PSAT Math Multiple-Choice Practice Test 5: Math Techniques

1. If , what is the value of x?


Based on the system of equations above, what is the value of v?

3. An alloy needs to contain between 10 and 15% of titanium. Which of the following inequalities represents the amount in kilograms, x, of a 20% titanium alloy that should be mixed with a 5% titanium alloy to produce 10 kilograms of an alloy with the acceptable percentage of titanium?

4. If 10 pecks are equivalent to 2.5 bushels, then 4 bushels are equivalent to how many pecks?

5. A forest fire is burning an area of forest that is 10 square miles. An air squad is able to reduce the size of the fire by 7% every 12 hours. If F(t) is the area being burned by the fire, which expression for F(t) represents the area of forest still on fire after t hours?

6. A student took five tests. He scored an average (arithmetic mean) of 80 on the first three tests and an average of 90 on the other two. Which of the following must be true?

I. The student scored more than 85 on at least one test.

II. The average (arithmetic mean) score for all five tests is less than 85.

III. The student scored less than 80 on at least two tests.


Maggie and Glenn both leave from the same house to go for a jog along a trail. Shortly after leaving, Maggie realizes she forgot her iPhone and returns home to find it before heading back out onto the same trail. The graph above shows how far each of them is from home for the first fifteen minutes of their jogs. Excluding the time she spends at home, which of the following is closest to Maggie's average speed, in meters per second, during the portion of her jog shown?

8. In a political poll, 500 voters were first asked whether they were registered as Democrat, Republican, or Independent. The voters were then asked whether they planned to vote for Candidate A, for Candidate B, or were Undecided. The table below shows the results of the poll.

The number of registered Republicans who plan to vote for Candidate B is what percent greater than the number of registered Democrats who plan to vote for Candidate B?

9. The college that Everett attends in Chicago is exactly 200 miles from his parents' home. When his parents come to visit him at school, they drive at an average speed of 45 miles per hour for maximum safety. When Everett drives home for winter break, his average speed is x% greater than the average speed at which his parents drive when they make the trip. Which of the following represents the time Everett saves on the 200-mile trip compared with his parents' average time, in hours?

10. A survey company gathered data regarding people's transportation habits in four major U.S. cities. The survey asked participants in each of these cities to indicate whether they regularly used a personal vehicle, public transportation, or neither to commute. Participants were not limited to one response and could check both personal vehicle and public transportation. The results are shown below.

Which one of the following statements is supported by the data shown above?

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