What should come in place of the question mark (?) in the given series? 70 69 65 56 ? 15

DSSSB October 2024

Reasoning

Hard

Appeared in: DSSSB October 2024

Explanation

The series follows a pattern of subtracting consecutive perfect squares (1², 2², 3², 4², 5²).
The first difference is 70 - 69 = 1, which is 1².
The second difference is 69 - 65 = 4, which is 2².
The third difference is 65 - 56 = 9, which is 3².
Following this pattern, the next number is found by subtracting 4² (16) from 56, which results in 40.
The final step, 40 - 5² (25) = 15, confirms that the pattern is consistent throughout the series.

Option A: If the missing number were 52, the difference from 56 would be 4. The sequence of differences would be 1, 4, 9, 4, which does not follow a logical progression.
Option C: If the missing number were 50, the difference from 56 would be 6. The sequence of differences would be 1, 4, 9, 6. This sequence has no clear mathematical rule.
Option D: If the missing number were 60, it would be larger than the previous number (56), breaking the clear descending trend of the series.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain This question tests the ability to identify patterns in a number series, a common component of logical reasoning and quantitative aptitude assessments as background academic context rather than a clinical decision trigger.
While not a clinical question, logical reasoning is a key skill for nurses. It is essential for prioritizing tasks, troubleshooting equipment, and making sound clinical judgments under pressure.
Number series questions in nursing entrance exams assess a candidate's analytical and problem-solving abilities, which are crucial for interpreting patient data, calculating medication dosages, and managing complex care plans.
What if the differences were consecutive prime numbers instead of squares? If the series started at 70 and subtracted primes (2, 3, 5, 7...), the series would be 70, 68, 65, 60, 53... This highlights the importance of checking for various patterns like squares, cubes, primes, or simple arithmetic progressions.

How to Approach the Question

First, analyze the relationship between the numbers in the series. Notice that the numbers are decreasing.
Calculate the difference between each consecutive pair of numbers: 70-69=1, 69-65=4, 65-56=9.
Examine the sequence of differences you found: 1, 4, 9. Recognize that these are the perfect squares of consecutive integers (1², 2², 3²).
Hypothesize that the pattern is subtracting the next perfect square. The next square is 4², which is 16.
Apply this pattern to the last known number in the series: 56 - 16 = 40.
Verify your answer by applying the next step in the pattern to see if it matches the final number in the series: 40 - 5² = 40 - 25 = 15. Since it matches, your answer is correct.

Concept Tested & Keywords

Concept Tested: This question tests the ability to identify patterns in a number series, a common component of logical reasoning and quantitative aptitude assessments.
Stem keywords: number series, logical reasoning, missing number
Lead-in keywords: What should come in place of the question mark

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