Question

The greatest number with four digits which when divided by $3,5,7,9$ leaves the remainders $1,3,5,7$ respectively, is _______.

• A. $9763$
• B. $9673$
• C. $9367$
• D. $9969$

Answer 1

Answer: (A)

$9763$

Since on dividing by $3$ the remainder is $1$, the sum of digits of the number must add upto a number, dividing which by $3$ we get remainder $1$

Since on dividing by $5$ remainder is $3$, unit place digit has to be either $3$ or $8$

Since on dividing by $9$ remainder is $7$, sum of digits should give remainder $7$ when divided by $9$

Only options (A), (B) satisfy these criteria

Since (A) is bigger, we divide it by $7$ and find remainder which turns out to be $5$.