Question

An integer is chosen at random. The probability that, sum of the digits of its square is 24 is:

• A. $\frac{1}{39}$
• B. $\frac{2}{39}$
• C. $\frac{1}{11}$
• D. $0$

Answer 1

The correct option is D $0$

Let x be such a number. Then sum of digits of $x^2$ is 24. 24 is divisible by 3.3 is prime and divides $x^2$ so it must divide x.
3 divide $z\Rightarrow 3^2=9$ must divide $x^2$
$\Rightarrow 9$ divides a number, sum of whose digits is 24 which is not true.
Hence, there is no such integer and so, probability is 0.