Select the suitable alternative to complete the series. 512, 64, 16, 8, 8, 16, \ \ \ \ \ \ & x20; - ESIC Nursing Officer 2016 (Shift -2)

ESIC Nursing Officer 2016 (Shift -2)

Reasoning

Hard

Appeared in: ESIC Nursing Officer 2016 (Shift -2)

Explanation

The series follows a multiplicative pattern where the multiplier itself changes at each step.
The first term (512) is multiplied by 1/8 to get 64. The second term (64) is multiplied by 1/4 to get 16.
The pattern of the multipliers is that they are doubling at each step: 1/8, 1/4, 1/2, 1, 2.
To find the next term, the previous multiplier (2) is doubled to get 4.
The last term (16) is then multiplied by 4, resulting in 64.

Option B: This would be the answer if the multiplier was 1. This would mean repeating the number 16, which does not follow the established pattern.
Option C: This would be the answer if the multiplier was 2. This would mean the multiplier did not change from the previous step (8 × 2 = 16). The established pattern is that the multiplier doubles at each step.
Option D: This number does not fit any logical mathematical progression from the previous term (16). It is an arbitrary value inconsistent with the series' geometric pattern.

Visual 1: Flowchart - A flowchart showing each term of the series connected by an arrow. The operation (e.g., '× 1/8', '× 1/4', '× 1/2') would be written on each arrow to visually demonstrate the doubling pattern of the multiplier.

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, logical reasoning and pattern recognition are fundamental skills for nurses.
These skills are crucial for interpreting trends in patient vital signs, recognizing subtle changes in a patient's condition, and making timely decisions.
For example, a nurse might notice a pattern of gradually decreasing urine output or a steady increase in heart rate, which requires identifying the trend and intervening promptly.

How to Approach the Question

Step 1: Analyze the relationship between the first few consecutive numbers to identify the initial operation. Here, 512 becomes 64 (division by 8 or multiplication by 1/8) and 64 becomes 16 (division by 4 or multiplication by 1/4).
Step 2: Notice that the operation is not constant. The operation changes from multiplying by 1/8, to 1/4, to 1/2, to 1, and then to 2.
Step 3: Identify the pattern in the multipliers themselves. The sequence of multipliers is 1/8, 1/4, 1/2, 1, 2.
Step 4: Recognize that each multiplier is double the previous one (a geometric progression with a common ratio of 2).
Step 5: Determine the next multiplier in the sequence by doubling the last one (2 × 2 = 4).
Step 6: Apply this multiplier to the last term in the series (16 × 4) to find the missing number, which is 64.

Concept Tested & Keywords

QPklowuP3S4pe2eyJd5-hq