A number when divided by 7, 11 and 13 (the prime factor of 1001) successively leaves the remainder 6, 10 and 12 respectively. Find the remainder if the number is divided by 1001.

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900

1000

1200

1500

answer is B.

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Detailed Solution

Concept-Here we need to find the remainder using the basic concept of division. So first we need to find the numbers that are divisible by the numbers 7, 11 and 13 and omit the remainder. Divide this number by 1001 to get the remainder.
L.C.M. of 7, 11 and 13 =1001
So, the required no. can be 1001 - 1 = 1000
or 2002 - 1 = 2001 and so on
∴ The remainder when it is divided by 1001 is always = 1000
Hence, the correct option is 2.

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