I am studying the Surveyor Reference Manual (7th edition), and there is a practice problem that says "State whether single proportionate measure (S), single proportionate measure on a latitudinal (curved east-west) line (SC), or double proportionate measure (D) is used in restoring the following corners (assume none of the township boundaries are standard parallels).
1) northeast corner of sec 10
2) northeast corner of sec 12
3) south quarter-section corner of sec 12
4) southeast corner of sec 36
5) southwest corner of sec 36
Given answers: 1) D 2) S 3) S 4) D 5) SC
Am I thinking about this wrong or are a few of these answers incorrect?
They are all incorrect, you put them at the fence corner.
But I figure that's not what they want, it's difficult to read a test maker and I will guess your answers are correct, with the caveat that technically 3 should be SC, yet practically it's normally done as S. I was recently at a seminar and the presenter said S for #3, there wasn't any pushback. If I find a monument prorated at 3 either way I will accept it.
If I'm remembering right you only do the latitudinal proportion on standard parallels and since, according to the description, none of the township boundaries are on a standard parallel you won't use SC at all.