…, n. If the total number of wrong answers is 4095, then value of n is
The number of students answering at least r questions incorrectly is 2n–r.
∴ The number of students answering exactly r(1 ≤ r ≤ n – 1) questions incorrectly is 2n–r – 2n–(r + 1).
Also, the number of students answering all questions wrongly is 20 = 1.
Thus, the total number of wrong answers is
Now, 2n – 1 = 4095 ⇒ 2n = 4096 = 212 ⇒ n = 12