Question #1
After a couple dances for three hours in a charity dance-a-thon, they earn $50 per half-hour of additional dancing. Assuming they dance for at least three hours, which expression represents the total number of dollars earned by a couple who dances continuously for h hours?
Correct Answer: D
Use the information in the question to write your own expression, then look for the answer choice that matches. Simplify your expression only if you don’t find a match. If a couple earns $50 per half-hour that they dance, then they earn 50 x 2 = $100 per hour. Multiply this amount by the number of hours (not including the first 3 hours). This can be expressed as 100(h − 3). This is not one of the answer choices, so simplify by distributing the 100 to get 100h − 300, which is (D).
If you're struggling with the algebra, try picking numbers. Pick a number of hours a couple might dance, such as 5. They don't earn anything for the first 3 hours, but they earn $50 per half-hour for the last 2 hours, which is 50 times 4 half-hours, or $200. Now, find the expression that gives you an answer of $200 when h = 5 hours: 100(5) − 300 = 500 − 300 = 200. If you use Picking Numbers, remember that it is possible that the number you choose satisfies more than one answer choice, so plug it into the other three choices. In this case, h = 5 does not give a value of 200 in any other expression, which confirms that (D) is correct.
Question #2
A pizzeria charges $17 for Pizza A and $13 for Pizza B. Ingredient costs are $450 per week for Pizza A and $310 per week for Pizza B. Last week, the pizzeria sold an equal number of both pizza types, and the weekly profit from the sale of each pizza type was the same. If x represents the number of Pizza B sold, what is the value of x?
Correct Answer: B
Write expressions to represent the profit generated by selling each type of pizza. You're told Pizza A sells for $17 each and that its ingredients cost the pizzeria $450 per week. This means the weekly profit generated by this pizza's sales can be represented by the expression 17x − 450. Do the same for Pizza B: each one sells for $13, but the pizzeria loses $310 to pay for ingredients each week. Therefore, the weekly profit from this pizza can be represented by 13x − 310. To determine the value of x at which the profit from the sale of each type of pizza is the same, set the two profit expressions equal to each other and solve:
17x − 450 = 13x − 310
4x = 140
x = 35
Thus, (B) is correct.
Question #3
Malik’s salary is $25,500 per year, which he expects will increase by a constant dollar amount annually. In 12 years, his salary will have doubled. Assuming salary increases take place only at the end of a full year, how many years must Malik wait until his salary is at least $40,000 annually?
Correct Answer: B
First, notice that the actual dollar amount of the increase each year is unknown, so assign a variable like d. After 12 increases, his salary will rise by $25,500, so write a formula: 12d = 25,500. Solve for d to find that Malik will receive an increase of $2,125 per year The question asks how many years must go by until Malik's salary is at least $40,000; the number of years is another unknown, so assign it a variable like n. Multiplying n by the amount of each increase will give you the total increase of dollars over n years, but don’t forget to add in the current salary to reflect his total salary amount:
25,500 + 2,125n = 40,000
2,125n = 14,500
n ≈ 6.8
The question asks you to assume that salary increases only take place at the end of a full year. If you are unsure and want to prove that the answer is not 6, check by using n = 6 to calculate the total dollar amount: 25,500 + 2,125(6) = 38,250. Six years is not long enough; enter 7.
Question #4
21x − 6y = 54
9 + y = 3.5x
The system of equations shown has how many solutions?
Correct Answer: D
Note that (C) is impossible. There are only three possibilities: the lines intersect, in which case there is one solution; the lines are parallel, in which case there is no solution; or the equations describe the same line, in which case there are infinitely many solutions. Get the two equations into the same format so that you can distinguish among these possibilities:
21x − 6y = 54
3.5x − y = 9
Now it's easier to see that the first equation is equivalent to multiplying every term in the second equation by 6. Both equations describe the same line, so there are infinitely many solutions; (D) is correct.
Question #5
hx − 4y = −10
kx + 3y = −15
If the graphs of the lines in this system of equations intersect at (–3, 1), what is the value of k/h?
Correct Answer: C
If the graphs intersect at (−3, 1), then the solution to the system is x = −3 and y = 1. Substitute these values into both equations and go from there:
So, k/h = 6/2 = 3, making (C) correct.
Question #6
The following text is from Jules Verne's 1863 novel Five Weeks in a Balloon.
Notwithstanding fatigues of every description, and in all climates, Ferguson's constitution continued marvelously sound. He felt at ease in the midst of the most complete privations; in fine, he was the very type of the thoroughly accomplished explorer whose stomach expands or contracts at will; whose limbs grow longer or shorter according to the resting-place that each stage of a journey may bring; who can fall asleep at any hour of the day or awake at any hour of the night.
As used in the text, what does the word "constitution" most nearly mean?
Correct Answer: C
In this passage, Ferguson's "constitution" is "sound," despite its "fatigue," and "he felt at ease." The broad context of this passage includes mention of his stomach, limbs, and ability to sleep at "any hour." Predict that his "constitution" most nearly means his body or health. Choice (C) matches and is correct. Choices (A), (B), and (D) all have similar meanings: variances of law or decree.
Question #7
In 1990, Carl Woese proposed that bacteria and archaea were disparate domains of prokaryotes based on the analysis of their ribosomal RNA, the genetic material that plays an active role in the formation of proteins. Today, the phylogenetic branches of bacteria, archaea, and eukarya form the basis of the three-domain system of classification that is still in use.
As used in the text, what does the word “branches” most nearly mean?
Correct Answer: D
For this Words in Context question, predict a word to replace "branches" that retains the original meaning of the sentence. That sentence says, "The ... branches ... form the basis of the ... system of classification," so categories would be a good prediction. This matches (D), the correct answer.
(A), (B), and (C) are alternative definitions of "branches" that do not make sense in the context of the passage. The text is not discussing branches of trees (boughs), branches of a business (offices), or branches of a club (chapters). Using the correct strategy will help when confronted with unfamiliar words. Having a strong prediction before you review the answer choices will aid in avoiding tempting choices or selecting the unfamiliar.
Question #8
The following text is from Jane Austen's 1813 novel Pride and Prejudice.
"Well," said Charlotte, "I wish Jane success with all my heart. And if she were married to him tomorrow, I should think she had as good a chance of happiness as if she were to be studying his character for a twelvemonth. Happiness in marriage is entirely a matter of chance. If the dispositions of the parties are ever so well known to each other, or ever so similar beforehand, it does not advance their felicity in the least. They always continue to grow sufficiently unlike afterwards to have their share of vexation; and it is better to know as little as possible of the defects of the person with whom you are to pass your life."
Which choice best states the main purpose of the text?
Correct Answer: B
When determining the purpose of a text, consider its structure. This passage consists of Charlotte giving an opinion about Jane’s chances of finding happiness in marriage and then elaborating on Charlotte's reasoning for that opinion. Thus, the text is structured to tell us about Charlotte's philosophy. Since she believes that happiness in marriage is ultimately up to random chance, find the answer choice that best fits Charlotte's philosophy, which would be (B).
Although Charlotte believes Jane has the same odds of finding happiness in marriage whether or not she rushes into things, (A) is incorrect because it misstates Charlotte's philosophy, which is that happiness is random and cannot be influenced. Choices (C) and (D) are not supported by the passage, as Charlotte is talking about marriage in the abstract rather than her own beliefs and marriage specifically.
Question #9
The following text is from H.G. Wells' 1898 novel The War of the Worlds.
No one gave a thought to the older worlds of space as sources of human danger, or thought of them only to dismiss the idea of life upon them as impossible or improbable. It is curious to recall some of the mental habits of those departed days. At most terrestrial men fancied there might be other men upon Mars, perhaps inferior to themselves and ready to welcome a missionary enterprise. Yet across the gulf of space, minds that are to our minds as ours are to those of the beasts that perish, intellects vast and cool and unsympathetic, regarded this earth with envious eyes, and slowly and surely drew their plans against us.
Which choice best states the function of the bold portion in the text as a whole?
Correct Answer: D
When identifying the author's reason for including a portion of the passage, consider the structure of the entire passage. Here, the text starts with a discussion of how alien life was once considered "impossible or improbable." In the underlined portion, the narrator mentions how "curious" some of the ideas in "those departed days" were. However, nothing specific is listed until the next sentence, which discusses how humans might have "fancied" the existence of Martians and how they were "inferior" to humans. With that in mind, predict what function the underlined portion might serve: it establishes that people used to have funny ideas about the Martians, without giving details. This best fits (D).
Choice (A) is incorrect because the focus is on humans and what they once believed. (B) is incorrect because no contrast exists; in fact, the underlined sentence builds upon the ideas of the previous sentence. Choice (C) is incorrect as the text does not offer specific examples until the subsequent sentence.
Question #10
Urban agriculture has been proposed as a potential solution to the food insecurities that occur in densely populated communities with high economic disparity. Specifically, rooftop gardens can help improve access to fresh fruits and vegetables, ______ the residents in a collective purpose, and beautify the skyline. However, the space is very limited, and rooftop gardeners would benefit from consistent crop rotation and strategic plant selection.
Which choice completes the text so that it conforms to the conventions of Standard English?
Correct Answer: B
The sentence is a list that includes present tense, single-action words: "improve" and "beautify." This is a verb parallelism question. Select the answer choice that is a present tense, single-action verb. Choice (B) is correct because it is the only option that meets all those conditions.
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