TOLC-med 2008 logical reasoning

The floor of a rectangular room, with sides of 4 and 6 meters respectively, was covered with tiles similar in shape to the rectangle of the floor. The cost of each tile was €4 and that of all the tiles €1,600.
What are the dimensions of each tile?
A) 12cm and 18cm
B) 18cm and 27cm
C) 25cm and 50cm
D) 10cm and 15cm
E) 20cm and 30cm

the answer is E)
can anyone solve this question with a faster method?

this is my work:
1600/4=400 tiles and 400 * 600 = 240000 cm²
240000=400(x * y)
i then used the values from the possible solutions as x and y
i tested every single possible option
for option E) 400(20 * 30) = 240000