Select the option to replace ? to continue with the pattern in given number series.
5, 7, 11, ?, 35, 67

Appeared in: RRB Staff Nurse Ahmedabad-2015

Explanation

The series follows a pattern where the difference between consecutive numbers doubles at each step.
The initial difference is 7 - 5 = 2.
The next difference is 11 - 7 = 4, which is 2 x 2.
Following this pattern, the next difference must be 4 x 2 = 8.
Adding this difference to the previous term gives the missing number: 11 + 8 = 19.
This is confirmed by the subsequent terms: 19 + (8x2) = 19 + 16 = 35, and 35 + (16x2) = 35 + 32 = 67.

Option B: If the missing number were 22, the difference would be 22 - 11 = 11. The sequence of differences would be 2, 4, 11, which does not follow a consistent mathematical pattern (like doubling).
Option C: Choosing 28 would result in a difference of 28 - 11 = 17. The sequence of differences (2, 4, 17) disrupts the doubling progression.
Option D: If 17 were the missing number, the difference would be 17 - 11 = 6. The sequence of differences would be 2, 4, 6. While this is an arithmetic progression (adding 2), the next step would be 17 + 8 = 25, not 35, so it breaks the overall series pattern.

Visual 1: Flowchart: A flowchart illustrating the step-by-step calculation: Start with 5 -> Add 2 -> Get 7 -> Add 4 -> Get 11 -> Add 8 -> Get 19 -> Add 16 -> Get 35 -> Add 32 -> Get 67. This visualizes the doubling of the added value.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Number Series Pattern Recognition as background academic context rather than a clinical decision trigger.
While not a clinical question, this type of logical reasoning is a foundational skill for nurses.
Nurses use pattern recognition daily to identify trends in patient vital signs, lab results, and symptoms, which is crucial for early detection of patient deterioration.
Problem-solving skills are essential for troubleshooting equipment, managing complex patient care scenarios, and making sound clinical judgments under pressure.

How to Approach the Question

First, examine the given series: 5, 7, 11, ?, 35, 67.
Calculate the difference between the first few consecutive terms to identify a potential pattern. (7-5=2; 11-7=4).
Observe the relationship between the differences themselves. Here, the difference doubles (2, 4, ...).
Formulate a hypothesis for the pattern: The difference between consecutive terms is a geometric progression with a common ratio of 2.
Apply this pattern to find the missing term. The next difference should be 4 * 2 = 8. So, the missing term is 11 + 8 = 19.
Verify your answer by checking if the pattern holds for the rest of the series. (19 + 16 = 35; 35 + 32 = 67). Since it does, the answer is correct.

Concept Tested & Keywords

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Practise the full RRB Staff Nurse Ahmedabad-2015

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