Complete the series, 6, 11, 21, 36, \ \ \ ? \ \ \ , 81, 111. - RRB Staff Nurse Kolkata-2015

RRB Staff Nurse Kolkata-2015

Reasoning

Hard

Appeared in: RRB Staff Nurse Kolkata-2015

Explanation

The core logic is that the difference between consecutive numbers is not constant but increases by a fixed amount (5) at each step.
The sequence of differences is 5, 10, 15, 20, 25, 30.
To find the missing term, the difference of 20 (which is 15 + 5) must be added to the preceding term, 36.
Calculation: 36 + 20 = 56.
The subsequent terms (81 and 111) confirm this pattern, as 56 + 25 = 81 and 81 + 30 = 111.

Option A: If 46 were the answer, the difference would be 46 - 36 = 10. This breaks the established pattern where the difference must increase (from 15 to 20), not decrease.
Option B: If 51 were the answer, the difference would be 51 - 36 = 15. This would mean the difference repeated (15, 15), which contradicts the pattern of the difference increasing by 5 at each step.
Option D: If 71 were the answer, the difference would be 71 - 36 = 35. This jump is too large and does not fit the arithmetic progression of the differences (5, 10, 15, ...). The next difference should be 20.

Visual 1: Flowchart: A flowchart illustrating the step-by-step calculation. It would show the initial series, arrows pointing to the differences calculated below (5, 10, 15), another layer showing the constant second-level difference (+5), and then using that to find the next difference (20) and the final answer (56).

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain This question tests the ability to identify patterns in a number series, specifically a series with a second-order arithmetic progression (the differences between terms form an arithmetic progression) as background academic context rather than a clinical decision trigger.
While not a clinical question, logical reasoning and pattern recognition are crucial skills for nurses.
These skills are applied in interpreting trends in a patient's vital signs, recognizing patterns in lab results over time, and anticipating changes in a patient's condition.
For example, a nurse might notice a patient's heart rate steadily increasing by 5-10 bpm every hour, a pattern that indicates a worsening condition and requires intervention.

How to Approach the Question

First, read the series carefully: 6, 11, 21, 36, __, 81, 111.
Calculate the difference between each consecutive pair of numbers provided.
Step 1: 11 - 6 = 5
Step 2: 21 - 11 = 10
Step 3: 36 - 21 = 15
Analyze the sequence of differences you found: 5, 10, 15. Identify the pattern in this new sequence. Here, the pattern is adding 5 each time.

Concept Tested & Keywords

Concept Tested: This question tests the ability to identify patterns in a number series, specifically a series with a second-order arithmetic progression (the differences between terms form an arithmetic progression).
Stem keywords: Complete the series, Number series, Logical reasoning
Lead-in keywords: Complete the series

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