NIMCET 2010 — Reasoning PYQ

The series is divided into groups of three. Notice the number $5$ appearing at every third position:

• $1^{st}$ number: $28$

• $2^{nd}$ number: $25$

• $3^{rd}$ number: $5$

• $4^{th}$ number: $21$

• $5^{th}$ number: $18$

• $6^{th}$ number: $5$

• $7^{th}$ number: $14$

Step 2: Identify the decreasing pattern.

Look at the numbers excluding the constant $5$:

• $28\stackrel{-3}{\to }25$

• $25\stackrel{-4}{\to }21$

• $21\stackrel{-3}{\to }18$

• $18\stackrel{-4}{\to }14$

The pattern of subtraction is alternating between $-3$ and $-4$, but if we look at the first two numbers of each group:

• $(28,25)$ $\to$ Difference is $-3$

• $(21,18)$ $\to$ Difference is $-3$

• $(14,\text{?})$ $\to$ The next number should be $14-3=11$.

Step 3: Determine the next two numbers.

• The $8^{th}$ number (following $14$) is $14-3=11$.

• The $9^{th}$ number must be the constant $5$.

Conclusion:

The next two numbers are $11$ and $5$.

The correct answer is (a) 11, 5.