Subject: General Aptitude · Chapter: Problems on Numbers · Exam: 2008 · Marks: · Difficulty:
If the square of a two-digit number is reduced by the square of the number formed by reversing the digits of the number, the final result is
(a)divisible by 11 and
(b)divisible by 9
(c)necessarily irrational
(d)Both
Answer
Answer (as printed): D
Explanation
Let the two-digit number be $10 x+y$. Then, number formed by reversing the digits $=10 y+x$.Difference of squares of the numbers $$\begin{aligned} & =(10 x+y)^{2}-(10 y+x)^{2} \\ & =\left(100 x^{2}+y^{2}+20 x y\right)-\left(100 y^{2}+x^{2}+20 x y\right) \\ & =99\left(x^{2}-y^{2}\right), \text { which is divisible by both } 9 \text { and } 11 \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.