Question

How many three digit would you find,which when divide by 3,4,5,6,7 leave the remiander 1,2,3,4 and 5 respectively?

Answer 1

let the no be x
 
now ATQ

x = 2q + 1 ..........................................................................eq.1
x = 3q + 2...........................................................................eq.2
x =  4q +  3 and so on until 7q +5
 from eq1 and 2 
equating  the values of x 

we get q = -1
and x = -1 for all values.