Question

Kanchan is thinking of a $5$ digit number. The number is a multiple of $5$. The ten's place digit is the highest common factor of $16$ and $24$. The hundred's place digit is the smallest odd number. The ten thousand's place digit is an even prime number. The thousand's place digit is the third multiple of the sum of the ten thousand's place and hundred's place digit. There are only $2$ even digits in the number. What number is Kanchan thinking of?

• A. $23180$
• B. $23185$
• C. $29182$
• D. $29185$

Answer 1

The correct option is D $29185$

The number is multiple of $5$. So, one's place digit is either $0$ or $5$.
Highest common factor of $16$ and $24$ is $8$
$\therefore$ Ten's place digit of the number is $8$
Smallest odd number is $1$
$\therefore$ Hundred's place digit of the number is $1$
$2$ is the only even prime number
$\therefore$ Ten thousand's place digit of the number is $2$
Sum of ten thousand's place and hundred's place digit$=2+1=3$
$\therefore$ Thousand's place digit of the number is $3\times 3=9$
Given that, onl $2$ even digit are there in the number
$\therefore$ one's place digit of the number should be $5$
So, the required number is $29185$