From the given alternatives, select the number which can come in place of the question mark (?) in the following series? 12, 17, 23, 31, 42, ?

1. A

   55

2. B

   57

3. C

   60

4. D

   53

Appeared in: UP CHO - 10 September 2021

Explanation

• The series follows a pattern where the difference between consecutive numbers is not constant.
• To find the pattern, we calculate the first-order differences: 17-12=5, 23-17=6, 31-23=8, 42-31=11.
• The first-order differences are 5, 6, 8, 11.
• Next, we calculate the second-order differences (the difference of the differences): 6-5=1, 8-6=2, 11-8=3.
• The second-order differences form a simple arithmetic progression: 1, 2, 3. The next term is 4.
• Therefore, the next first-order difference is 11 + 4 = 15. Adding this to the last term of the series gives 42 + 15 = 57.

Why Other Options Were Wrong

• Option A: Choosing 55 would mean the final difference is 13 (55-42). The sequence of first differences would be 5, 6, 8, 11, 13. The second differences would be 1, 2, 3, 2, which breaks the logical pattern of a simple arithmetic progression.
• Option C: Choosing 60 would result in a final difference of 18 (60-42). This large jump does not fit the established pattern of gradually increasing differences.
• Option D: Choosing 53 implies the final difference is 11 (53-42), the same as the previous difference. This contradicts the pattern where the differences are clearly increasing at each step.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Number Series with Double Difference as background academic context rather than a clinical decision trigger.
• This type of logical reasoning question, while not directly clinical, assesses critical thinking and pattern recognition skills.
• Nurses frequently use pattern recognition to identify changes in a patient's condition, interpret trends in vital signs, and anticipate potential complications.
• Strong analytical skills are essential for effective problem-solving in complex healthcare environments.

How to Approach the Question

• First, read the series and identify the terms: 12, 17, 23, 31, 42.
• Calculate the difference between each consecutive pair of numbers (the first-order difference).
• Examine the sequence of differences (5, 6, 8, 11). If the pattern isn't immediately obvious, take the next step.
• Calculate the difference between the consecutive numbers in your new sequence of differences (the second-order difference).
• Identify the pattern in the second-order differences (1, 2, 3). It's a simple progression.
• Use this pattern to predict the next term in the second-order difference (4), then the first-order difference (11+4=15), and finally the missing number in the original series (42+15=57).

Concept Tested & Keywords

• Concept Tested: Number Series with Double Difference
• Stem keywords: number series, question mark, 12, 17, 23, 31, 42
• Lead-in keywords: select the number

Question ID

QaNoJnlJ4eHrn4xu4X2ibU

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