PSAT Math Quiz: Tables, Statistics, and Probability

Test your PSAT readiness by taking this PSAT Math quiz!

Question 1
The table below summarizes the results of a survey about the favorite sports of a group of high school students. Assume that every student has a favorite sport and that students could select only one favorite.

Based on the table, which of the following is NOT a true statement?
A. About 27% of the entrants in the freshman prize drawing voted for basketball as their favorite sport.
B. About 23% of the entrants in the sophomore prize drawing voted for basketball as their favorite sport.
C. About 27% of the entrants in the junior prize drawing voted for basketball as their favorite sport.
D. About 30% of the entrants in the senior prize drawing voted for basketball as their favorite sport.

Answer 1

D: The question asks for the answer choice that is NOT a true statement, so test each one. Use the table to determine the correct percents for each choice. Notice that all choices are about the estimated percent of students in each class who voted for basket- ball as their favorite sport, so use the percent formula, percent (part / whole) = 100%. In each case, the part is the number of students in each class who voted for basketball, while the whole is the total number of students in that class:
(A) (370 / 1350) x 100% = 0.274 ≈ 27%
(B) (314 / 1355) x 100% = 0.231 ≈ 23%
(C) (365 / 1349) x 100% = 0.270 ≈ 27%
(D) (291 / 1340) x 100% = 0.217 ≈ 22%
Hence, (D) must be correct since the statement was about 30% and NOT about 22%.

Question 2
Liam is conducting a market research study to determine the effectiveness of advertisements on social networking sites. He surveyed a randomly selected group of 2,000 young adults on how likely they are to purchase from a company based on its advertisements on social networking sites. Respondents rated their likelihood to purchase on a scale from 1 to 7, with 1 being “Not at all likely” and 7 being “Definitely.” Which of the following statements is NOT true based on the survey results below?

A. mode = 3
B. median = 3
C. mean < median
D. 2 < mean < 5

Answer 2

C: Examine the bar chart to evaluate the choices.
(A): The bar for “Unlikely” (which is 3 on the scale given in the question) is clearly the tallest, so this is the mode. Eliminate (A).
(B): There are 2,000 responses, so the median is the average of responses 1,000 and 1,001. The total of the first two bars is about 600. Since the third bar is about 700, that means that the median response is indeed within this bar. Eliminate (B).
(C): The data is skewed to the right, meaning that the extreme values on the right will weight the mean calculation to make the mean greater than the median. Thus, (C) is not true and is the correct choice.
(D): If you were not certain that (C) was the correct choice, you could see that the substantial majority of values are between 2 and 5 inclusive, so the mean has to be somewhere within that wide range. Eliminating (D) confirms (C) as correct.

Question 3
The graph below shows the yearly profits of an organic produce company. If the company’s profits continue to grow at the same rate, in which year will it have a yearly profit that is 100% greater than its profit in 2013?

A. 2019
B. 2020
C. 2021
D. 2022

Answer 3

A: According to the bar graph, the company’s yearly profits have been growing by about $10 million annually. To reach yearly profits that are 100% greater than (or double) its profits in 2013, the company would need yearly profits of 2 × $60 million = $120 million. This is $50 million more than in 2014. At $10 million more per year, reaching this target would take 5 more years. Thus, the company should double its 2013 profits in 2014 + 5 = 2019, which is (A).

Question 4
The table below shows the distribution of applicants by age and level of education for a management trainee program offered at a retail store. According to the data, which age group had the smallest percentage of people with a high school diploma only?

A. 18–25
B. 26–35
C. 36–45
D. Older than 45

Answer 4

B: To calculate the percentage of people in each age group who had a high school diploma only, divide the number of people in that age group with only a high school diploma by the total number of applicants in that age group. Choice (B) is correct because (16 / 44) ≈ 0.364 = 36.4%, which is a lower percentage than that of the other age groups (18 to 25 ≈ 60.5%, 36 to 45 ≈ 42.3%, and Older than 45 = 50%).

Question 5
A medical testing company conducted an experimental study to determine which of three anti-histamines is most effective for alleviating allergy symptoms. If the only allergies treated in the course of the study were pollen allergies, which of the following is true?
A. The antihistamine that is found to be the most effective will work for all allergies.
B. The antihistamine that is found to be the most effective will work only for pollen allergies.
C. The study will be able to produce results concerning the effects of the antihistamines only on pollen allergies.
D. The study is clearly biased and, therefore, not relevant to determining which antihistamine is most effective.

Answer 5

C: The study only looked at pollen allergies, so the sample was limited. You can eliminate (A) because not all allergies were included in the sample—you can’t say anything about them one way or the other. You can eliminate (B) by similar reasoning: the antihistamine found to be most effective for pollen allergies may or may not be the most effective one for other types of allergies as well; there is just no way to tell. You can eliminate (D) because the question doesn’t tell you anything about the data collection methods, so you can’t determine whether the study was biased. This means that (C) is correct—the study will be able to produce results concerning the effects of the antihistamines only on pollen allergies.

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