Find the next number in the series: 50, 200, 10, 40, 2, ?

Appeared in: KGMU 2023

Explanation

The series follows a clear alternating pattern of mathematical operations: multiplication by 4, followed by division by 20.
The sequence of operations is: 50 (×4) → 200 (÷20) → 10 (×4) → 40 (÷20) → 2.
To find the next number, the pattern dictates that we must multiply the last number (2) by 4.
Therefore, the calculation is 2 × 4 = 8.
An alternative method is to see two interleaved series (50, 10, 2) and (200, 40, ?), where each term is the previous one divided by 5. This also yields 40 ÷ 5 = 8.

Option A: The number 6 does not fit the established mathematical pattern. Arriving at 6 would require an operation of 2 × 3, which is inconsistent with the repeating '× 4' operation.
Option C: The number 10 is incorrect as it breaks the sequence. This would imply an operation of 2 × 5, which does not align with the '× 4' pattern.
Option D: The number 12 is incorrect. This would require an operation of 2 × 6, which is not part of the identified '× 4' and '÷ 20' logic.

Visual 1: Flowchart. A diagram showing the two different methods to solve the series. One path illustrates the alternating '×4' and '÷20' operations applied sequentially. The second path shows the main series splitting into two interleaved sub-series, with the '÷5' rule applied to each to find the next term.

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 tests logical and analytical reasoning, a fundamental skill for nurses and other healthcare professionals.
Nurses use pattern recognition daily, for example, in identifying trends in a patient's vital signs, recognizing subtle changes in their condition, or anticipating medication needs.
Strong analytical skills are crucial for accurate drug dose calculations, interpreting lab results, and making sound clinical judgments, especially under pressure.

How to Approach the Question

First, analyze the relationship between consecutive numbers. In this case, 50 to 200 is ×4, and 200 to 10 is ÷20.
Check if this initial pattern repeats. Notice that 10 to 40 is again ×4, and 40 to 2 is again ÷20. This confirms a consistent alternating pattern.
Apply the next logical operation in the sequence. After a '÷20' operation, the pattern calls for a '×4' operation.
Calculate the final answer: 2 × 4 = 8.
As a verification step, consider other possible patterns, such as interleaved series. Split the sequence into odd-positioned numbers (50, 10, 2) and even-positioned numbers (200, 40, ?).
Identify the pattern in each sub-series (in this case, division by 5) to confirm the answer is 8.

Concept Tested & Keywords

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Practise the full KGMU 2023

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