[A]bout

[Odessa Dawn]

[A]bout 4,000 individuals die each year while in the queue to get a kidney. Kidney exchanges, introduced in 2005, and other efforts to greatly reduce the waiting time have produced little overall benefit. In fact, the average waiting time rose from 4 years in 2005 to the 6 years wait at present.
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Why was A in the underlined part enclosed in a bracket?

[HanibalII]

[A]bout 4,000 individuals die each year while in the queue to get a kidney. Kidney exchanges, introduced in 2005, and other efforts to greatly reduce the waiting time have produced little overall benefit. In fact, the average waiting time rose from 4 years in 2005 to the 6 years wait at present.
More: What Money Can

Why was A in the underlined part enclosed in a bracket?

I've never actually seen it before, and it made me curious. I've seen reporters do it with a whole word before, usually when they've quoted a fragment of a sentence. I did some googling and came across this explanation.

Because in the original text, that word was the first letter of its sentence and had to be capitalized, but when it is quoted they change the capitalization to fit its place in the new sentence.

Why do people sometimes put a bracket [ ] in the first letter of the first word ...

[BobK]

[A]bout 4,000 individuals die each year while in the queue to get a kidney. Kidney exchanges, introduced in 2005, and other efforts to greatly reduce the waiting time have produced little overall benefit. In fact, the average waiting time rose from 4 years in 2005 to the 6 years wait at present.
More: What Money Can

Why was A in the underlined part enclosed in a bracket?

Lazy editing. The 'journalist' got (cut & pasted) his/her information from another source, in which the 'a' wasn't capitalized. S/he should have got rid of the "[]", or (better still) credited the author and used quotation marks.

b

[Tdol]

Because in the original text, that word was the first letter of its sentence and had to be capitalized, but when it is quoted they change the capitalization to fit its place in the new sentence.

What you're quoting doesn't make much sense to me- if it's the first letter and you're quoting it as the first letter, then it's still a capital letter- there's no change and no need for the square brackets. If it's not the beginning of a sentence and you're making it the beginning, then it works better IMO.