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In a certain ...

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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, 2, 3, ......, n. If the total number of wrong answers given is 2047, then n is equal to

A

13

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B

12

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C

10

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D

11

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Solution

The correct option is D 11
The total number of wrong answers $= n . 2^{0} + (n - 1) 2^{1} + (n - 2) 2^{2} + . . . . + 12^{n - 1} = 2047$

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