This question may trip you up if you are not in the habit of reading the sentence completely.
The entry point to this question is in the non-underlined portion – there is already a ‘which supported’ towards the end of the sentence.
All you need now is an option that exhibits parallelism.
(A) In the 1980s the federal government was the largest single provider of day care for children,
offering
(B) The federal government was the largest single provider of day care for children in the 1980s,
which offered(C) In the 1980s the federal government was the largest single provider of day care for children
and offered(D) The largest single provider of day care for children in the 1980s was the federal government,
offering(E) In the 1980s the largest single provider of day care for children was the federal government,
which offeredGo ahead and
eliminate Options A, C, and D. Now the choice is between B and E.
Option B says - The federal government was the largest single provider of day care for children in the 1980s, which offered
On the GMAT, ‘which’ follows the proximity rule – it modifies the most eligible noun that comes before it. This does not happen with Option B.
Eliminate. Option E is the best choice. Hope this helps!