Grammar
Question: One of the artist's most famous images showed Tweed with a bag of money in place of his head.
A) NO CHANGE
B) famous and well-known
C) famous and commonly known
D) famous, commonly known
Answer: A) NO CHANGE is correct because its the most concise and all answers are grammatically correct.
Question: For i=√−1, what is the sum (7+3i) + (−8+9i)?
A) −1+12i
B) −1−6i
C) 15 + 12i
D) 15−6i
Answer: First, add the real parts of each complex number, 7+(-8) = -1. Next, add the imaginary parts, 3i+9i=12i. Your results will be A) −1+12i.
Question: A function is defined by the equation f(x)=(x^2/4) - 11. For this function, which of the following domain values corresponds to a range value of 14 ?
A) -4
B) 10
C) 38
D) 100
Answer: CHOICE A is correct. The notation k(4) is equivalent to the output value of the function when 4 is substituted for the input x, and k(1) is the output value of the function when 1 is substituted for the input x. Substitute 4 and 1 into the function, one at a time, and then subtract the results:
k(4) = 5(4)+2=20+2=22
k(1) = 5(1)+2=5+2=7
k(4) - k(1) = 22-7 = 15
Choice (A) is correct. Caution--subtracting 1 from 4 and then substituting 3 into the function will give a different and incorrect result.
Question:
“Most of Greenland’s interior is covered by a thick layer of ice and compressed snow known as the Greenland Ice Sheet. The size of the ice sheet fluctuates seasonally: in summer, average daily high temperatures in Greenland can rise to slightly above 50 degrees Fahrenheit, partially melting the ice; in the winter, the sheet thickens as additional snow falls, and average daily low temperatures can drop to as low as 20 degrees.”
Which choice most accurately and effectively represents the information in the graph?
A) NO CHANGE
B) to 12 degrees Fahrenheit.
C) to their lowest point on December 13.
D) to 10 degrees Fahrenheit and stay there for months.
Answer: Choice B is the best answer because the graph clearly indicates that, on March 5, average low temperatures are at their lowest point: 12 degrees Fahrenheit.
Choice A is incorrect because the phrase “as low as” suggests that the temperature falls lower than 20 degree Fahrenheit, but the chart shows that in January, February, and March, the temperature frequently falls below that point. Choices C and D are incorrect because the information each provides is inconsistent with the information on the chart.
Question: A right triangle, one angle measures x°, where sinx°= 4/5. What is cos(90°−x°) ?
Answer: The correct answer is 4/5 or 0.8.
Question: A large company that provides breakfast for all its employees wants to determine how many of them are likely to be within a healthy weight range, given that all the employees take advantage of the free breakfast all five weekdays. If the company has 3,000 employees, and assuming the participants in the study are a good representative sample, about how many of the employees are likely to be within a healthy weight range?
A) 825
B) 1,030
C) 1,900
D) 2,400
Answer: CHOICE D is correct. The question asks about employees who eat breakfast every weekday, so focus on the "5-7 times per week" column in the table. Assuming the participants in the study were a good representative sample, 36 out of 45, or 80%, of the 3,000 employees are likely to be within a healthy weight range. Multiply 0.8x 3,000 to arrive at 2,400, which is (D).
Question: Because today’s students can expect to hold multiple jobs—some of which may not even exist yet—during our lifetime, studying philosophy allows them to be flexible and adaptable.
A) NO CHANGE
B) one’s
C) his or her
D) their
Answer: Choice D is the best answer because it provides a possessive pronoun that is consistent with the sentence’s plural subject “students,” thus creating a grammatically sound sentence. Choices A, B, and C are incorrect because each proposes a possessive pronoun that is inconsistent with the plural noun “students,” the established subject of the sentence.
If t>0 and t^2−4=0,what is the value of t?
Answer: The correct answer is 2. To solve for t, factor the left side of t^2 , giving (t-2)(t+2). t = 2 and t=-2. If t Is greater than 0, then t must be 2.
Question: Briana is writing a 60-page paper for a law school class. She estimates that she will average 45 words per minute while typing. If one page contains approximately 500 words, which of the following correctly estimates the number of pages, p, remaining as a function of the number of minutes, m, that Briana types?
A) p(m) = 60 - (9m/100)
B) p(m) = (60-100)/9m
C) p(m) = 60 - (100/9m)
D) p(m) = (60-9m)/100
Answer: CHOICE A is correct. Use the two given rates to determine Briana's typing rate in pages per minute. She types 45 wprds per minute, which becomes :
(45words/1minute)×(1 page/500words)=(45 pages/500 minutes)= (9 pages/100 minutes)
Multiplying this rate by m gets you the number of pages typed after m minutes, whihc can then be subtracted from the starting page count, 60, to get the number of pages Briana has left to type. The function should read 𝑝(𝑚)=60−(9𝑚/100), which matches (A).