The reason why the first example does not use an article while the two others do is because the first does not refer to a specific amount.
If instead of an unspecific number of minutes you were to say it crashed in ten minutes then you would instead write:
The plane crashed a mere ten minutes after take-off.
On the other hand, if we were to rephrase the other examples so that they do not refer to specific quantities then we could drop the "a":
It cost mere cents. (I changed dollars to cents, because though
grammatically correct either way, cents sounds a lot better in this
context).
The city receives mere percentage points of the parking revenues.
In a sense, you are wrong when you say dollars and 20% are plural nouns. In these usages, they are effectively being treated as if they were singular. The "mere" is not qualifying the items in the set individually as would be the case in the phrase "the boys are hungry", but the set as a whole. It is the 20 dollars as a collective unit that is mere. The case is not that each individual dollar is mere and there simply happens to be 20 of them.
To reveal this fact further, consider the grammatically correct phrase:
He quit his job after a mere 2 day period.
versus
He quit his job after mere days.
and
He quit his job after a mere 2 days.
As you can see both the "a mere 2 day period" and "a mere 2 days" are treated the same way. This is because they are both referring to a 2 day chunk of time. A chunk of time that is taken as a whole and said to be meager.
21mere is starting to look weird now.. – user2397282 – 2018-07-31T14:18:32.750
Sometimes "a mere..." should be used even when there's no specific amount mentioned (e.g. "a mere pittance.") – Daniel – 2018-07-31T16:37:39.913
1@Daniel "a mere pittance" falls in the same category as "a mere dollar". A specific amount is mentioned and that amount is one. Yes, it might not look like it in the case of "pittance" since the word refers to an ambiguous amount of money but that doesn't change the fact that the number of pittances (the actual thing which is described as mere) is indeed one. The same is the case for "a mere pile of sugar". Indeed, we are not told how many grains of sugar make up the pile but that is irrelevant as it is the pile itself that is being qualified, not the sugar grains. – AngelPray – 2018-07-31T16:51:21.123
1@user2397282 If you aren't familiar with the term already, look up "semantic satiation." – John Montgomery – 2018-07-31T17:59:40.853
2Another piece of evidence that "20 dollars" as a value is singular: "20 dollars is a lot to pay." – Joe – 2018-07-31T20:55:22.240
"The reason why the first example does not use an article while the two others do is because the first does not refer to a specific amount." But, sorry, no. That's not the reason. (The redundancies in the sentence are a different matter, though.) – Kris – 2018-08-01T12:39:54.457
This answer is great. I would also add that at least to me the use of the word "mere" without the article 'a' or 'the' can be awkward, uncommon, and somewhat unnatural sounding. "The plane crashed mere minutes after take-off." "He quit his job after mere days." Both sound a little awkward to me. "He bought it for mere pennies" and "I was away from my desk for mere minutes" sound slightly better, but still wouldn't be used commonly in conversation, at least in the US. – Conor Henry – 2018-08-01T02:59:01.423
If 20 dollares is singular, how come you can say it cost some mere 20 dollars ? – Artefacto – 2018-08-01T16:14:38.170