What will come in place of Question mark (?) in the following number series?

445, 221, 109, (?), 25, 11,4

Appeared in: DHS Staff Nurse - 2018 (Shift-2nd)

Explanation

The question requires identifying the logical pattern in a decreasing number series.
The pattern is to subtract 3 from the current number and then divide the result by 2 to get the next number in the sequence.
Applying this rule to 109, the number before the question mark: (109 - 3) / 2 = 106 / 2 = 53.
To verify, we can apply the rule to 53: (53 - 3) / 2 = 50 / 2 = 25, which is the next number in the series, confirming the pattern.

Option A: 46 does not fit the established pattern. If 46 were the answer, the next number would be (46 - 3) / 2 = 21.5, not 25.
Option B: 57 does not fit the established pattern. If 57 were the answer, the next number would be (57 - 3) / 2 = 27, not 25.
Option D: 59 does not fit the established pattern. If 59 were the answer, the next number would be (59 - 3) / 2 = 28, not 25.

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 component of nursing entrance and competitive exams.
Strong analytical and problem-solving skills are essential for nurses in clinical practice for tasks like calculating drug dosages, interpreting lab results, and making critical decisions under pressure.
What if the pattern was (x/2) - 3? The series would be completely different. For example, starting with 445, the next term would be (445/2) - 3 = 222.5 - 3 = 219.5. This demonstrates the importance of correctly identifying the order of operations.

How to Approach the Question

First, observe the series to determine if it's increasing, decreasing, or alternating. This series is decreasing.
Calculate the difference or ratio between consecutive terms to find a simple pattern. (e.g., 445 - 221 = 224; 221 - 109 = 112). Notice that 224 is double 112, which suggests a division-based pattern.
Test for more complex patterns involving multiple operations (addition/subtraction and multiplication/division). Try applying a potential rule like (x - a) / b to the first few terms.
In this case, test the rule (Previous Number - 3) / 2. (445 - 3) / 2 = 221. It works for the first pair.
Apply the confirmed rule to find the missing number: (109 - 3) / 2 = 53.
Verify the answer by applying the rule to your result to see if it produces the next number in the series: (53 - 3) / 2 = 25. It does, so the answer is correct.

Concept Tested & Keywords

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Practise the full DHS Staff Nurse - 2018 (Shift-2nd)

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