Find the next number in the series. 78, 65, 82, 69, 86, ?

Appeared in: RRB Nsg. Superintendent-20 July 2019 (Shift-1)

Explanation

The sequence contains two alternating series, each increasing by 4.
The first series (odd positions) is 78, 82, 86 (+4).
The second series (even positions) is 65, 69, ... (+4).
Following the pattern for the second series, the next number is 69 + 4 = 73.
Alternatively, the pattern between consecutive numbers is subtracting 13 and adding 17.
The last operation was 69 + 17 = 86, so the next is 86 - 13 = 73.

Option B: This number does not fit either of the identified patterns. It would require a subtraction of 27 from 86, which breaks the '-13, +17' sequence.
Option C: This number would result from subtracting 3 from 86, which does not follow the established '-13, +17' pattern.
Option D: This number would result from subtracting 7 from 86. This does not align with the consistent '-13, +17' alternating difference pattern.

Visual 1: Flowchart: A diagram illustrating the two methods. One branch shows the two alternating series (78, 82, 86 and 65, 69, 73) with '+4' arrows. The other branch shows the single sequence with '-13' and '+17' arrows between consecutive numbers.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain This question tests logical reasoning and the ability to identify patterns in a number series as background academic context rather than a clinical decision trigger.
While not a clinical question, logical reasoning is a critical skill for nurses.
It helps in prioritizing tasks, interpreting patient data, and making sound clinical judgments under pressure.
For example, recognizing a pattern of deteriorating vital signs requires similar analytical skills to solving a number series.

How to Approach the Question

First, examine the relationship between adjacent numbers. Calculate the differences: 78 to 65 is -13, 65 to 82 is +17, 82 to 69 is -13. This reveals an alternating pattern of '-13, +17'.
Apply the next step in the pattern to the last number: 86 - 13 = 73.
As a check, look for an alternating series pattern. Separate the numbers at odd positions (78, 82, 86) and even positions (65, 69, ?).
Identify the pattern in each sub-series. The odd-position series increases by 4. The even-position series also increases by 4.
Apply the pattern to the relevant sub-series to find the missing number: 69 + 4 = 73.
Since both methods yield the same result, you can be confident in the answer.

Concept Tested & Keywords

Concept Tested: This question tests logical reasoning and the ability to identify patterns in a number series.
Stem keywords: number series, logical reasoning, pattern recognition
Lead-in keywords: Find the next number

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Practise the full RRB Nsg. Superintendent-20 July 2019 (Shift-1)

Attempt every question from this paper in a timed mock, then review the full solution for each one.