Visiting the historical monuments a tourist asked, 'How old' is this monument ? The guide replied, "the monument is over fifty years old. Its exact age was a square number two years ago, and will be a cube number two years hence." What is the age of the monument ?

Options

A. 216
B. 64
C. 343
D. 123

Answer

D

Explanation

According to the question The monument is over fifty years old. It means that the age of the monument is more than fifty years:
Hit and trial method:
From the given choices, it is clear that only 123 satisfies all the conditions i.e. age of the monument two years ago = `(123 - 2) = 121 = 11^2` = Square number. Age of the monument two years hence `= (123 + 2) = 125 = 5^3` = Cube number.
Therefore, the age of the monument = 123 years.