Hello!
I think the best way to understand which answer makes the most sense is to replace the word "it" with what that word is referring to - the age of thirty. So let's write out each answer after we make this quick change, and see what we have:
A. According to public health officials, in 1998 Massachusetts became the first state in which more babies were born to women over the age of thirty than under the age of thirty.
This one is the best answer because it's clear we're comparing women over 30 to women under 30, rather than comparing the babies being born to women over/under 30. It also uses parallel structure, which makes this easier to understand.
B. According to public health officials, in 1998 Massachusetts became the first state in which more babies were born to women over the age of thirty than born under the age of thirty.
This one is wrong because it oddly suggests the babies were born under the age of 30, which is true, but not really the point. It leaves out who gave birth to the babies! It would have been okay to say "...than born to women under the age of thirty," which makes it clearer who is doing the birthing!
C. According to public health officials, in 1998 Massachusetts became the first state in which more babies were born to women over the age of thirty than they were under the age of thirty.
This one doesn't really make sense when you read it out loud. It kind of suggests that in Massachusetts, there were more women over the age of 30 than under the age of 30, which is not what we're talking about - we're talking about the number of babies being born, not mothers who existed at the time.
D. According to public health officials, in 1998 Massachusetts became the first state in which more babies were born to women over the age of thirty than there had been under the age of thirty.
Again, this answer is trying to compare how many women existed at the time who were over/under the age of 30, and not comparing the number of babies being born to each group. It also just sounds overly wordy and awkward.
E. According to public health officials, in 1998 Massachusetts became the first state in which more babies were born to women over the age of thirty than had been born under the age of thirty.
E has the same problem as B - it suggests the babies were born under the age of 30, not that the women who gave birth to them were! It would have been fine if they added in the women to the phrase and said something like "...than had been born to women under the age of thirty."
For the most part, this questions has to do with using parallel structure - and what goes wrong with meaning if we don't use parallel structure. I hope this explanation helps clear things up, and gives you a better idea of how to answer questions like this in the future!
I'm available if you'd like any follow up.