List of practice Questions

The following appeared in a health newsletter.
"Nosinia is an herb that many users report to be as effective as prescription medications at fighting allergy symptoms. Researchers recently compared Nosinia to a placebo in 95 men and women with seasonal allergies to ragweed pollen. Participants in the study reported that neither Nosinia nor the placebo offered significant relief. However, for the most severe allergy symptoms, the researchers reported that Nosinia was more effective than the placebo in providing relief. Furthermore, at the end of the study, participants given Nosinia were more likely than participants given a placebo to report feeling healthier. We, therefore, recommend using Nosinia to help with your severe allergy symptoms."
The best way to solve environmental problems caused by consumer-generated waste is for towns and cities to impose strict limits on the amount of trash they will accept from each household.
Write a response in which you discuss the extent to which you agree or disagree with the claim. In developing and supporting your position, be sure to address the most compelling reasons and/or examples that could be used to challenge your position.
Claim: Though often considered an objective pursuit, learning about the historical past requires creativity.
Reason: Because we can never know the past directly, we must reconstruct it by imaginatively interpreting historical accounts, documents, and artifacts.
Write a response in which you discuss the extent to which you agree or disagree with the claim and the reason on which the claim is based.
The following appeared in a letter to the editor of a Relannian newspaper.
Industry analysts report that the number of dairy farms in Relanna has increased by 25 percent over the last decade. Also, recent innovations in milking technology make it possible for farmers to significantly increase the efficiency of the milking process, allowing them to collect more milk in less time with minimal human intervention. In fact, data from the Relannian Department of Agriculture indicate that labor costs at the majority of Relannian dairy farms are actually lower now than they were ten years ago. Despite increased efficiency and lower labor costs, a carton of cream — a dairy product made from milk — at the local food market costs twice as much as it did two years ago. The only explanation for this dramatic price increase is that farmers are inflating the price of cream to increase their profits.
Write a response in which you discuss one or more alternative explanations that could rival the proposed explanation and explain how your explanations can plausibly account for the facts presented in the argument.
According to an independent poll of 200 charitable organizations, overall donations of money to nonprofit groups increased last year, but educational institutions did not fare as well as other organizations. Donations to international aid groups increased the most (30 percent), followed by donations to environmental groups (23 percent), whereas donations to educational institutions actually decreased slightly (3 percent). Meanwhile, some of the major economic indicators suggest that consumer spending is higher than average this year, showing that potential donors have ample disposable income. Therefore, the clearest explanation for the decline in donations to educational institutions is that people actually value education less than they did in the past.
Write a response in which you discuss the extent to which you agree or disagree with the argument and explain your reasoning.
The following memo appeared in the newsletter of the West Meria Public Health Council. “An innovative treatment has come to our attention that promises to significantly reduce absenteeism in our schools and workplaces. A study reports that in nearby East Meria, where consumption of the plant beneficia is very high, people visit the doctor only once or twice per year for the treatment of colds. Clearly, eating a substantial amount of beneficia can prevent colds. Since colds are the reason most frequently given for absences from school and work, we recommend the daily use of nutritional supplements derived from beneficia. We predict this will dramatically reduce absenteeism in our schools and workplaces.”
Write a response in which you discuss one or more alternative explanations that could rival the proposed explanation and explain how your explanation(s) can plausibly account for the facts presented in the argument.
The following appeared in an e-mail sent by the marketing director of the Classical Shakespeare Theatre of Bardville.
“Over the past ten years, there has been a 20 percent decline in the size of the average audience at Classical Shakespeare Theatre productions. In spite of increased advertising, we are attracting fewer and fewer people to our shows, causing our profits to decrease significantly. We must take action to attract new audience members. The best way to do so is by instituting a ‘Shakespeare in the Park’ program this summer. Two years ago the nearby Avon Repertory Company started a ‘Free Plays in the Park’ program, and its profits have increased 10 percent since then. If we start a ‘Shakespeare in the Park’ program, we can predict that our profits will increase too.”
Write a response in which you discuss one or more alternative explanations that could rival the proposed explanation and explain how your explanation(s) can plausibly account for the facts presented in the argument.

Of the 20 lightbulbs in a box, 2 are defective. An inspector will select 2 lightbulbs simultaneously and at random from the box. What is the probability that neither of the lightbulbs selected will be defective? 

What is the least positive integer that is not a factor of \( 25! \) and is not a prime number?

The total stopping distance for the car traveling at 60 miles per hour is approximately what percent greater than the total stopping distance for the car traveling at 50 miles per hour?

Approximately what is the total stopping distance, in feet, if the car is traveling at a speed of 40 miles per hour when the driver is signaled to stop?

The speed, in miles per hour, at which the car travels a distance of 52 feet during reaction time is closest to which of the following?

\( AB \) is a diameter of the circle. Compare: 
Quantity A: The length of \( AB \) 
Quantity B: The average (arithmetic mean) of the lengths of \( AC \) and \( AD \). 

In the sequence above, each term after the first term is equal to the preceding term plus the constant \(c\). If \(a_1 + a_3 + a_5 = 27\), what is the value of \(a_2 + a_4\)?

 

Which of the following statements individually provide sufficient additional information to determine the area of triangle ABC? 

If \( s \) is a speed, in miles per hour, at which the energy used per meter during running is twice the energy used per meter during walking, then according to the graph above, \( s \) is between

If \( \frac{1}{(2^{11})(5^{17})} \) is expressed as a terminating decimal, how many nonzero digits will the decimal have?
The total amount that Mary paid for a book was equal to the price of the book plus a sales tax that was 4 percent of the price of the book. Mary paid for the book with a 10 bill and received the correct change, which was less than 3.00. Which of the following statements must be true?

In the figure above, if \( m \parallel k \) and \( s = t + 30 \), then \( t = \dots \)

In a graduating class of 236 students, 142 took algebra and 121 took chemistry. What is the greatest possible number of students that could have taken both algebra and chemistry? 
Fraction answer: 

Given the triangle with angles of \( 40^\circ \), \( 50^\circ \), and \( 90^\circ \), compare the legs of this triangle to those of a \( 45^\circ \)-\( 45^\circ \)-\( 90^\circ \) triangle. 

O is the center of the circle above. 

Decaffeinated coffee: 0 mg
Percolated coffee: 95 mg
Drip-brewed coffee: 145 mg
Instant coffee: 65 mg
Brewed tea: 45 mg
Instant tea: 35 mg
Cocoa: 25 mg
Caffeinated soft drinks: 40 mg
Weight-loss drugs: 10 mg
Diuretics and stimulants: 15 mg
Pain relievers: 0 mg
Cold/allergy remedies: 10 mg
If \( 0<a<1<b \), which of the following is true about the reciprocals of \( a \) and \( b \)?
In the figure above, \( O \) and \( P \) are the centers of the two circles. If each circle has radius \( r \), what is the area of the shaded region?