PERT Test: Practice & Info

Answer & Explanation
The correct answer is (A).

The line equation is where slope and 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).

Sarah wants to build eight identical wooden chairs for the new dinner table in her house. One pound of wood costs three and a half dollars. She uses sixteen and a half pounds to build three chairs.

How much will it cost her to build all the chairs she wants?

Answer & Explanation
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)

Look at the scores of the final English exam:

What is David's score, if the mean is 75?

Answer & Explanation
The correct answer is (B).

• The mean is the average of a data set (exam scores in this case). To find it, you add up all the data set items and divide the sum by the number of items.
  
  
• In this question, you are given most of the data set and its mean, so you can find the missing value by creating an equation and marking David's score with a variable (x):

• To solve this equation, multiply both sides by 6:

• Using the formed equation, you could discover the missing item of the data set, David's score on the exam (70), and therefore (B) is the correct answer.
  
  
• Another way of solving is by using the mean's property- the sum of the distances from the mean must be zero. If you then add the differences of all scores, including David's, from 75, it should be equal to zero.
  
  
• You can create an equation of the distances of all scores from 75 and mark David's score difference from 75 as x:
  
  88 is 13 points higher than 75 (+13), 62 is 13 points lower than 75 (-13), 100 is 25 points higher than 75 (+25), 49 is 26 points lower than 75 (-26), and 81 is 6 points higher than 75 (+6).
  Now you can create the equation to find David's difference and discover his score:
     
• David's score should be 5 points lower than 75 (-5): 75 - 5 = 70 → David's score in the exam is 70 and (B) is the correct answer.

Read the passage below before answering the questions.

Little benefit is expected from climate change, but scientists have found at least one species that seems to be better off in a rapidly warming world. The Brown Argus butterfly has increased its range in England northward by about 50 miles over the past two decades. While not unexpected—many species have already responded to recent warming by moving—what makes the Brown Argus butterfly different is that the change in range has actually benefited the species.

In its caterpillar form, the Brown Argus feeds off wild geranium plants, but only in warmer summers—which is exactly what’s been happening in England and much of the rest of the world thanks to climate change. Over the past 20 years, the Brown Argus, which was considered scarce in the 1980s, has spread northward and now flourishes in much of southern England.

As David Roy of the Centre for Ecology and Hydrology in the U.K. put it, "The change in diet represents a change to the interactions between species—in this case between a butterfly and the plants that its caterpillars eat—caused by climate warming. Changes to the interactions between species are often predicted to alter the rate at which species shift their distribution in response to climate change; and now we have demonstrated this in nature."

But the Brown Argus butterfly is likely to be the exception to climate change, not the rule. Past periods of sudden climate change in the earth’s history have led to a reduction in biodiversity and even great extinction waves. If warming keeps up at the expected rate—and we’re doing little to slow it down—far more species will suffer.

On the other hand, mostly in regard to mourning days initiated by the people, such as the day of Princess Diana’s funeral in the UK, they reflect a spontaneous bout of pure grief, sometimes manifested in the closing of shops and banks and the cancellation of sports and theater and cinema showings.

1. Which of the following sentences contains an opinion?

Answer & Explanation

1. The correct answer is (A) because the description "seems to be better off" is an opinion. The rest of the answers are facts stated in the passage.

2. The correct answer is (C) as it encapsulates both main points of the passage: the butterflies have benefitted from climate change, but most species are expected to suffer from it.

3. The correct answer is (D) Global warming has "caused" a beneficial "effect" for the Brown Argus butterfly.

4. The correct answer is (B). Consider the following breakdown of the second paragraph:

"In its caterpillar form, the Brown Argus feeds off wild geranium plants, but only in warmer summers—"
In other words: warmer summers → caterpillars feed on geranium

"which is exactly what's been happening in England and much of the rest of the world thanks to climate change."
In other words: climate change → warmer summers → butterflies feed on the geranium

"Over the past 20 years, the Brown Argus, which was considered scarce in the 1980s, has spread northward and now flourishes in much of southern England."
In other words: climate change → warmer summers → butterflies feed on the geranium → caterpillars spread northward → butterflies flourish in Southern England

Antonio Vivaldi was an 18th century Italian composer, violinist, teacher, and Catholic priest. He is recognized as one of the greatest Baroque composers, and his influence during his lifetime was widespread across Europe.

He is known mainly for composing many instrumental concertos for the violin and a variety of other instruments, as well as more than forty operas. His best-known work is a series of violin concertos known as The Four Seasons. Despite his prolific career, Vivaldi died in poverty.

From this passage one may conclude that Vivaldi ______

Answer & Explanation
Answer (D) is correct.

The passage discusses Vivaldi’s work, influence, and for what he is known. However, the passage also states that “Vivaldi died in poverty,” implying that he did not reap monetary benefits for his art.

Which of the following sentences is grammatically correct?

Answer & Explanation
The correct answer is (B).

The subject and the verb in a sentence must always agree. If the subject is singular, the verb should be singular as well. Singular verbs usually end in -s or
-es.
If the subject is plural, the verb should be plural too. Plural verbs usually do not end in -s or -es.
The only sentence in which the subject and the verb agree is in answer (B). Both the subject (two boys) and the verb (go) are plural. Therefore, the correct answer is (B).

Which of the following sentences includes an example of vague pronoun use?

Answer & Explanation
The correct answer is (A).

A pronoun is a word that refers to a specific noun in a given context, and its antecedent is the word that is being referred to. Vague pronoun use is when it is unclear what the antecedent is, as there are multiple fitting subjects or objects that could be what the pronoun in the sentence is referring to.

In the sentence in option A, the word “which” is a relative pronoun referring to something that “was the reason [Callie] was late for work.” It is unclear, however, which antecedent it is referring to—the fact that she “styled her hair in a French braid,” or “the heavy rain outside.” That is why it is considered vague pronoun use.

Which title of a work of art is capitalized correctly?

Answer & Explanation
The correct answer is (A).

The major words in the titles of works of art (but not short prepositions or the articles "the," "a," or "an," if they are not the first word of the title) should always be capitalized. Therefore, the correct answer is (A).

Choose the word that is spelled correctly.

Answer & Explanation
The correct answer is (A). 

Answer (B) is incorrect as it contains a mistake: temparature should be temperature.
Answer (C) is incorrect as it contains a mistake: cataloge should be either catalogue or catalog.
Answer (D) is incorrect as it contains a mistake: phisician should be physician.