I think this is one of the problems where doing algebra may be quite painful. Just understanding the problem and coming up with the algebraic expressions would consume more than 2 minutes.
So, what I did was to understand the problem and then get the numbers of posts in each side by applying trial and error
Since I knew one side had the double number of posts than the other side (including the corners), I started trying the next couple of numbers
2 and 4 --> I thought about this one, but I didn't even try it because clearly they don't add up 20
3 and 6 --> This would make 6*2+3*2-4=14 (I deducted 4 because the two first terms of the expression are counting the 4 corners twice so I need to deduct all the corners once --- This is similar to what we do in combinations problems!!)
4 and 8 --> This would make 4*2+8*2-4=20 BINGO!
So i know that short sides have 4 posts (including the corners) and long sides have 8 posts (including the corners)
Note that to calculate the total distance of a side in "questions of fences" when we know the spearation of each fence is always the same thing.
Distance always equals the distance between each post * number of posts (including the corners)-1 (this -1 is because we have always one space less than number of posts. i.e, 3 posts would be 2 spaces, 5 posts would be 4 spaces)
Lenght of short side (4-1)*4=12
Lenght of long side (8-1)*4=28
Area=12*28=280+2*28 ≈330 (Note I don't calculate the full multiplcation. Instead I approximate since answers are well spread out)
OPTION BTakeaways:
(1) In foreseen complex algrebaric expressions, don't even try to come up with them. Choosing 3 groups of numbers in this kind of questions is much faster than coming up with the equations, solving them and still be sure that you got the right numbers
(2) Don't calculate final numbers (even when the multiplications is not so difficult) if you can approximate and save 2 seconds (every second counts!). In these questions if answer choices would have been 333, 334, 335, 336 and 337. Ok, fair enough, do the whole multiplication, but in all quant questions you should spend 2 sec in looking at the answer choices (after reading the question) to decide if they are sufficiently spread out and therefore to eventually do an approximation when you have come up with the equation that gives the final result
Remember all the takeaways that you get from all the quant questions and don't forget to apply them whenever it's possible so you can get used to them and apply them automatically in the exam day
Please hit the Kudos button if you liked my approach and reflection