How can I shorten this python code?

Instead of ((a*10+c)*10)+d we can use ((a*2+c)*2)+d to distinguish the colors.

 r=((a*2+c)*2)+d
 if r==0:e="black"
 elif r==4:e="red"
 elif r==1:e="blue"
 elif r==2:e="green"
 elif r==5:e="magenta"
 elif r==3:e="cyan"
 elif r==6:e="yellow"
 else:e="white"

Ah, but now we're just distinguishing between values from 0 to 7, so we can index into an array instead!

 r=a*4+c*2+d
 e=["black","blue","green","cyan","red","magenta","yellow","white"][r]
 # or even shorter:
 e="black blue green cyan red magenta yellow white".split()[r]

Combining with Uriel's changes we get down to 136 bytes (164 bytes saved).

exec'x,r,g,b=map(int,raw_input().split());print"black blue green cyan red magenta yellow white".split()[x/r%2*4+x/g%2*2+x/b%2];'*input()

Try it online!

For the repetition use an exec statement,

map(int, for the conversion of string input into numerals,

shorten calculating r with r=a*100+c*10+d, then put the calculations of each variable (a, c, d) instead of the variable,

and for the conditions use a dictionary with a get query.

Finally, mash everything into one line.

Final result (updating):

exec'x,r,g,b=map(int,raw_input().split());print({0:"black",100:"red",1:"blue",10:"green",101:"magenta",11:"cyan",110:"yellow"}.get((x/r%2)*100+(x/g%2)*10+x/b%2,"white"));'*input()

Bytes saved: 121.