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Problem based on remainders 2 (Updated On Tuesday, July 08, 2014)

A number N when divided by 2, 3, 5, 8 and 10 leaves a remainder of 1 in each case. Which of the following could N be?

1. 481    2. 600   3. 119   4. 151    5.221


Answer:

Every number can be represented as - Number = divisor x quotient + remainder.

Let N be the number

N= 2 x quotient1 + 1.(N-1)= 2 x quotient1

N= 3 x quotient2 + 1(N-1)= 3 x quotient2

N= 5 x quotient3 + 1(N-1)= 5 x quotient3

N= 8 x quotient4 + 1(N-1)= 8 x quotient3

N= 10 x quotient5 + 1(N-1)= 10 x quotient4


(N-1) is the multiple of quotient 1,2,3,4.

In fact (N-1) is the common multiple of all the numbers 2,3,5,8,10.


Hence (N-1) can be computed by finding the LCM of 2,3,5,8 and 10.

LCM = 480

N-1=480, N=481

The number can be 481.



 

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