Ahmed, Farida, Tala, and Yousef are debating how to measure Summer Oly

Official Explanation

1. Suppose that another person, Aisha, asserts that weighted totals, calculated according to the method indicated in the Graph tab, should provide the sole criterion of Olympic achievement. For each of the following participants in the Discussion, select Compatible if the participant’s stated recommendation is compatible with Aisha’s measure of Olympic success. Otherwise, select Incompatible.

RO1

Ahmed believes that Olympic success should be measured by a simple count of all medals won by a country. Aisha’s method weights the medals according to type (gold, silver, or bronze) rather than simply counting them, so Ahmed’s method is not compatible with hers.

The correct answer is Incompatible.

RO2

Farida believes that to be fair, a measure of Olympic success must in some way include consideration of a country’s population. Since Aisha’s method includes no mention of population, Farida’s method is incompatible with hers.

The correct answer is Incompatible.

RO3

Yousef wants to count each silver medal as half a gold, and each bronze medal as half a silver. Aisha’s method assigns 4 points for each gold, 2 points for each silver, and 1 point for each bronze, which satisfies and is therefore compatible with Yousef’s criteria.

The correct answer is Compatible.

2. For each of the following measures of Olympic achievement by countries, select Yes if the information given clearly indicates that 1 of the 6 countries discussed received a higher ranking than the other 5 by that measure in the year indicated, and which country this is. Otherwise, select No.

RO1

The graph provides Olympic medal information for 2004 but in total number of points, not total number of medals, where a gold medal is worth 4 points, a silver is worth 2 points, and a bronze is worth 1 point. Thus, several different total numbers of medals could yield the same point value. For example, the graph shows that Country C won 61 points in 2004. This number could be won by earning 61 bronze medals, 1 bronze medal plus 30 silver medals, 1 bronze medal plus 15 gold medals, or other combinations. There is not enough information to determine the total medal count of any country in 2004, nor which country won more total medals than any other country that year.

The correct answer is No.

RO2

Yousef wants to count each silver medal as half a gold, and each bronze medal as half a silver. In other words, a gold medal is one weighted medal, a silver is a weighted medal, and a bronze is a weighted medal. The ranking method described in the Graph tab assigns points in the same proportions as Yousef’s method: 4 points for each gold, half that amount (2 points) for each silver, and half again (1 point) for each bronze. One of Yousef’s weighted medals is therefore equivalent to 4 points on the graph—the value of one gold medal.

The graph shows that in 2008 Country C had more weighted medals (41÷4=10.25) than did Country D (16÷4=4) or Country H (24÷4=6). Furthermore, the information provided indicates that Countries B, E, and G have point totals lower than Country D in every year. Thus, the graph indicates that Country C had more weighted medals in 2008 than did any of the other five countries.

The correct answer is Yes.

RO3

As explained in the analysis of RO2, four points on the graph is equivalent to one weighted medal. Thus, in 2012 Country H had more weighted medals (44÷4=11) than did Country C (32÷4=8) or Country D (19÷4=4.75). Since Countries B, E, and G have point totals lower than Country D, Country H had more weighted medals in 2012 than did any of the other five countries.

The correct answer is Yes.

3. Suppose that the participants in the Discussion are aware of the information given in the table and the graph. Which of the following statements about the relative achievement in the 2008 Summer Olympics of the six countries referred to in the table and graph is most clearly supported?

Ahmed wants to rank countries by a simple count of all medals won. According to the Table, in 2008 Country C ranked first in total medals, so Ahmed would agree that Country C had the greatest achievement (A). Farida believes that a fair measure of Olympic achievement must in some way include consideration of a country’s population. Thus, she would accept only the per capita measurements on the Table tab. Although the table shows that Country B had the most gold medals per capita in 2008, it ranked last among the six countries for total medals per capita. Thus, it is not clear that Farida would agree that Country B had the greatest achievement (excluding B). Tala desires to count only gold medals. The Table shows that in 2008 Countries G and H tied for the most number of gold medals; therefore, Tala would not agree that Country E had the greatest achievement (excluding C). Yousef wants to weight countries’ medals, counting each silver medal as half a gold, and each bronze medal as half a silver. But it is unclear from the discussion whether Yousef would calculate these weightings per capita, which the table clearly indicates would put Country C second to County E in the rankings (excluding D). The language introducing the graph clearly indicates that under the weighted point system, which Yousef favors, Countries B, G, and E each had lower point totals than Country D (excluding E).

The correct answer is Ahmed would agree that Country C had the greatest achievement.