Question

A man born in the first half of the nineteenth century was $x$ years old in the year $x^2$. He was born in:

• A. 1836
  
• B. 1849
• C. 1812
  
• D. 1806

Answer 1

The correct option is D 1806

We seek an integer whose square is between 1800 and 1850 . There is one, and only one, such integer, namely $1849={43}^2.\therefore 1849-43=1806$, the year of birth.
∴ (B) is the correct option.