Official Explanation
Using common sense, you would guess that this statement is incorrect—surely New York is more densely populated than that—but you should not evaluate it that way. Rather, evaluate it using mathematics. The key here is that the population figures are given in millions of people, while the area figures are given in thousands of square miles. Thus, in order to find a state’s exact population, you should multiply the given figure by 1,000,000, and in order to find its area, you should multiply the given figure by 1000. So, New York’s population per square mile is:
\(\frac{19.5*1,000,000}{54.6*1000}=0.357*1000=357\)
The correct answer is No.
You did not have to re-sort the table for Question 1, but you should re-sort it by “Population: Rank” for Question 2. There are 18 listed states in total, so the median population among them will be the average of the populations of the two states that are 9th and 10th among the listed states (not ranked 9th and 10th among all U.S. states). These are Washington and Arizona, which have populations of 6.8 million and 6.5 million, respectively. Thus, the median population among the listed states is 6.65 million, not 6.5 million. (Note that, if all 30 states with the highest population were given, then the median population would have been the average of the populations of the 15th and 16th states. Since some states are missing, however, don’t worry about what the population of the 15th-most populous state may be, but rather just work with what you are given.)
The correct answer is No.
Re-sort the table by “Area: U.S. Rank.” Oklahoma, which is the 20th-largest state in the country, is the largest of the listed states whose area is less than 70,000 square miles. You might think, then, that since only from the 20th state down does size get smaller than 70,000 square miles, that fewer than half of the top 30 states are smaller than 70,000 square miles in size. Once again, however, that’s not what the question is asking! You’re only interested in the states that appear in the table, and among them 10 have an area less than 70,000 square miles, while only 8 have an area greater than 70,000 square miles. Thus, the statement is correct. Note the importance of reading the data and the statements carefully. Had you re- sorted by all four categories, you would have wasted some time. You needed to re- sort only by Population: Rank and Area: U.S. Rank.
The correct answer is Yes