Question

A number when divided by 7, 11 and 13 (the prime factor of 1001) successively leave the remainders 6, 10and 12 respectively. Find the remainder if the number is divided by 1001.​
A.900
B.1000
C.1200
D.1500

Answer 1

Hint: Here we have to use the basic concept of division to find the remainder. So firstly we have to find the number that is divisible by the numbers 7, 11 and 13 and leave the said remainders. Then after finding that we will divide that number by 1001 then we will get the remainder.

Complete step-by-step answer:
It is given that the number when divided by 7, 11 and 13 (the prime factor of 1001) successively leave the remainders 6, 10and 12 respectively.
Here we have to note that the remainder is 1 less than the actual number i.e. remainder is 6 when the number is divided by 7 or remainder is 10 when the number is divided by 11 or remainder is 12 when the number is divided by 13.
This means that the number must be 1 less than the LCM of the 7, 11 and 13 which is 1001.
Therefore the number must be \[1001 - 1 = 1000\] or the number might be \[2002 - 1 = 2001\] and so on.
So, when we will divide the number by 1001 we will always get 1000 as the remainder.
Hence, 1000 is the remainder if the number is divided by 1001.
So, option B is the correct option.

Note: Here we have to note that the number will not be the multiplicative of 1000 but rather it will be 1 less than the multiplicative of LCM of the number 7, 11 and 13 i.e. 1001.
Remainder is the value of the left over when a number is not exactly divided by the other number. Zero is the remainder when the number is exactly divided by the other number.
 Also we should know how to find the LCM (Least Common Multiple) of the numbers. LCM is the smallest positive integer that is divisible by the numbers.