Amber book PA planning question
This is an Amber book question that was not clearly explained, so if anyone could help solve this that will be highly appreciated. If this kind of question ever appears on the exam, is there a quick way to approach it?

This one super stumped me as well! I think it could have been worded better; I also believe this is an attempt at throwing every areabased programming concept into one problem, which is much more difficult than a typical exam question. I interpreted the parking requirement as each unit needs 2 spaces directly adjacent to the townhouse, whereas the answer indicated that the townhouses can be clustered with a separate parking area.

I did all the math to subtract area of setbacks, streets, etc., then divided what was left by the area of a townhouse plus required yards plus two parking spots to get the number of townhouses that would fit on the available buildable area.....but didn't get the correct answer either haha. I think the best way is to just lay out all the required items on the site allowing for setbacks in a way that makes sense but that takes a little longer then the planned 2ish minutes spent per question.

Augustus  I would approach this similarly to how you did, but I'd consider the frontage, not the area. Questions like this require a good deal of site planning practice to identify the limiting factor so that you can solve this quickly  I think the limiting factor here will be frontage.
The site is 200' deep (ignore the throughlot portion for now, consider it as two separate 200' deep lots). The townhouses need a 30' front setback, will be 32' long, and require a 20' fenced rear yard, therefore each townhouse will be on an 82' deep lot. Since each townhouse requires two parking spaces, we can fit those directly behind each townhouse lot, with a drive aisle going along the rear. Parking spaces are 18' deep and we need a 24' deep drive aisle, so these easily fit in the remainder of space behind the townhouse lots (200'  82' = 118'). Since townhouses themselves are 20' wide and the spaces are 9' wide, we can easily fit two next to each other behind the townhouses.
Now that we've determined that depth isn't an issue here, let's move on to frontage.
The site has 640 feet of frontage but you need to consider each separately for division purposes. There are some required side yards which I'm going to assume can overlap with the required side yards at the townhouses themselves, but that really should be clarified in the question.
OK  townhouses are 20' wide and require two side yards of 12' each. This is again a little confusing in the question  it's unclear if two adjacent townhouses need to be 12' apart or 24' apart, but let's assume each townhouse lot has two side yards, so the total lot width is 20' + 12' + 12' = 44'.
Divide that lot width by the two frontages and round down  you can't fit a fractional lot.
Day Avenue: 160' / 44' = 3.63, so 3 lots. Since 28' will be left over, put the 24' wide drive aisle in that space.
Also, remember those 15' required setbacks at adjacent lot lines? Let's make sure those work out. The Day Ave frontage would actually be 15' side yard, 20' townhouse, 24' space, 20' townhouse, 24' space, 20' townhouse, 12' space, 24' drive aisle (with one extra foot to spare!).
Elm Street: 480' / 44' = 10.90 lots, so 10 lots. We can easily account for the extra 3' of side yards on the ends to comply with the 15' side yard requirement here.
So, 10 lots on Elm and 3 on Day is 13 total lots. Not sure if that's the correct answer given because of the couple of assumptions that I made, but that's the type of math you can do on a question like this to solve it.
I agree that there are a bit too many variables here for an ARE question  this is more akin to the vignettes that were part of ARE 4.0.
Chris Hopstock RA
Black Spectacles
ARE Community 
If I saw this question on the ARE, I'd skip it. I'd advise anyone to skip lengthy complicated questions that could easily have MANY correct solutions. This question could easy take 20 minutes to 2 hrs to a full day to a full week.
Not sure where this came from, but if it hasn't been vetted, that's concerning.
Rebekka O'Melia, R.A., NCARB, B. Arch, M. Ed, NOMA, Step UP ARE 5.0 Courses
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