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Subject Test Math 1

Question 27 of 32

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SAT Subject Test
The figure shows a horizontal bar graph. The graph is titled '2000 Population.' The horizontal axis is labeled 'Population in millions.' The integers 0 to 50, in increments of 10, are indicated on the horizontal axis. The vertical axis is labeled 'Age Group in years,' and there are 9 age groups indicated along the vertical axis. The age groups are 0 to 9, 10 to 19, 20 to 29, 30 to 39, 40 to 49, 50 to 59, 60 to 69, 70 to 79, and the ninth age group is 80 plus. For each age group, there is a horizontal bar associated with it. The length of the bar represents population. The 2000 population for the 9 age groups are as follows. Age group 0 to 9, 39 million. Age group 10 to 19, 40 million.
The figure shows a horizontal bar graph. The graph is titled '2050 Projected Population.' The horizontal axis is labeled 'Population in millions.' The integers 0 to 60, in increments of 10, are indicated on the horizontal axis.  The vertical axis is labeled 'Age Group in years,' and there are 9 age groups indicated along the vertical axis. The age groups are 0 to 9, 10 to 19, 20 to 29, 30 to 39, 40 to 49, 50 to 59, 60 to 69, 70 to 79, and the ninth age group is 80 plus. For each age group, there is a horizontal bar associated with it. The length of the bar represents population.

The graphs above show United States Census Bureau population figures for the year 2000 for various age groups, together with projections for the year 2050. Of the following age groups, for which is the projected percent increase in population from 2000 to 2050 greatest?

Select an Answer

30 minus 39

Correct Answer: 
No

40 minus 49

Correct Answer: 
No

50 minus 59

Correct Answer: 
No

60 minus 69

Correct Answer: 
Yes

70 minus 79

Correct Answer: 
No

The correct answer is D.

To determine for which of the five age groups in the options the projected percent increase in population from 2000 to 2050 is greatest, estimate the ratio of the projection for the year 2050 to the population figure for 2000 for each age group. Each of the ratios described is equal to 1 plus the decimal corresponding to the projected percent increase in population from 2000 to 2050, so the greatest ratio will correspond to the greatest projected percent increase in population.

For the 30 minus 39 age group, the ratio is less than fraction numerator 60 over denominator 40 end fraction equals 1.5, since the 2050 projected population is less than 60 million and the 2000 population is greater than 40 million. Thus the projected percent increase in population from 2000 to 2050 for this age group is less than 50percent.

For the 40 minus 49 age group, the ratio is less than fraction numerator 50 over denominator 40 end fraction equals 1.25, since the 2050 projected population is less than 50 million and the 2000 population is greater than 40 million. Thus the projected percent increase in population from 2000 to 2050 for this age group is less than 25percent.

For the 50 minus 59 age group, the ratio is less than fraction numerator 50 over denominator 30 end fraction equals 1.6 stack 6 with bar on top, since the 2050 projected population is less than 50 million and the 2000 population is greater than 30 million. The projected percent increase in population from 2000 to 2050 for this age group is less than 66 percent.

For the 60 minus 69 year age group, the ratio is approximately 41 million to 20 million, or as a decimal, 2.05, corresponding to an approximate 105 percent increase in population for this age group.

For the 70 minus 79 year age group, the ratio is approximately 31 million to 16 million, or as a decimal, approximately 1.94, corresponding to an approximate 94 percent increase in population for this age group.

Therefore, the 60 minus 69 year age group has the greatest projected percent increase in population from 2000 to 2050 among the given options.

Question Difficulty: 
hard