NIMCET 2009 — Reasoning PYQ

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Question

NIMCET 2009 — Reasoning PYQ

NIMCET | Reasoning | 2009

Direction : Read the following passage to answer the questions
Rajita has a 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 the 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 20th question Rajita answers ?

Choose the correct answer:

Explanation

To find the $20^{th}$ question, we need to track the order in which Rajita attempts the questions based on her specific A.P. pattern.

Step 1: Pass 1 (Forward Direction)

Start: Question $1$ .
Common Difference ( $d$ ): $+3$ .
Sequence: $1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49$ .
Questions Answered: $17$ questions.

Step 2: Transition to Reverse Direction

At question $49$ , the next in sequence would be $52$ , which is out of bounds ( $>50$ ). Rajita now reverses her direction starting with the first unanswered question from the end.

The questions remaining at the end of the paper are $50, 48, 47, \dots$
The first unanswered question from the end is $50$ .

Step 3: Pass 2 (Reverse Direction)

Start: Question $50$ .
Common Difference ( $d$ ): $-3$ .
Sequence:
- $18^{th}$ Question: $50$
- $19^{th}$ Question: $50 - 3 = 47$
- $20^{th}$ Question: $47 - 3 = 44$

Conclusion:

By following the sequence, the $20^{th}$ question attempted is $44$ .

Correct Option: (d) 44