Question

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

Answer 1

Let p, q, r, s, t , u and v be some positive integers.

N = 2 p + 1  = 3 q + 2  = 4 r + 3   = 5 s + 4 = 6 t + 5  = 7 u + 6 = 8 v + 7
    = 2 (p+1) - 1 =   3 (q+1) - 1 =   4 (r+1) - 1    =  5(s+1) - 1   .....

Thus    N+1 is divisible by 2, 3, 4, 5, 6, 7 and 8.  

LCM of these num. = 2*3*2*5*7*2 = 840

N+1 = 840 * k          where   k = a positive integer.

For  k = 2 ,   N = 1679        that lies between 1000 and 2000.

Answer 2

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