First a stolen answer from BTG member: manpsingh87, then thoughts about how you might approach this in a quicker way.
-------START stolen answer
let length of square wooden plaque be x, and length of square brass be y;
as per question, are of brass/area of wooden= 25/39;
hence y^2/x^2-y^2=25/39;
39y^2+25y^2=25x^2
x/y=8/5;
width of wooden strip would be x-y=x-5/8x=3/8x;
if x=8/3, then width=1,
if x=8, width=3;
if x=32/3, width =4;
as all values are possible, hence E
-------END stolen answer
I think this is really a computation trap. That is, the test wants to trap you into doing the above calculation even though you don't need to. How can you solve this faster?
I instead use a mental exercise with extremes to shortcut the process:
Imagine a fixed width wooden border (1" wide, or any other number) around a brass inlay.
If the width of the brass inlay is 0", the ratio of Brass:Wood is [area brass]/[area wood] = [0] / [some number] = 0
If the width of the brass inlay is HUGE", the ratio of Brass:Wood is [area brass]/[area wood] = [HUGE] / [some number] = HUGE
Therefore, the potential ratios range from 0 to huge, for any width of wood. In other words, a strip of any width can be accomodated and the answer is E. The answer is all of the above for any group of positive numbers. It's a trivial solution that takes about 20 seconds for a problem that otherwise looks very complicated.
