List of practice Questions

Which of the following numbers has the greatest number of unique digits?

If x and y are positive integers, what percent of three more than y is twice the value of x?

A new Coffee Bean & Tea Leaf coffee drink consists only of certain amounts of espresso and sugar. What is the ratio of espresso to sugar in the new drink?
(1) There are 15 ounces of sugar in 35 ounces of the new drink.
(2) There are 40 ounces of espresso in 70 ounces of the new drink.

Matthew, Jared, and Richard all bought flowers. The number of flowers Matthew purchased was equal to a single digit. Of the numbers of flowers purchased by Matthew, Jared, and Richard, only one was divisible by 3. The number of flowers one of them bought was an even number. Which of the following could represent the numbers of flowers each purchased?

Circle P is inside Circle Q, and the two circles share the same center X. If the circumference of Q is four times the circumference of P, and the radius of Circle P is three, what is the difference between Circle Q's diameter and Circle P's diameter?

A yellow taxi cab went from Downtown to the Beachside and back at an average speed of 2/3 miles per hour. If the distance from Beachside to Downtown is 1 mile, and the trip back took half as much time as the trip there, what was the average speed of the yellow taxi cab on the way to Beachside?

Circle B's diameter was multiplied by 1.8. By what percent, approximately, was the area increased?

Lady Edith bought several necklaces at the jewelry store, and each necklace cost 16 dollars. Lady Mary also purchased several necklaces, at a cost of $20 each. If the ratio of the number of necklaces Lady Edith purchased to the number of necklaces Lady Mary purchased is 3 to 2, what is the average cost of the necklaces purchased by Lady Edith and Lady Mary?

In recent years, scholars have begun to use social science tools to analyze court opinions. These scholars have justifiably criticized traditional legal research for its focus on a few cases chosen for their perceived doctrinal importance, arguing that such research may distort our understanding of the law. Social scientists endeavor to study court opinions systematically, analyzing samples of cases that are selected randomly or that constitute the entire universe of cases within certain bounds. However, social science approaches themselves have limitations. By focusing primarily on the influence of factors such as the identity of the judge or the ideological orientation of the court, social scientists may overlook the influence of legal doctrine itself. Their research designs, which usually involve analyzing the quantitative relationship between characteristics of cases and their outcomes, are good at detecting the influence of factors that can be easily quantified but not as good at assessing the influence of factors such as the reasoning of the judge. Social science approaches have also been criticized for ignoring the distinction between the holding of a case (the part of the opinion that is legally binding) and the dicta (nonbinding statements). Finally, these approaches are better suited to analyzing the decisions of appellate courts, which generally issue written opinions, than the decisions of trial courts, which often do not.

In the field of Native American history, scholars have increasingly recognized the need to un- derstand indigenous cultures and perspectives. However, achieving this goal is difficult, partly because Native American oral traditions are rarely accorded the same legitimacy as written accounts. Historian Joanne Rappaport observes that written sources are privileged in histori- cal scholarship, and she argues that this privileging reflects a view that literacy is superior to orality. Rappaport suggests that the link between writing and truth is historically contingent, arising from the encounter between Native Americans and Spanish colonizers. She points out that while the Spanish privileged written documents as records of events, the Native Americans of the Andes regarded oral traditions and ritual performances as the principal means of record- ing the past. When Andean societies were forced to adopt alphabetic writing, they adapted it to meet their needs. For example, indigenous authors used alphabetic writing not only to record events but also to express Andean understandings of the cosmos. Moreover, Andean communities continued to rely on oral traditions and ritual performances to transmit historical knowledge. Rappaport argues that scholars should recognize the parity of oral and written modes of transmitting knowledge and strive to incorporate both into their historical accounts.

Although economic analysis of collective bargaining has traditionally focused on wages, recent studies have increasingly focused on the effects of unionization on fringe benefits such as pen- sions and health insurance. Because the costs of providing fringe benefits are tax deductible for employers, fringe benefits are effectively subsidized by the government. This tax treatment creates an incentive for employers to increase the proportion of employee compensation that is paid in the form of fringe benefits. However, not all workers value fringe benefits equally. Since the value that workers place on fringe benefits is likely to rise with their income (because the tax savings associated with fringe benefits increase with income), higher-income workers are likely to prefer a greater proportion of their compensation in the form of fringe benefits than are lower-income workers. Unions, which typically represent lower-income workers, should therefore be expected to oppose the substitution of fringe benefits for wages. However, unions often support such substitutions. One explanation for this puzzling behavior is that unions take into account the preferences not just of current members but also of potential members, who are typically younger and higher-income than current members. Another explanation is that unions are willing to accept lower wages in exchange for fringe benefits because fringe benefits help to retain workers and reduce labor turnover, thereby increasing the union’s bargaining power.

Recent studies of the gender gap in entrepreneurship have produced somewhat conflicting re- sults. Some studies suggest that the gender gap is narrowing, while others suggest that it is widening. One difficulty in interpreting these results is that the studies often measure en- trepreneurship in different ways. Some studies define entrepreneurs as those who start their own businesses, while others define them as those who own or manage businesses. Moreover, studies vary in their focus, with some examining the proportion of entrepreneurs who are women and others examining the proportion of women who are entrepreneurs. Despite these differ- ences, however, the studies generally agree that women are less likely than men to become entrepreneurs. Several factors have been proposed to explain this gender gap. Some scholars point to differences in access to financial capital, arguing that women are less likely than men to be able to obtain the funding needed to start or grow a business. Others point to differences in human capital, suggesting that women are less likely than men to have the education, expe- rience, and skills needed for entrepreneurship. Still others point to differences in social capital, arguing that women are less likely than men to have access to the networks and connections that can facilitate entrepreneurial success.

In studying the evolution of vertebrae, biologists have often focused on the notochord, a flexible rod found in the embryos of all vertebrates. The notochord appears early in development and is later replaced by the vertebral column, or spine. Because the notochord is essential for the formation of the spine, it has been argued that the evolution of the spine must have followed the evolution of the notochord. However, recent research on the lancelet, a small invertebrate chordate, challenges this view. Lancelets are thought to resemble the ancestors of vertebrates, and they possess a notochord but lack vertebrae. This suggests that the notochord evolved before the spine. Moreover, studies of lancelet development have shown that the notochord is not required for the formation of the tissues that give rise to the spine in vertebrates. Instead, the notochord appears to play a role in organizing the development of other structures, such as the nerve cord and the muscles. These findings suggest that the notochord and the spine evolved independently, with the notochord arising first to serve functions other than spinal development. The spine may have evolved later as a means of providing support and protection for the body.

A set of data consists of the numbers: 5, 8, 12, 15, 20.
Part 1: The median of the data set is equal to the mean of the data set.
Part 2: If the number 10 is added to the data set, the new median will be less than the original median.
Evaluation: Part 1: False. Part 2: False.

What is the probability that a randomly chosen student from a class is a girl?
(1) There are 30 students in the class.
(2) The ratio of boys to girls in the class is 2:3.

What is the value of y?
(1) y is 20% greater than x.
(2) x + y = 55.

If 4x + 1 = 9, what is the value of x?

If p = 3m and m = k/6, what is the value of p when k = 36?

If a = 2b and b = 3c, what is the value of a when c = 4?

If a certain vase contains only roses and tulips, how many tulips are there in the vase?
(1) The number of roses in the vase is 4 times the number of tulips in the vase.
(2) There is a total of 20 flowers in the vase.