Aspire Faculty ID #16487 · Topic: NIMCET 2009 · Just now
NIMCET 2009

Rajita has unique way of attempting the question paper having 50 questions. She starts from question 1 and attempts all questions which are in A.P. with a common difference of 3 in the forward direction and 3 in reverse direction. If she reaches a stage when she cannot attempt any more question, she starts in the reverse direction with the first unanswered question. She repeats the same process and when she reaches a stage when she can not process any further, she reverses her direction again starting with the first unanswered question.
Which is the last question that she answers if she attempts all the 50 questions?

Solution

1st round (forward starting from 1):
1, 4, 7, 10, …, 49 → all multiples of form 1 + 3k

Unanswered after first round:
2, 3, 5, 6, 8, 9, …, 50

2nd round (reverse starting from 50):
50, 47, 44, 41, …, 2 → all backwards with difference −3

Unanswered after second round:
3, 6, 9, 12, …, 48

3rd round (forward starting from 3):
3, 6, 9, …, 48 → finishing at 48

So the last answered question = 48.
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