If (73)² is subtracted from the square of a number, the answer so obtained is 5075. What is the number? · ABC26GN1668
Subject: General Aptitude · Chapter: Problems on Numbers · Exam: L.I.C.A.D.O. 2007
If $(73)^{2}$ is subtracted from the square of a number, the answer so obtained is 5075. What is the number?
(a)96
(b)98
(c)102
(d)106
Answer
Answer (as printed): C
Explanation
Let the number be $x$. Then, $x^{2}-(73)^{2}=5075 \Leftrightarrow x^{2}-5329=5075$ $$\begin{aligned} & \Leftrightarrow x^{2}=5075+5329=10404 \\ & \Leftrightarrow x=\sqrt{10404}=102 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.