NIMCET 2011 — Reasoning PYQ

1. Analyze the pattern of the series:

The pattern follows a logic where a term is the sum of the two preceding terms (similar to a Fibonacci-type sequence).

2. Test the pattern:

• First term: $5$

• Second term: $12$

• Third term: $5+12=17$ (But the series shows 19)

• Fourth term: $12+19=31$ (But the series shows 33)

Since the later terms are also affected, let's re-verify the logic starting from the first two terms:

• $5+12=17$ (If $19$ is wrong and replaced by $17$)

• $12+17=29$ (If $33$ is wrong and replaced by $29$)

Let's check if there is an alternative pattern based on differences:

• $12-5=7$

• $19-12=7$

• $33-19=14$

• $47-33=14$

• $75-47=28$

• $104-75=29$

3. Identify the inconsistency:

Looking at the differences: $7,7,14,14,28,\dots$

The differences are doubling every two steps:

• Pair 1: $+7,+7$

• Pair 2: $+14,+14$

• Pair 3: Should be $+28,+28$

4. Recalculate with the identified pattern:

• $5+7=12$

• $12+7=19$

• $19+14=33$

• $33+14=47$

• $47+28=75$

• $75+28=103$

In the given series, the last term is 104, but according to the pattern ($+7,+7,+14,+14,+28,+28$), it should be 103.

Correct Option: (d) $104$