Official Explanation
Question #1
Which one of the following pieces of information would, on its own, provide the strongest evidence that the given artifact was actually produced on Kaxna?
Evaluate
Options A and C provide information about the date of an artifact’s creation, but not about the location where the artifact was made. A radiocarbon date of 1050 BC for a wooden bowl (option A) implies that the tree from which the bowl was made was harvested during the years 1250–850 BC, the time period of the Kaxna Kingdom; but the bowl need not have been produced on Kaxna. Likewise, if TL dating establishes that a fired-clay artifact was produced during that period (option C), it cannot establish the location where it was made. In contrast, option E provides information about location, but since a statue found near a quarry need not have been made at that quarry, the evidence is not very strong.
Options B and D provide information about artifact element ratios. In option B, IRMS analysis of an artifact made of bones and teeth may reveal similarities between the element ratios of the artifact and the element ratios of similar artifacts known to be created on Kaxna, but additional research would be required to determine whether those element ratios were unique to Kaxna. But, in option D, ICP-MS analysis of a metal artifact reveals element ratios known to be unique to a mine on Kaxna, offering far stronger evidence that the artifact was made on Kaxna. Thus, option D offers the strongest evidence among the options listed.
The correct answer is D.
Question #2
For each of the following combinations of Kaxna artifacts, select Yes if, based on the information provided, the cost of all pertinent techniques described can be shown to be within the museum's first-year Kaxna budget. Otherwise, select No.
RO1: Strategize
According to Techniques, fired-clay statues are analyzed using TL dating and bronze statues are analyzed using ICP-MS. According to Budget, the first-year budget of $7,000 is equal to the cost of 4 TL tests plus 15 radiocarbon tests, or the cost of 40 ICP-MS tests. Budget also notes that, for each test, the museum is charged a fixed price per artifact. Therefore each ICP-MS test costs \(\small \frac{\$7,000}{40}\), or $175, so 10 ICP-MS tests cost $1,750. Since 4 TL tests cost no more than $7,000, the cost of 2 TL tests can be no greater than \(\small \frac{\$7,000}{2}\), or $3,500. Thus the total cost of 2 TL tests and 10 ICP-MS tests is no greater than $3,500 + $175, or $3,675. This is well within the first-year budget of $7,000.
The correct answer is Yes.
RO2: Strategize
According to Techniques, fired-clay statues are analyzed using TL dating and tin implements are analyzed using ICP-MS. As in RO1, each ICP-MS test costs $175 and each TL test costs no greater than \(\small \frac{\$7,000}{4}\), or $1,750, so the cost of 3 TL tests and 5 ICP-MS tests is no greater than 3($1,750) + 5($175), or $6,125, which is again less than $7,000.
The correct answer is Yes.
RO3: Strategize
Techniques stipulates that the fired-clay pots be analyzed by TL dating, while the wooden statues are subjected to radiocarbon dating, requiring a total of 4 TL tests and 20 radiocarbon tests. The entire first-year budget is exactly enough to cover 4 TL tests and 15 radiocarbon tests, so 5 of the required radiocarbon tests cannot be covered under that budget.
The correct answer is No.
Question #3
For each of the following artifacts in the museum’s Kaxna collection, select Yes if, based on the museum’s assumptions, a range of dates for the object’s creation can be obtained using one of the techniques in the manner described. Otherwise, select No.
RO1: Apply
Based on the information in Techniques, the only technique the museum would use on a bronze statue is ICP-MS, which yields information on the ratios of traces of metallic isotopes present but would not provide information about the statue’s age.
The correct answer is No.
RO2: Apply
According to Techniques, TL dating can be used to estimate the time at which the clay was fired to produce the pot. According to the assumptions in Artifacts, the date so obtained is considered accurate to within ±100 years, so TL dating produces a 200-year range of dates for the creation of the pot.
The correct answer is Yes.
RO3: Apply
Since wood is a form of plant matter, radiocarbon dating (Techniques) can be used to estimate the date of death of the tree from which the wooden statue was made. The assumption that radiocarbon dating is accurate to within ±200 years (Artifacts) produces a 400‑year range of dates for the death of the tree. The assumption that the statue was almost certainly created within 2 years of the tree’s death (Artifacts) yields a 400‑year range of dates for the creation of the wooden statue.
The correct answer is Yes.
Question #4
For each of the following results of tests performed on Kaxna artifacts, select Yes if, based on the museum’s assumptions, the result confirms that the artifact was created during the time of the Kaxna Kingdom. Otherwise, select No. Yes No
RO1: Apply
The description of the museum’s practices (described in Techniques and Artifacts) does not specify that IRMS is used as a means of dating. Furthermore, the source material does not establish a connection between specific element ratios and specific time periods, so the results do not decisively link the necklace to the time of the Kaxna Kingdom.
The correct answer is No.
RO2: Apply
Techniques clearly indicates that the museum uses TL dating for fired-clay objects. Based on the museum’s accuracy assumptions (Artifacts), a TL date of 1050 BC dates the firing of the clay to the years 1150–950 BC, which is well within the period of the Kaxna Kingdom: 1250–850 BC, specified in Artifacts.
The correct answer is Yes.
RO3: Apply
According to the description of ICP-MS in Techniques, trace metal ratios in copper artifacts are determined by the location where the sample was obtained. But the information provided does not support the conclusion that particular trace metal ratios are characteristic of a particular time (e.g., the period of the Kaxna Kingdom). Moreover, the description of the museum’s practices (described in Techniques and Artifacts) does not include the use of ICP-MS as a means of dating.
The correct answer is No.
Question #5
For each of the following combinations of Kaxna artifacts, select Yes if, based on the information provided, the cost of all pertinent techniques described can be shown to be within the museum’s first- year Kaxna budget. Otherwise, select No.
RO1: Strategize
According to Techniques, the 2 bone implements should be analyzed using IRMS testing, while the 5 fired-clay cups require TL dating . Since the first-year budget allows for unlimited IRMS testing, TL dating is the potentially limiting expense. The budget of $7,000 is enough to cover 4 TL tests plus 15 radiocarbon tests (Budget). While the museum can clearly cover the cost of 4 TL tests, it is impossible to determine whether they can cover the cost of a fifth test without knowing something about the cost of radiocarbon dating.
The correct answer is No.
RO2: Strategize
Using Techniques once again, analysis of 7 wooden statues requires 7 radiocarbon tests and analysis of 20 metal implements requires 20 ICP-MS tests. Each test has a fixed charge per artifact tested (Budget). Let T, R, and C denote the per-test cost, in dollars, of TL testing, radiocarbon testing, and ICP-MS testing, respectively. Using the pricing scheme given in Budget, 15R + 4T = 7,000. Since 7R must be strictly less than half that amount, it follows that 7R < 3,500. Likewise, since 40C = 7,000 and 20C = \(\small \frac{1}{2}(40C)\), it follows that 20C is exactly equal to 3,500. Thus, 7R + 20C is strictly less than 2(3,500), or 7,000. In other words, the total cost, in dollars, of 7 radiocarbon tests and 20 ICP-MS tests is strictly less than $7,000 and hence within the first-year budget for the Kaxna collection.
The correct answer is Yes.
RO3: Strategize
Based on Techniques, complete analysis of the 15 statues requires 15 IRMS tests (for bone) and 15 radiocarbon tests (for wood). Since the first-year budget allows for unlimited IRMS testing and will cover the cost of 4 TL tests plus 15 radiocarbon tests (Budget), the budget can certainly cover the cost of the 15 radiocarbon tests alone.
The correct answer is Yes.
Question #6
Among the Kaxna artifacts is a wooden box containing both a small fired-clay bead and some river sediment containing clay and plant matter. Based on the museum’s assumptions, which one of the following details about the bead can be determined by applying one of the tests in the manner described?
Techniques indicates that the only test the museum will apply directly to the fired-clay bead is TL dating, which determines a range of dates during which the clay was fired (as detailed in Artifacts). Hence it is possible for the museum to determine a range of dates for the bead’s manufacture (option A). There is no clear relationship between the sediment and plant matter in the box and the location of the bead’s manufacture (options B and C), the time of the bead’s placement in the box (option D), or the source of clay for the bead (option E).
The correct answer is A.
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