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

Appeared in: RRB Staff Nurse Mumbai-2015

Explanation

The series follows a pattern where the difference between consecutive numbers doubles at each step.
This pattern holds true if the first number, -5, is treated as a typo for 5, which is a common error in such questions.
The sequence of differences is 2, 4, 8, 16, 32, which are successive powers of 2 (2¹, 2², 2³, 2⁴, 2⁵).
Following this logic, the missing term is calculated by adding the third difference (8) to the preceding term (11), resulting in 11 + 8 = 19.

Option B: If 22 were the missing number, the difference would be 11 (22 - 11). The sequence of differences would be 2, 4, 11, 13, 32, which does not follow any logical mathematical pattern.
Option C: If 28 were the missing number, the difference would be 17 (28 - 11). The sequence of differences would be 2, 4, 17, 7, 32, which lacks a discernible pattern.
Option D: If 17 were the missing number, the difference would be 6 (17 - 11). The sequence of differences would be 2, 4, 6... This suggests an arithmetic progression (adding 2 each time). However, the next difference would need to be 8, but the actual difference is 18 (35 - 17), breaking the 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.

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.
This question assesses logical reasoning and pattern recognition, which are essential cognitive skills for nurses.
Nurses use pattern recognition daily to identify changes in a patient's condition, interpret trends in vital signs, and recognize adverse drug reactions from subtle cues.
Strong analytical skills help in making quick, accurate decisions in high-pressure clinical environments.

How to Approach the Question

First, examine the series to identify the relationship between consecutive numbers. Look for simple arithmetic (addition/subtraction) or geometric (multiplication/division) progressions.
Note any potential typos or unusual starting numbers. In this case, '-5' seems out of place. Test the hypothesis that it's a typo for '5'.
Calculate the differences between consecutive terms (assuming the first term is 5): 7 - 5 = 2; 11 - 7 = 4.
Analyze the sequence of differences (2, 4, ...). Notice that the difference is doubling at each step (a geometric progression).
Hypothesize the rule: The next difference should be 4 × 2 = 8.
Apply the rule to find the missing number: 11 + 8 = 19.

Concept Tested & Keywords

QVhmrAOejUzJE5AB0QWZZI

Practise the full RRB Staff Nurse Mumbai-2015

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