Question

A number lying between $1000$ and $2000$ is such that on division by $2,3,4,5,6,7$ and $8$ leaves remainders $1,2,3,4,5,6$ and $7$, respectively. What is the number?

• A. $1679$
• B. $1579$
• C. $1779$
• D. $1879$

Answer 1

The correct option is A $1679$

The difference between the divisors and the corresponding remainders is 1
$(2-1=3-2=4-3=5-4=6-5=7-6=8-7=1)$
$\therefore$ LCM of $2,3,4,5,6,7$ and $8$$=2\times 2\times 3\times 5\times 7\times 2=840$
$\therefore$ Required number $=840K-1$
Since the number lies between $1000$ and $2000$, $K=2$.

The number $=840\times 2-1=1679$