# Find how many 3 digits numbers satisfy all the following conditionsif it is divided by 2, the remainder is 1,if it is divided by 3, the remainder is 2,if it is divided by 4, the remainder is 3,if it is divided by 5, the remainder is 4,if it is divided by 8, the remainder is 7,

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by bhavyag

2014-10-10T17:19:01+05:30

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Let the number N satisfy the conditions.
Let x, y, z, w, v be some integers.

N can be written as 2 x + 1 or  2 x - 1.  so let us write N as

N = 2 x - 1
N = 3 y - 1            or   3 x' + 2      where x' = y -1
N = 4 z - 1           or    4 z' + 3     where z' = z - 1
N = 5 w - 1          or    5 w' + 4
N = 8 v - 1          or    8 v' + 7

So N + 1 = 2 x = 3 y = 4 z = 5 w = 8 v

N+1 is a multiple of 2,3,4,5, and 8

N+1 is a multiple of  lcm of them.

LCM  =  2*3*2*5*2 = 120

Three digit multiples of 120 are 120, 240, 360, 480, 600, 720, 840, 960

N = 119, 239, 359, 479, 599 , 719, 839, 959

There are eight of them.