Additionally, I was always under the assumption that "two times the number" and "twice as many" were two separate idioms. I thought that "twice the number" was unidiomatic. I'm guessing that my assumption is wrong there as well since the OA uses it.
there's nothing wrong with "twice ____", as long as "____" is some sort of numerical quantity.
twice the price/amount/extent/duration/quantity/number/average/rate/etc.
the
last two choices, however, are problematic, because "twice as many trucks" must mean exactly that--i.e., twice
as many trucks. as in, 2 • (previous # of trucks).
this sentence contains no information about the previous number of trucks; there's only a combined figure for trucks and cars. so, that doesn't work.
"
that number", by contrast, refers to the number actually cited, regardless of what it's originally counting.
e.g.,
Ray has four children and twice that number of suits --> ray has 4 kids and 8 suits.