Identify the next one-63, 48, 35, 24......?

Appeared in: HSSC Staff Nurse - 2015

Explanation

The series follows a pattern where the difference between consecutive numbers decreases by 2.
The differences are 15 (63-48), 13 (48-35), and 11 (35-24). The next logical difference is 9.
Subtracting 9 from the last term (24) gives the next term: 24 - 9 = 15.
Alternatively, the series can be represented by the formula n² - 1, where n decreases by 1 for each term, starting with n=8.
The first term is 8²-1=63, the second is 7²-1=48, and so on. The next term is calculated as 4² - 1, which equals 15.

Option A: This might be chosen if one incorrectly calculates 4² as the next term without subtracting 1, based on the n²-1 pattern.
Option C: This number does not fit either of the identified patterns (decreasing differences or n² - 1). It appears to be a random incorrect value.
Option D: This number does not follow the established mathematical progression of the series. It might be chosen by guessing or a calculation error.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Number Series and Pattern Recognition as background academic context rather than a clinical decision trigger.
Number series questions are a standard component of aptitude and reasoning tests, designed to evaluate logical and analytical thinking.
Proficiency in solving these problems demonstrates an ability to recognize patterns, a skill that is valuable for systematic problem-solving in many professional contexts, including healthcare.
These skills are transferable to clinical settings for tasks like interpreting data trends in vital signs or lab results over time.

How to Approach the Question

First, observe the given series: 63, 48, 35, 24.
Calculate the difference between consecutive terms to check for a simple arithmetic progression. (63-48=15, 48-35=13, 35-24=11).
Analyze the sequence of differences (15, 13, 11). Notice that this new sequence has a constant difference of -2.
Extrapolate the pattern to find the next difference: 11 - 2 = 9.
Apply this difference to the last term of the original series to find the answer: 24 - 9 = 15.
As a check, look for alternative patterns. Test for squares or cubes. Notice that each term is close to a perfect square (63 is near 64, 48 is near 49, etc.). This leads to the n² - 1 pattern, which confirms the answer.

Concept Tested & Keywords

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Practise the full HSSC Staff Nurse - 2015

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