SOLUTION: A man born in the first half of the 19th century was x years old in the year x2. He was born in: (A) 1849 (B) 1806 (C) 1812 (D) 1825
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Question 1132177: A man born in the first half of the 19th century was x years old in the year x2. He was born in: (A) 1849 (B) 1806 (C) 1812 (D) 1825 Found 2 solutions by josgarithmetic, ikleyn:Answer by josgarithmetic(39618) (Show Source):
The 19-th century is the time period from 1801 to 1900, inclusively.
= 42.44 (approximately);
= 43.59 (approximately).
Therefore, the only positive integer number x, whose square lies between 1801 and 1900 is 43.
= 1849.
So, the problem says that the man was 43 years old in the year 1849.
Hence, he was born in the year 1849 - 43 = 1806. ANSWER
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This problem is very well known, and it was solved at this forum MANY TIMES (about 10 times).