Ultimate Guide to Acing the PERT Test

Answer & Explanation
The correct answer is (A).

The line equation is

where: 

m = slope
n = the intersection point of the line and the y axis.

The slope can be found by the difference of the two points:

Use the set of given points:

 and find the slope:

Hence:

Find the intersect point of the line with the y axis. Use the line equation formula:

and one of the points given in the problem.
For example, use

Therefore:

Accordingly, the correct answer is (A).

If you chose answer (B), review your calculations, paying attention to the signs. If you chose answer (C), review your calculations, especially the line equation definitions. If you chose answer (D), review your calculations, especially of n.

Answer & Explanation

The correct answer is (D).

To solve this question, you need to perform the two main steps involved in calculating the missing sides using the Pythagorean theorem.

According to the theorem, a right-angled triangle (illustrated in the picture above) contains a hypotenuse square equal to the other two sides' sum. It can also be represented in the formula: (a^2+b^2=c^2)

Look at the right-angled triangle in the question. Two sides of it are given so you can find the hypotenuse using the Pythagorean theorem. Notice that the triangle's hypotenuse is also the rectangle's missing side, which will be valuable in the next step to find its diagonal. To find the hypotenuse, place the given values in the formula (mark the missing hypotenuse with h):

Note: since all rectangle angles are right angles, and the parallel sides are equal, the diagonal of the rectangle (\(m\)) creates two equal right-angled triangles.

With the Pythagorean theorem, you can use the given side length and the length of the missing side that you found, and calculate the triangle's hypotenuse, which is the rectangle's diagonal (m)

Therefore, the correct answer is (D).

The correct answer is (D).

• First, you need to find the amount of wood required to build eight chairs. You should start by finding the amount required for one chair. It is pointed out that Sarah uses 16.5 pounds for three chairs, so in order to find the amount required for 1 chair, you need to divide it by three:

16.5÷3=15÷3+1.5÷3=5+0.5=5.5 Pounds.

• Next, multiply the result by 8 to find the amount required to build all chairs:

5.5×8=(5×8)+(0.5×8)=40+4=44 (Pounds).

• Finally, to find the cost of all the wood required, you need to multiply the amount found by the cost of one pound of wood, which is three and a half dollars:

44×3.5=(44×3)+(44×0.5)=(40×3)+(4×3)+(44÷2)=120+12+22=154 (Dollars).

Therefore, the correct answer is (D).

The correct answer is (B).

Explanation:

Using the Mean Formula:
The mean is found by adding all scores and then dividing by the number of scores. With six students and a mean of 75, the equation is:

Sum of the Known Scores:
First, add the five known scores:

So, the equation becomes:

Solve for 𝑥:
Multiply both sides of the equation by 6:

Now, subtract 380 from both sides:

Therefore, David’s score is 70.

Alternative Approach – Using Deviations from the Mean:
Another method is to consider the differences between each score and the mean (75). The differences are:

Sum these differences:

For the overall mean to be 75, the sum of all deviations (including David's deviation, 𝑥−75x−75) must equal 0:

The correct answer is D.

This answer is directly supported by the final sentence of the passage: "Despite his prolific career, Vivaldi died in poverty." This statement clearly indicates that despite Vivaldi's significant contributions to music (described as "prolific"), he did not receive adequate financial compensation, ultimately dying poor. The contrast created by "despite" emphasizes this unfortunate outcome.

Let's examine why the other options are incorrect:

Option A claims Vivaldi "was best known for his operas," but the passage specifically states he is "best-known" for "The Four Seasons," which are violin concertos, not operas.
Option B suggests Vivaldi "taught violin," but while the passage mentions he was a teacher, it does not specify what he taught.
Option C states Vivaldi "lived in the 1800s," but the passage clearly identifies him as an "18th century" composer (the 1700s, not the 1800s).

The correct answer is A.

This statement contains an opinion because of the subjective phrase "seems to be better off." This phrasing indicates a judgment or interpretation rather than a verifiable fact. The word "seems" signals uncertainty or interpretation, and "better off" represents a value judgment about the butterfly's condition.
The other options present measurable, verifiable facts:

Option B states the butterfly's diet as caterpillar, which is a biological fact.
Option C provides specific geographical measurement (50 miles) and timeframe (two decades) that could be objectively verified.
Option D combines two factual statements about the butterfly's historical population status ("scarce in the 1980s") and its geographical movement (spreading northward).

The correct answer is C.
This option accurately captures the dual focus of the passage: both the specific case of the Brown Argus butterfly benefiting from climate change and the broader context that such benefit is unusual. The passage establishes this contrast explicitly in multiple places:

"Little benefit is expected from climate change, but scientists have found at least one species..."
"...what makes the Brown Argus butterfly different is that the change in range has actually benefited the species."
"But the Brown Argus butterfly is likely to be the exception to climate change, not the rule."
"...far more species will suffer."

Options A and B each capture only one aspect of this dual focus, making them incomplete representations of the main idea. Option D contradicts the passage's conclusion that the butterfly is "the exception to climate change, not the rule" and that scientists expect "far more species will suffer."

The correct answer is D.

The first paragraph exhibits a cause-effect structure because it:

Identifies a cause: climate change/warming world
Presents an effect: the Brown Argus butterfly increasing its range northward by 50 miles
Makes an explicit connection between the two: "...in a rapidly warming world"

The paragraph specifically focuses on how one phenomenon (climate change) has led to another (the butterfly's range expansion). It establishes this relationship as notable because the effect is beneficial rather than harmful.
The other text structures don't apply because:

Sequence (A): The paragraph doesn't present events in chronological order.
Problem-solution (B): While climate change is a problem, the paragraph doesn't present the butterfly's adaptation as a solution.
Definition-example (C): The paragraph doesn't define a term and then illustrate it with an example.

The correct answer is B.

This sentence demonstrates correct subject-verb agreement. The subject is "The two boys who played together," which is plural, and it correctly pairs with the plural verb form "go."

Let's analyze why the other options are incorrect:

Option A: "Some of them are from other countries, but all speaks English well."
The subject "all" is plural but is incorrectly paired with the singular verb "speaks." It should be "all speak."
Option C: "Here is the books you were looking for all morning."
The subject "the books" is plural, but it's matched with the singular verb "is." It should be "Here are the books..."
Option D: "My favorite basketball team are the Houston Rockets."
While "the Houston Rockets" is plural, the subject is actually "team," which is singular. The correct form would be "My favorite basketball team is the Houston Rockets."

The correct answer is A.

This sentence contains vague pronoun use because the relative pronoun "which" has an unclear antecedent. "Which" could refer to:

The fact that Callie styled her hair in a French braid
The heavy rain outside

Since both could logically be the reason she was late for work, the pronoun "which" is ambiguous.
The other options have clear pronoun references:

Option B: "Don't listen to them about anything." While "them" isn't specified in this isolated sentence, this isn't a case of vague pronoun use but rather an unspecified antecedent (likely clear in the broader context).
Option C: "Amelie and Jemma went to the mall to try on clothes, and they had a great time." The pronoun "they" clearly refers to both Amelie and Jemma.
Option D: "It isn't wise to have a tank of fish without a filter because it will get dirty." The first "it" is a dummy subject, and the second "it" clearly refers to "a tank of fish."

The correct answer is A.

This title follows standard capitalization rules for titles, which require:

Capitalizing the first word
Capitalizing the last word
Capitalizing all major words (nouns, pronouns, verbs, adjectives, adverbs)
Not capitalizing articles (a, an, the), short prepositions, and coordinating conjunctions unless they are the first or last word

"The Raft of the Medusa" correctly capitalizes:

"The" (first word)
"Raft" (noun)
"Medusa" (proper noun)
While correctly leaving "of" (short preposition) in lowercase.

The other options contain capitalization errors:

Option B: "In Advance Of the Broken Arm" - incorrectly capitalizes "Of" (preposition)
Option C: "Through The Night Softly" - incorrectly capitalizes "The" (article) in the middle of the title
Option D: "I Love You With my Ford" - incorrectly leaves "my" (possessive pronoun) in lowercase while incorrectly capitalizing "With" (preposition)

The correct answer is A.

Option A: "plateau" - correctly spelled noun referring to a flat, elevated landform
Option B: "temparature" - incorrectly spelled; the correct spelling is "temperature" (note the "e" after "p" and before "r")
Option C: "cataloge" - incorrectly spelled; the correct spelling is either "catalog" (American English) or "catalogue" (British English)
Option D: "physician" - the explanation incorrectly states that this option contains a mistake ("phisician should be physician").