Question

A number lying between $1000$ and $2000$ is such that on division by $2,3,4,5,6,7$ and $8$ leaves remainders $1,2,3,4,5,6and7$ respectively. The number is

• A. $518$
• B. $416$
• C. $364$
• D. $1679$

Answer 1

The correct option is D $1679$

The common difference between the divisors and the respective remainders $=(2-1)=(3-2)=(4-3)=......=(8-7)=1$
LCM of 2, 3, 4, 5, 6, 7 and 8 $=840$
$\therefore Requirednumber=840k-1$
The number lies between 1000 and 2000 so $k=2$
$\therefore Requirednumber=(840\times 2)-1=1680-1=1679$