NIMCET 2008 — Reasoning PYQ

The series follows a cumulative grouping pattern where each group contains sums of elements. Let's break the series down into growing segments:

• Group 1: $(1)$

• Group 2: $(1,2)$

• Group 3: $(1,2,2,3)$

• Group 4: $(1,2,2,3,2,3,3,4)$

• Group 5: $(1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5)$

2. Identify the Internal Logic:

Each group is formed by taking the previous group and creating two versions of it:

1. The original group.

2. The original group with each element increased by $1$.

Let's trace it:

• $G_1=[1]$

• $G_2=[1]+[1+1]=[1,2]$

• $G_3=[1,2]+[1+1,2+1]=[1,2,2,3]$

• $G_4=[1,2,2,3]+[2,3,3,4]=[1,2,2,3,2,3,3,4]$

• $G_5=[1,2,2,3,2,3,3,4]+[2,3,3,4,3,4,4,5]$

3. Find the Missing Numbers:

The series provided in the image ends during the second half of Group 5.

The sequence given is:

$1,2,2,3,2,3,3,4$ (First half of $G_5$)

followed by:

$2,3,3,\dots$ (Beginning of the second half of $G_5$)

Following the logic of the second half of $G_5$ (which is $G_4+1$):

• $1+1=2$

• $2+1=3$

• $2+1=3$

• $3+1=4$

• $2+1=3$

• $3+1=4$

The next three numbers are 4, 3, 4.

Final Answer:

The next three numbers in the pattern are 4, 3, 4.

Correct Option: (d)