...or a snarky one? My understanding is that Jews and arabs both trace their descent from Noah through Shem (but I'm simply repeating what I've read, of course-- your mileage may vary). The Ashkenazim are presumably descendents of middle eastern Jews transported to Europe (and around the Mediterranian basin) via Rome. This BEGS for genetic analyses, and naturally that has been attempted:
http://en.wikipedia.org/wiki/Ashkenazi_Jews#Who_is_an_Ashkenazi_Jew.3FA study of haplotypes of the Y chromosome, published in 2000, addressed the paternal origins of Ashkenazi Jews. Hammer et al<8> found that the Y chromosome of most Ashkenazi and Sephardic Jews was of Middle Eastern origin, containing mutations that are also common among Palestinians and other Middle Eastern peoples, but uncommon in the general European population. This suggested that the male ancestors of the Ashkenazi Jews could be traced primarily to the Middle East.
The first research on Ashkenazi maternal ancestry was less conclusive. A 2002 study by Goldstein et al<9> found that "the women's origins cannot be genetically determined", but that "his own speculation" was that "most Jewish communities were formed by unions between Jewish men and local women."
More recent research indicates that a significant portion of Ashkenazi maternal ancestry is also of Middle Eastern origin. A 2006 study by Behar et al<10>, based on haplotype analysis of mitochondrial DNA (mtDNA), suggested that about 40% of the current Ashkenazi population is descended matrilineally from just four women. These four "founder lineages" were "likely from a Hebrew/Levantine mtDNA pool" originating in the Near East in the first and second centuries CE. According to the authors, "The observed global pattern of distribution renders very unlikely the possibility that the four aforementioned founder lineages entered the Ashkenazi mtDNA pool via gene flow from a European host population."
Both the extent and location of the maternal ancestral deme from which the Ashkenazi Jewry arose remain obscure. Here, using complete sequences of the maternally inherited mitochondrial DNA (mtDNA), we show that close to one-half of Ashkenazi Jews, estimated at 8,000,000 people, can be traced back to only four women carrying distinct mtDNAs that are virtually absent in other populations, with the important exception of low frequencies among non-Ashkenazi Jews. We conclude that four founding mtDNAs, likely of Near Eastern ancestry, underwent major expansion(s) in Europe within the past millennium.David Goldstein of Duke University has argued that sample populations in these studies were small and not randomly selected, and that the results may not be statistically significant.