An exam question is driving me crazy.
Find the mistake in the following:
Four years are a long time to spend away from family and friends.
Literally everyone solved it by replacing are with is.
Could it be "a long" to "long"?
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Four years [
are/ is ] a long time to spend away from family and friends.
You have several things happening here:
The main clause is a copular clause.
A subject that is realized by a measure phrase ("Four years").
A predicative complement (PC) that is a singular noun phrase ("a long time . . .").
Copular clauses seem to have their own rules (my personal opinion), and a native English speaker usually has to rely on their ear, especially on matters like this.
For subject-verb agreement, some of the major factors are the context and the speaker's intent (besides the formal number of the subject). Specifically, in your example, the subject noun phrase ("Four years") is plural, and it is a measure phrase. Since your subject is a measure phrase in a copular clause, then, in general, its number can usually be optionally overridden (the singular override). Sometimes the singular override is optional, or strongly preferred, or even obligatory.
But in your case, since the PC is a singular NP ("a long time …"), the singular override is (supposedly) mandatory. Thus,
Here is a related excerpt from a vetted grammar source, the 2002 CGEL, page 504:
18.3 Further overrides and alternations
(a) Measure phrases
We have already noted that plural measure nominals can be respecified as singular for the purposes of agreement and selection within the NP. This carries over to subject-verb agreement, whether or not there is any marker of singular number within the NP:
i. [That ten days we spent in Florida] was fantastic.
ii. [Twenty dollars] seems a ridiculous amount to pay to go to the movies.
iii. [Five miles] is rather more than I want to walk this afternoon.
iv. [Three eggs] is plenty.
This is the opposite of the collective override: here an NP that is formally plural is conceptualized as referring to a single measure (of time, money, distance, or whatever) and accordingly takes a singular verb. The measure override is characteristically found with be or other complex-intransitive verbs (such as seem in [ii]).
In [ii], where the predicative complement is a singular NP, the override is obligatory (*Twenty dollars seem a ridiculous amount to pay); in [iii-iv] it is optional but quite strongly preferred.
Notice that your example (OP's example) is similar in construction to CGEL's [14.ii] example--for it has a singular NP as the PC.
Note: The 2002 CGEL is the 2002 reference grammar by Huddleston and Pullum et al., The Cambridge Grammar of the English Language (CGEL).