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. $1849$
• B. $1825$
• C. $1812$
• D. $1836$
• E. $1806$

Answer 1

Answer: (E)

$1806$

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 is, therefore, $1800+6=1806$.