LittleFuss,
One man's food is another man's poison. What you like, I might not, and vice versa.
Maths is quite like that. However, the GMAC thinks that anyone who needs to be an MBA needs to be good in "some type of maths", and there you are - stuck with Maths in GMAT.
I am not very good at Maths myself, though I've had an engineering background - replete with transforms, partial differential equations, multiple integration, bessel functions and the likes. None of them make or break you - they're just out of scope
Let me answer some specifics that you asked
littlefauss
Is it necessary to understand Partial Differential Equations and Abstract Algebra before you can understand the GMAT quant?
Absolutely not. In fact, leave alone partial differential equations, they don't even require you to calculate a maxima or a minima by differentiating !!
If you don't trust me, spend the next couple of days reading the posts here and you'd know the kind of questions posted here (and I assume, that they'd be very representative of the actual GMAT questions).
littlefauss
Or is it just a matter of mastering some basic stats and probability principles that my wife may have overlooked? She only taught one course in it, she took only one stats course in grad (she focused on pure rather than applied math) and she never took a stats class in UG.
Most likely she overlooked. But its also possible that she never focussed on the trivial applications. If you're a fighter aircraft pilot, it doesn't automatically make you able to ride a bicycle
littlefauss
Either burst my bubble or comfort me, but don't leave me hanging!
I'd say if you can calculate easily that how much you would pay if you're buying a pound of broccoli and half pound of tomatoes, when broccoli costs thrice as much as tomatoes, and tomatoes cost 99c/lb, you'd do well in Maths!!.
[Try it - honestly its not at all as complex as it sounds - if all all it sounds complex]
Welcome to the club and hope this helps