they dont really just measure "logical thinking" at all, that's a myth. at their core IQ tests measure a holistic intuitive mental quality (which is mediated by a plethora of identified physiological neural processes) that, among other things, impacts upon mental processing speeds, the ability to educe relationships and correlations, memorise rapidly and solve problems. IQ tests themselves attempt to capture this quality, but do so imperfectly; as well as measuring this quality, they also measure specific training and broader, but still specific, abilities, such as 'verbal ability' and 'spatial ability', as well as bias/momentary mental states, etc. "cultural bias" as etiology of certain inter-group differences on IQ tests has long been an explanation wanting for substantiation, and has largely not held up to relevant statistical analyses.
no one has really figured out a way to "train" people in the primary quality of IQ tests attempt to measure because that quality is general; training people to solve problems in a specific way reduces the extent to which those problems actually measures the principal component of IQ tests, which dilutes their overall predictive value.
trump's IQ is probably between 115-125, to the extent to which one can guess from facile surface characteristics/background information. not genius level, but not "dumb" either. eggheads have very rarely fared well in american presidential politics anyway (nixon excepted), as hillary clinton found out the hard way.