m/n= 1/3 + 1/1999 + 1/5 + 1/1997 + 1/17 + 1/1985 + 1/19 + 1/1983 + 1/23 + 1/1979

 

m/n = 1999+3/3*1999 + 1997+5/5*1997 + 1985+17/17*1985 + 1983+19/19*1983 + 1979+23/23*1979

 

taking 2002 common

 

m/n = 2002 (1/3*1999 + 1/5*1997   + 1/17*1985 + 1/ 19*1983  + 1/ 23*1979)

 

let  1/3*1999 + 1/5*1997   + 1/17*1985 + 1/ 19*1983  + 1/ 23*1979 = k

 

m/n = 2002*k

 

m/n is divisible by 2002. This is how we can approach this problem. But k may

 

or may not be an integer  so we cant say surely wether it is divisible by 2002 or

 

not.Since you have given two options i ll assume k is a number. so 2002 is right

 

choice.