The following graph is a training log for a triathlete. It documents the number of hours she trained each week at each of three disciplines over a four week period.

0.7
5.1
36.4
44.6
161.0

Solution

Remember that Rate = Distance / Time. Since you are solving for distance, rearrange to get Distance = Rate × Time. In this case Rate = 7 miles per hour, and from the graph,Time = 5.2 hours. 7 × 5.2 = 36.4.

The following graph is a training log for a triathlete. It documents the number of hours she trained each week at each of three disciplines over a four week period.

The athlete aims to spend between 12 and 16 percent of her weekly training time swimming. For which of the weeks does her swimming fall within that range?

Solution

To determine the percent of training time dedicated to swimming, divide the time spent swimming by the total training time and multiply by 100. For example, in week 1, the athlete swims 2.1 hours and trains a total of 14.7 hours, so she spent a little over 14% of her training time swimming. Week 2, swimming represents about 19%; week 3, 20%; and week 4, 23%. Week 1 is the only week for which swimming represents between 12 and 16% of total training time, so choice (A) is the correct answer.

The following graph is a training log for a triathlete. It documents the number of hours she trained each week at each of three disciplines over a four week period.

Which of the following fall within the range of ratios of hours spent biking to hours spent swimming per week in this four week period?

Indicate all possible values.

Solution

C, D

You could calculate the ratio for each week and determine the range from the most extreme values. Alternatively, you might notice that hours biked remain relatively constant while hours swam increase, so weeks 1 and 4 will represent the ends of the ratio. In week 1, she biked about 7.8 hours and swam about 2.1, which, dividing 7.8 by 2.1, reduces to a ratio of ~3.7:1. In week four she biked about 8.5 hours and swam about 4.5 hours, which reduces to a ratio of ~ 1.9:1.The range of ratios, from 1.9:1 to 3.7:1, includes 2:1 and 3:1, but none of the others.The ratio 3:2 can be rewritten as 1.5:1, and then it’s easy to see that doesn’t fall within that range.

To the nearest percent, what was the percentage increase for the country that experienced the greatest percent increase in number of departures between 1990 and 2001 ?

Solution

285

By inspecting the departures for all the countries in the table,China by far has the greatest increase in percentage of total number of departures. While no other country has even doubled its departure percentage,China has nearly quadrupled its percentage. Once you notice that, you need to remember the percentage change formula:

$\frac{X_{present}-X_{past}}{X_{past}}$

Then you can just plug in 2.0 for X_past and 7.7 for X_present and find the correct answer: 285

The population of the U.S. grew by 29% between 1979 and 2004, during which time per capita energy consumption doubled. If average per capita energy used from coal was 25 MBTUs in 1979, which of the following are in the range of per capita energy, measured in MBTUs, provided by a single fossil fuel (coal, natural gas or oil) in 2004 ?

Indicate all possible values.

Solution

C, D, and E

Ignore the population growth:The question is asked in per capita terms, so it’s asking about the population as a whole.Coal production was 25 in 1979, when, according to the graph, coal represented 27% of energy; since 25 is 27% of 92.6, the total energy was 92.6 in 1979, and double that, or 185.2, in 2004.The lower end of the range is oil, at about 17%, and 17% of 185.2 is about 31.5; the upper end of the range is coal, at about 34%, or about 63.Choices (C), (D), and (E) fall within the range.

Shinmark spends ¹⁄₂ of its GDP on military expenditures, while Pluton spends of ¹⁄₄ its GDP on military expenditures. For which years does Shinmark’s military spending exceed Pluton’s?

Indicate all possible values.

Solution

A,B,C,E, and F

You could calculate and compare ¹⁄₂ of Shinmark’s GDP to ¹⁄₄ of Pluton’s for each year. Alternatively, multiply both of the fractions by 4 to make the numbers easier to deal with; compare twice Shinmark’s GDP to all of Pluton’s. Looking at the graph, the only year that twice Shinmark’s GDP isn’t greater than Pluton’s is 2009, so for all the other years, Shinmark’s military spending exceeds Pluton’s.

In which year was the change from the prior year of the combined GDP of the two countries the least?

Solution

2010

The question asks you to sum the two countries’ GDPs for each year and determine the year in which the change from the year prior was the least.Rather than determining the GDP for each country for each year and adding and subtracting, glance at the graph and see if any years stand out as having significantly less increase than the others. In 2010, Pluton’s GDP shrank by about $1.5 billion and Shinmark’s grew by $0.5 billion, for a net decrease of about $1 billion. In no other year was there a combined decrease, so 2010 must be the correct answer.

Approximately what was the percentage growth of Pluton’s GDP from 2010 to 2011 ?

4%
15%
25%
40%
115%

Solution

Remember the percent change formula:

$\frac{X_{present}-X_{past}}{X_{past}}$

All the values are in billions, so you can ignore all the zeroes and just use the smaller numbers from the graph. In this case,X_past is Pluton’s 2010 GDP, or about 24.5,and X_present is Pluton’s 2011 GDP, or about 28.2. Plug those into the percent change formula and use your on-screen calculator to get an answer of 15.1%, making choice (B) the best answer.

How many maple trees had a diameter greater than 49.4 cm?

Solution

8

On each side of the mean, 34% of individuals fall within one, 14% of individuals fall within two, and 2% of individuals fall within three standard deviations. 49.4 cm is exactly one standard deviation above the mean maple tree diameter.Therefore, 16% of the maple trees will have a larger diameter larger than 49.4. 16% × 50 trees = 8 trees.

Golf equipment manufacturing in the United States experienced the same percent growth rate from 2001 to 2008 as it did from 1994 to 2001. If the share of golf supplies production made up of bags, balls and training aids each increased anywhere from 1% to 5% from 2001 to 2008, which of the following could be the sum of the value of bags, balls and training aids produced in the United States in 2008, in millions of dollars?

Indicate all possible values.

1,550
1,627
1,855
2,197
2,339

Solution

C, D

First, find the total U.S. production of golf goods in 2008.Calculate the percent change from 1994 to 2001 using the percent change formula:

$\frac{X_{present}-X_{past}}{X_{past}}$

with values of 3,770 for X_present and 2,691 for X_past. The percent change from 1994 to 2001 was 40.1%. Multiply the 2001 value by 40.1% and add that to the original value to find the 2008 production value of 5,282. Next, figure out the percentage of 2008 production that could be from balls, bags and training aids. In 2001, those three categories together made up 17% + 7% + 4% = 28% of production. If each category’s share of total production increased between 1% and 5%, the minimum the three categories together could have grown is 3%, and the maximum they could have grown is 15%. So, the minimum percent of production they represent in 2008 is 28% + 3% = 31%, and the maximum is 28% + 15% = 43%. The minimum production value they represent then is 31% × 5,282 = 1,637, and the maximum is 43% × 5282 = 2,271.Correct choices (C) and (D) are the only answers that fall in that range.

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