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Percents

 

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8/7 Percents

Read the following SAT test question and then select the correct answer. 

 

When you work a percent problem, it is especially important to read the problem carefully because small words like “of” make all the difference in describing a percentage.  Once you have understood the question and identified the bottom line, assess your options and choose a method to attack the problem.  After you have finished the problem, loop back to verify that the answer addresses the bottom line.

 

The population of Norson, the largest city in Transitania, is 50 percent of the rest of the population of Transitania. The population of Norson is what percent of the entire population of Transitania?

Your bottom line is a percentage: the number of people in Norson as a percent of the entire population of the country of Transitania.  At the top of your scratch work, write N = ?%  Next, assess your options.  You don’t know how many people are in the country of Transitania, so solving the problem algebraically would be challenging. Instead, pick a number so that the problem will be more concrete.  When picking numbers on a percent problem, you should always pick 100 because 100 is the easiest number to use; the answer you find is already out of 100 so you will never need an extra step to find the correct percentage. Now you're ready to attack the problem. 

If you assume that there are 100 people total in all of Transitania, you still do not know how many people are in the city of Norson.  Use the variable “N” to represent the people in the city.  The problem tells you that the population of this city “is 50% of the rest of the population of Transitania.”  You know that Norson has half as many people as the rest of the population.  Think about it this way: for every person in Norson, there must be 2 people outside of the city.  Write an equation representing this knowledge and solve it.

 

 

N + 2N = 100

3N = 100

N = 33.33

You found that 33.33 people out of 100 live in the city of Norson, so you know that the percentage of people who live in Norson is 33.33%.  This matches the bottom line that you needed to find.

(A)               20%

(B)               25%

(C)               30%

(D)               33 1/3%

(E)                50%

The correct answer is (D).

 

On sat.collegeboard.org, 38% of answers were correct. 

 

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