Select the number from the given options which can replace the question mark (?) in the following series.

14, 126, 66, 462, 342, 1710, 1470, ?

1. A

   4500

2. B

   4460

3. C

   4380

4. D

   4410

Appeared in: DSSSB 12 August 2024

Explanation

• The series follows an alternating pattern of two different operations: multiplication and subtraction.
• The first operation is multiplication by a descending odd number (9, 7, 5, ...).
• The second operation is subtraction of a value that doubles each time (60, 120, 240, ...).
• The sequence of operations applied is: ×9, -60, ×7, -120, ×5, -240.
• The final step is to apply the next logical operation, which is multiplying the last term (1470) by 3 (the next odd number after 5).
• Calculation: 1470 × 3 = 4410.

Why Other Options Were Wrong

• Option A: This value does not result from multiplying 1470 by 3, which is the next logical step in the established pattern.
• Option B: This value breaks the established alternating mathematical sequence. It does not fit the pattern of multiplying by descending odd numbers.
• Option C: This is mathematically incorrect based on the established pattern. The next operation must be 1470 × 3.

Related Visual

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 is a non-nursing, general intelligence question designed to test logical reasoning.
• Strong logical reasoning and pattern recognition skills are crucial for nurses in clinical practice.
• Nurses must identify trends in a patient's vital signs, recognize patterns in lab results that may indicate a worsening condition, and calculate complex medication dosages accurately.

How to Approach the Question

• Start by examining the relationship between the first two numbers (14 and 126). Here, 14 × 9 = 126.
• Next, check the relationship between the second and third numbers (126 and 66). Here, 126 - 60 = 66.
• Since the operations are different (multiplication then subtraction), suspect an alternating pattern.
• Continue analyzing subsequent pairs to confirm the pattern: 66 × 7 = 462; 462 - 120 = 342.
• Identify the two separate progressions: one for the multiplication factor (×9, ×7, ×5...) and one for the subtraction value (-60, -120, -240...).
• Once the full pattern is confirmed, apply the next logical step to the last number in the series to find the missing term.

Concept Tested & Keywords

• Concept Tested: Number Series Pattern Recognition
• Stem keywords: number series, replace the question mark, following series
• Lead-in keywords: Select
• Negative lead-in flag: false

Question ID

QSj_8fO5iHLkS3sVo6Wlaq

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