PSAT/NMSQT Math Practice Test

Question 1

A research assistant chose 75 undergraduate students at random from a list of all students enrolled in a large university's 
psychology program. “How many minutes per day do you generally spend reading?” she questioned each of the 75 kids. 
The average reading duration in the sample was 89 minutes, with a margin of error of 4.28 minutes for this estimate. 
Another research assistant plans to duplicate the poll with the goal of reducing the margin of error. Which of the following
 samples has the smallest margin of error for the projected mean time students in the psychology program read every day?

Accepted Answer

300 undergraduate psychology students were chosen at random.

Answer

40 undergraduate students from all degree programs at the college were chosen at random.

Answer

40 undergraduate psychology students were chosen at random.

Answer

300 undergraduate students from all degree programs at the college were chosen at random.

Question 2

In a class, the ratio of boys to girls is 4:7. How many extra boys should be enrolled in a class with 44 students to achieve a 1:1 ratio?

Accepted Answer

12

Answer

5

Answer

10

Answer

14

Question 3

Jackson is staying at a hotel where a room costs $99.95 a night plus tax. The room rate is subject to an 8% tax, as well 
as a one-time untaxed fee of $5.00 imposed by the hotel. Which of the following is Jackson's total price for staying x nights
 in dollars?

Accepted Answer

1.08(99.95x) + 5

Answer

1.08(99.95 + 5)x

Answer

1.08(99.95x + 5)

Answer

(99.5+0.08x)+5

Question 4

A yellow box has a capacity that is 20% greater than a green box's capacity. How many of the same books can the 
green box hold if the yellow box can contain 30 of the same size books?

Accepted Answer

25

Answer

8

Answer

24

Answer

12

Question 5

The cost C, in dollars, of producing n goods, according to a corporate management, is C equals 7 n plus 350. Each item 
costs $12 at the company. When the total money from selling a number of products exceeds the total cost of producing
 that quantity of items, the company generates a profit. Which of the following inequalities contains all potential values
 of n for which the manager expects the company to profit?

Accepted Answer

n > 70

Answer

n < 70

Answer

n < 80

Answer

n > 80

Question 6

- 70 is the sum of six negative integers. What is the greatest possible value of one of the other five numbers if the smallest integers is -15?

Accepted Answer

-5

Answer

0

Answer

-3

Answer

-4

Question 7

Male primates on a primate reserve are on average 15 years old, whereas female primates are on average 19 years old. 
Which of the following statements concerning the combined group of male and female primates at the primate reserve's
 mean age, m, must be correct?

Accepted Answer

15 < m < 19

Answer

m = 20

Answer

m < 20

Answer

m > 20

Question 8

What is the ratio of the following function's minimum to maximum value?
−2≤𝑥≤3?𝑓(𝑥)=−3𝑥+1

Accepted Answer

- 8/7

Answer

8/7

Answer

7/6

Answer

-7/6

Question 9

For the population of 16-year-olds in the United States, a researcher began to find if there is an association between exercise 
and sleep. She gathered data from a random sample of 2000 16-year-olds in the United States and discovered strong evidence
 of a link between exercise and sleep. Which of the following conclusions is backed up by evidence?

Accepted Answer

There is a positive link between exercise and sleep among 16-year-olds in the United States.

Answer

For 16-year-olds all throughout the world, there is a link between exercise and sleep.

Answer

Using the study's definitions of exercise and sleep, an increase in sleep is induced by an increase in activity for 16-year-olds around the world.

Answer

For 16-year-olds in the United States, an increase in sleep is induced by an increase in activity, according to the study's definitions.

Question 10

When Jame's car travels at an average speed of 50 miles per hour, the gas mileage is 21 miles per gallon. At the start of 
a trip, the car's petrol tank contains 17 gallons of gas. Which of the following functions f represents the number of gallons
 of gas remaining in Jame's tank t hours after the trip begins if his car moves at an average speed of 50 miles per hour?

Accepted Answer

f(t) = 17 - 50t/21

Answer

f(t) = 17 - 21t/50

Answer

f(t) = 17 - 21/50t