Question #1
a < 6b + 4
3b < 8
Which of the following consists of all the a-values that satisfy the given system of inequalities?
A. a < 20
B. a < 16
C. a < 12
D. a < 8/3
Answer:
Correct Answer: A
The question offers a value range of a in terms of 6b and a value range for 3b. Therefore, use the known value range of 3b to find the value range of 6b.
Since 6b is two times 3b, multiply both sides of the second inequality by 2 to find the value range of 6b: 2 × 3b < 2 × 8, so 6b < 16.
Because the signs are the same in the two inequalities (both are less-than signs), you can plug 16 in for 6b in the first inequality: a < 16 + 4, or a < 20. Hence, (A) is correct.
Question #2
One proposal for reducing breakdowns on the New York City subway is to end 24-hour service and to shut down for a few hours nightly. Proponents of this plan argue that this would regularly allow time for preventative maintenance, leading to more consistent service; rather than shutting down for long periods of time, there would be shorter outages at night. This may seem a preferable outcome to the consequences of a shutdown resulting from a breakdown, but it has its liabilities. Most subway trips occur during rush hour, but not everyone works during the day. Doctors, nurses, bartenders, police officers, and firefighters are examples of occupations whose workers travel at all hours. Rather than be subjected to a period of inconvenience, these workers would find their commutes irrevocably altered. Clearly, the city must consider many factors to design a subway maintenance plan.
According to the text, what is true about non-rush-hour commuters?
A. They would risk losing public transportation options if 24-hour subway service were suspended.
B. They would face only minor inconveniences if 24-hour subway service were suspended.
C. They work primarily in health care and its related fields.
D. They are among the strongest advocates for a change to the current subway maintenance plan.
Answer:
(A) is correct.
The phrase "According to the text" shows this to be a Detail question. The correct answer will paraphrase a statement made explicitly in the text. The author discusses non–rush hour commuters toward the end of the text, listing some examples of these commuters-"doctors, nurses, bartenders, police officers, and firefighters"-and explaining that a cessation of 24-hour subway service could permanently alter their commutes. That matches choice (A), the correct answer here.
(B) is the opposite of what the passage says. The current system creates inconveniences for these workers when their subway lines are rerouted or closed for repair, but a suspension of 24-hour service would entail a permanent disruption. (C) distorts the paragraph. Doctors and nurses are among the non–rush hour commuters, but that doesn’t mean the commuters are primarily health care workers. The passage never states that health care workers are the majority of commuters. (D) is incorrect because the author does not discuss which occupations show the strongest support for a change in subway maintenance.
Question #3
In 2014, accusations were made that a global mobile communications carrier had clipped its clients for millions of dollars. The company was adding one-time and recurring service fees to its monthly bills without the clients' knowledge or consent. An investigation by the U.S. Federal Trade Commission resulted in substantial refunds to over 40% of its clients.
As used in the text, what does the word "clipped" most nearly mean?
A. Cut
B. Overcharged
C. Busted
D. Curtailed
Answer:
(B) is correct.
For this Words in Context question, use the context of the passage to determine the meaning of "clipped." Consider the context of the word: clients were clipped for millions of dollars, and then many received refunds. Predict that the company had scammed or overcharged; this matches choice (B) and is correct. Choices (A) and (C) are both incorrect because neither "cut" nor "busted" makes sense in this context. Eliminate (D); "curtail" means to make less, which is the opposite of what occurred.
Question #4
Suppose a scatterplot shows a weak negative linear correlation. Which of the following statements must be true?
A. The slope of the line of best fit will be a number less than −1.
B. The slope of the line of best fit will be a number between −1 and 0.
C. The data points will follow, but not closely, the line of best fit.
D. The data points will be closely gathered around the line of best fit.
Answer:
(C) is correct.
"Correlation" simply means relationship. The word "weak" refers to the strength of the relationship (how close the data lies to the line of best fit), which has no effect on slope. Be careful not to confuse slope and strength. The fact that a data set shows a weak correlation does not give you any information about the magnitude of the slope. This means you can eliminate (A) and (B). In a weak correlation, the data points will loosely follow the line of best fit, which makes (C) the correct answer. (D) describes a strong correlation.
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