Question

Find the digits $xy$ such that the number $47xy$ is divisible by $30.$

• A. $xy=30$
• B. $xy=20$
• C. $xy=50$
• D. $xy=80$

Answer 1

Answer: (B), (C), (D)

$xy=80$

Concept: 3 and 10 are relatively prime number.
Hence, any number, divisible by $30,$ must be divisible by $3$ and $10$.

For divisibility by $10,$ the number must end with 0.
$y=0\Rightarrow$ The number is $47x0.$

For the number to be divisible by $3$, its sum of digits $4+7+x+5=16+x$ should be divisible by $3.$

$\therefore x$ can be $2,5$ or $8,$

Hence, $xy$ can be $20,50$ or $80.$
And, the numbers are $4720,4750$ or $4780.$