I have a question regarding an LSAT Reasoning question and it drives me crazy
Until recently it was thought that ink used before the sixteenth century did not contain titanium. However, a new type of analysis detected titanium in the ink of the famous Bible printed by Johannes Gutenberg and in that of another fifteenth-century Bible is known as B-36, though not in the ink of any of numerous other fifteenth-century books analyzed. This finding is of great significance, since it not only strongly supports the hypothesis that B-36 was printed by Gutenberg but also shows that the presence of titanium in the ink of the purportedly fifteenth century Vinland Map can no longer be regarded as a reason for doubting the map’s authenticity.
The reasoning in the passage is vulnerable to criticism on the ground that:
(A) The results of the analysis are interpreted as indicating that the use of titanium as an ingredient in fifteenth-century ink both was, and was not, extremely restricted. (B) If the technology that makes it possible to detect titanium in printing ink has only recently become available, it is unlikely that printers or artists in the fifteenth-century would know whether their ink contained titanium or not (C) It is unreasonable to suppose that determination of the date and location of a document’s printing or drawing can be made solely on the basis of the presence or absence of a single element in the ink used in the document (D) Both the B-36 Bible and the Vinland Map are objects that can be appreciated on their own merits whether or not the precise date of their creation or the identity of the person who made them is known. (E) The discovery of titanium in the ink of the Vinland Map must have occurred before titanium was discovered in the ink of the Gutenberg Bible and the B-36 Bible.
Official Answer is:
The author first concludes that the presence of titanium in the ink of the Gutenberg and B- 36 Bibles supports the theory that Gutenberg printed both. Okay, this hinges on titanium’s being a rare ingredient in 15th-century ink and therefore characteristic of Gutenberg. Then the author concludes that the presence of titanium in the ink of the Vinland Map suggests that the map dates from the 15th century. But that conclusion hinges on titanium’s being typical of 15th-century ink. Clearly, both conclusions can’t be true: If titanium was typical of 15th-century ink, then the B-36 Bible could have been printed by anyone.
I don't understand why the author supposedly concluded that the presence of titanium in the ink of the Vinland Map suggests that the map dates from the 15th century and that this conclusion hinges on titanium’s being typical of 15th-century ink, since I don't find that in the text. The following is my reasoning, so please follow it and tell me where my error it:
I am not a native speaker, but my interpretation of the second part of the following sentence:
"This finding is of great significance since it not only strongly supports the hypothesis that B-36 was printed by Gutenberg but also shows that the presence of titanium in the ink of the purportedly fifteenth century Vinland Map can no longer be regarded as a reason for doubting the map’s authenticity.
There was strong evidence that the Vinland Map was from the 15th century, but the fact that it contained titanium was a reason to doubt it, since it was assumed that the probability to find titanium in ink from that century was smaller than the probability that the map was against all evidence from that century.
Meanwhile, numerous books from the 15th century had been analyzed, and they found titanium in at least two. Hence, the fact itself that it contained titanium was no longer a reason to doubt it since now the probability that it was a fake was much smaller than the probability to find titanium in ink from the 15th century
However, since it was still unlikely, it supports the hypothesis that B-36 was printed by Gutenberg
Let's make that clear with an example:
100 bibles from the 15th had been found. It is known that 10% of them had been printed by Gutenberg (G). Hence, the prior probability that a random bible (B-36) was printed by Gutenberg is P(G)=0.1.
Now, let's assume Gutenberg used titanium (Ti) for every second print p(Ti|G) = 0.5 and 30 bibles had been analyzed and titanium had been found in two of the bibles of which one was known to be from Gutenberg. Hence, the estimated probability to find titanium in a random bible is p(Ti)=0.07 +/- error (random sample 30 of 100 bibles of which 1 or more are Gutenberg bibles)
Then, p(G|Ti) = 0.5 * 0.1 / 0.07 = 0.714 +/- error. Accordingly, the finding strongly supports the hypothesis (0.1 -> 0.71).
The other way round, the Vinland Map might contain some special features (e.g. manufacturing techniques ...) which are found on only 0.01% of the maps outside the 15th century while the probability to find titanium in ink was considered to be much smaller: p << 0.01 Hence, this was a valid reason to doubt that it is from the 15th. However, after updating p(Ti) to 0.1 the probability that the Vinland Map was from the 15th century increased to 90% and thereby the fact that the ink contained titanium can no longer be regarded as a reason for doubting the map’s authenticity.
I checked several forums where this question was discussed and almost all people agreed that the official answer is without any doubts correct.
What is my fallacy?