Last year my age was a perfect square number. Next year it will be a cubic number. What is my present age?

Finding the Present Age Based on Mathematical Properties

Given the intriguing conditions about the nature of one’s age in relation to mathematical figures:

Stated Conditions:

• The age last year was a perfect square number.
• The age next year will be a cubic number.

Evaluation of Options:

Considering the options provided and applying the given conditions to each, we meticulously analyze to find the correct age:

– Option (a) 25 years: Not viable, as 24 (last year) is not a perfect square and 26 (next year) is not a cube.
– Option (b) 27 years: Not viable, as 26 (last year) is not a perfect square and 28 (next year) is not a cube.
– Option (c) 26 years: This is the correct choice. If the present age is 26, then:
– Last year’s age was 25 (\(5^2\)), a perfect square.
– Next year’s age will be 27 (\(3^3\)), a perfect cube.
– Option (d) 24 years: Not viable, as 23 (last year) is not a perfect square and 25 (next year) is not a cube.

Correct Answer:

The logical deduction based on the conditions clearly points to Option (c) 26 years as the present age. At 26 years old:

• Last year, the individual was 25 years old, aligning with the property of being a perfect square (\(5^2\)).
• Next year, they will be 27 years old, fulfilling the characteristic of being a cubic number (\(3^3\)).

Conclusion:

The individual’s current age, which perfectly transitions from a perfect square to a cubic number, is unequivocally 26 years. This finding not only satisfies the unique mathematical conditions presented but also underscores the harmonious relationship between sequential numerical properties and real-life scenarios.