There's a really good explanation for this question here:
http://www.beatthegmat.com/gmat-prep-ga ... 34256.html

It's funny, because I've done this sentence more than 5 times, and each time I'm just as hesitant. The link above is probably the most thorough explanation I have read for this particular sentence.

Answer: A


(A) Galileo did not invent the telescope, but on hearing, in 1609, that such an optical instrument had been made, he quickly built his own device...

A is made up of two independent clauses interlinked by "BUT"
(1) Galileo did not invent the telescope
(2) On hearing that such an optical instrument had been made, he quickly built his own device.

The verb tenses are also parallel in the two interlinked independent clauses:
(1) did not invent (simple past)
(2) built (simple past)

The verb on the "that such an optical instrument had been made" is also correct because it uses "had been made" to emphasize that this is a past event before another past event "built"

"on hearing that such..." also correctly modifies the subject "he"

Why the other sentences are wrong?

1. (B) and (E) are out!

Notice the split up of the 5 sentences on the verb usage: (B) "having been made", (E) "being made", and
(A,C,D) "had been made". The making of the telescope happened in 1609 so this calls for a past tense. Hence, B and E are out.


2. (C) is also out!

SENTENCE: Galileo, even though he had not invented the telescope, on hearing, in 1609 that such an optical instrument had been made, he

Let's re-arrange. Even though he had not invented the telescope, Galileo on hearing in 1609 that such an optical instrument had been made, he built...

The only clause with the verb is "even though he had not, ... , he built..." What's wrong with this? "Galileo on hearing in 1609..." is a sentence fragment between a dependent clause and an independent clause. This is a distorted structure.

3. (D) is also wrong.

Even though..., on hearing that such ..., [HE] quickly built...

Let's say "Even though ..., on hearing, in 1609 that such ..." is the dependent clause. There should be an independent clause. But "quickly built..." has no subject "he"