Praxis Core Exam Questions

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61.

The sentence below contains four portions that are identified with quotation marks. Read the sentence and determine which portion contains an error in diction, usage, idiom, or grammar.

To increase the “vineyard’s” grape yield, “they” fertilized and “sprayed” the vines on a “weekly” basis.

  • They

  • Vineyard’s

  • Sprayed

  • Weekly

  • No error

Correct answer: They

This sentence contains a pronoun error. A pronoun is being used as an ambiguous reference. The pronoun “they” does not have a clear antecedent and leaves the reader asking the question: Who fertilized and sprayed the vines? 

“Sprayed” is parallel with “fertilized,” and “vineyard’s” is written in the appropriate possessive form.

62.

What is the circumference of a circle that has an area of 36π m2?

  • 12π m

  • 6π m

  • 24π m

  • 4π m

  • 8π m

Correct answer: 12π m

1. Find the radius of the circle.

A = πr2

36π = πr2

36 = r2

r = 6 m

2. Find the circumference.

C = 2πr

C = 2π(6)

C = 12π m

63.

Choose the answer that expresses most effectively what is presented in the original sentence.

Cats may not enjoy getting a lot of attention, but a pet owner who doesn't tend to his animals' physical needs is not doing their job.

  • Is not doing his or her job

  • Is not doing their job

  • Are not doing their jobs

  • Are not doing their job

  • Should be doing their job

Correct answer: Is not doing his or her job

The pet owner in this sentence is singular, so you need a singular verb, pronoun, and direct object. The correct version of the sentence reads, "Cats may not enjoy getting a lot of attention, but a pet owner who doesn't tend to his animals' physical needs is not doing his or her job."

The remaining answer options are incorrect because they use plural versions of one or more of the verb, pronoun, or direct object.

64.

Find the product of the following:

-2 × 3 × -7 × -4 × -1

  • 168

  • -168

  • -112

  • 109

  • 160

Correct answer: 168

1. Remove the negative signs and find the product of the integers.

2 × 3 × 7 × 4 × 1 = 168

2. Because the number of negative integers in the problem is four (-2, -7, -4, and -1), an even number, the product is positive.

-2 × 3 × -7 × -4 × -1 = 

-6 × -7 × -4 × -1 = 

42 × -4 × -1 = 

-168 × -1 = 168

65.

If the value of y is between 2.089 and 3.180, which of the following could be the value of y?

  • 2.918

  • 2.078

  • 1.998

  • 3.189

  • 3.208

Correct answer: 2.918

First, eliminate any answer choice that is not greater than 2.089. This will eliminate answer choices 1.998 and 2.078.

Next, eliminate any answer choice that is not less than 3.180. This will eliminate answer choices 3.189 and 3.208.

The remaining answer choice is 2.918, the correct answer. 2.918 is located between 2.089 and 3.180.

66.

What is the measure of ∠AMQ?

  • 148º

  • 116º

  • 135º

  • 152º

  • 156º

Correct answer: 148º

First find ∠A. The total number of degrees in any triangle is 180. 

1. Subtract 74º from 180º.

180º - 74º = 106º

2. ∠B is a right angle, so subtract 90º from 106º.

106º - 90º = 16º

3. Since ΔAMQ is isoceles, we know that ∠AQM is also 16º. Subtract ∠AQM and ∠A from 180º to find ∠AMQ.

180º - 16º - 16º = 148º

67.

Read the passage and then answer the following question.

In this passage, "swinging" means which of the following?

  • Rhythmic and lively

  • Loud and brassy

  • Complicated

  • Emotionally-laden

  • Tranquil and soft

Correct answer: Rhythmic and lively

The passage states that the audience would "shout approval when something especially swinging was played." This indicates that by writing "swinging," the author is indicating that the music was exciting, rhythmic, and lively. 

The jazz music may have been loud and brassy, but this would not necessarily elicit shouts of approval. Swinging does not mean complicated or emotionally-laden, and certainly was not tranquil and soft.

68.

Last month, Kristina weighed 186 3/4 pounds. This month, she weighs 179 1/2 pounds. What is the difference between what she weighed this month and what she weighed last month?

  • 7 1/4

  • 6 3/4

  • 6 1/2

  • 6 1/4

  • 7 1/2

Correct answer: 7 1/4

To find the difference, convert all fractions to give them all the same denominator.

186 3/4 - 179 2/4 = 7 1/4.

If you use the Bowtie method, you will first need to convert the mixed numbers to improper fractions. 186 3/4 = 747/4, and 179 1/2 = 359/2.

Then, 747/4 - 359/2 = (1494 - 1436)/8 = 58/8 = 29/4 = 7 1/4.

69.

Read the passage and then answer the following question.

In this passage, aesthetic most nearly means:

  • Artistic

  • Common

  • Pleasing

  • Informal

  • Widespread

Correct answer: Artistic

Aesthetic refers to the concepts guiding the work of a particular art, such as jazz. Therefore, artistic is the best answer.

The meaning of aesthetic is not common, informal, or widespread. While something aesthetic can also be pleasing, pleasing does not fit the meaning of aesthetic in the context of the passage.

70.

In the first four hours of apple picking, Charlie picked 61, 57, 72, and 60 apples, respectively. If the average number of apples Charlie picked per hour for the first five hours was 60, how many apples did he pick in the fifth hour?

  • 50

  • 60

  • 55

  • 65

  • 70

Correct answer: 50

1. For the average of a set of data, the sum of the data entries is equal to the product of the average and the number of entries.

Average = Sum of data entries ÷ Total number of entries

Sum of data entries = Average × Total number of entries

2. Since the average number of apples picked during the first five hours is 60, the number of apples picked during that time was:

60 × 5 = 300 apples

3. The number of apples picked in the fifth hour is the number of apples picked in five hours minus the number of apples picked in the first four hours.

300 - (61 + 57 + 72 + 60) = 300 - 250 = 50 apples

71.

How many hours are there in three weeks?

  • 504

  • 168

  • 332

  • 24

  • 84

Correct answer: 504

In order to solve the problem, you need to convert the units from weeks to hours, as follows:

1 week * 7 days / 1 week * 24 hours / 1 day = 168 hours. There are 168 hours in one week.

Multiply by 3 to get 504 hours in three weeks.

72.

The diameter of a given sphere is 8 inches. What is the surface area of the sphere?

  • 64π in2

  • 12π in2

  • 28π in2

  • 72π in2

  • 60π in2

Correct answer: 64π in2

1. Find the radius of the sphere.

Diameter = 2r

8 = 2r

r = 4 inches

2. Find the surface area of the sphere.

Surface area of a sphere = 4πr2

A = 4π(42)

A = 4π(16)

A = 64π in2

73.

Choose the option that best expresses the intended meaning of the quoted portion of the original sentence; this answer should use proper grammar, diction, sentence construction, and punctuation.

“Having received science, medicine, along with business degrees,” Glenn Jones became a medicine man in South America.

  • After he had received science, medicine, and business degrees

  • Having received science, medicine, along with business degrees

  • Having received science, medicine, as well as business degrees

  • Having received science and medicine, and, also, business degrees

  • After receiving science, medicine, as well as business degrees

Correct answer: After he had received science, medicine, and business degrees

The original sentence contains errors with preposition use and failure to show a time relationship. 

The option “After he had received science, medicine, and business degrees,” corrects the issues by using the preposition “After” instead of the verb “Having” and replacing the preposition “along with” with the coordinating conjunction “and.”

74.

Choose the option that best expresses the intended meaning of the quoted portion of the original sentence; this answer should use proper grammar, diction, sentence construction, and punctuation.

When heavy snow is predicted, salt is spread on the highways “and they do this to keep the roads from becoming icy.”

  • To keep the roads from becoming icy.

  • And they do this to keep the roads from becoming icy.

  • And then the roads won’t become icy.

  • And they keep the roads from becoming icy.

  • Therefore they keep the roads from becoming icy.

Correct answer: To keep the roads from becoming icy.

The original sentence uses the pronoun “they,” for which there is no antecedent to show the relationship of the statement conveyed. The option “to keep the roads from becoming icy” eliminates the ambiguous pronoun and correctly expresses the reason for the salt being spread on the highways. 

The use of “and” to join the two clauses suggests that the two are equal, but it does not show the subordinate relationship of the second clause to the first.

75.

What is 0.3864 rounded to the nearest hundredth?

  • 0.39

  • 0.38

  • 0.4

  • 0.3

  • 0.386

Correct answer: 0.39

First, the answer must be rounded to the nearest hundredth, so eliminate answer choices 0.4, 0.3, and 0.386.

To round 0.3864 to the nearest hundredth, you need to look at the digit in the thousandths place. The digit is 6. Rounding tells you that if a digit is 5 or greater, round up.

Thus, you need to round the digit in the hundredth place from 8 up to 9: 0.39.

76.

Ruth bakes 25 pies every day. How many pies does Ruth bake in 15 days?

  • 375

  • 40

  • 125

  • 250

  • 425

Correct answer: 375

In order to find out how many pies were baked over the 15-day period, you need to multiply:

25 * 15 = 375

77.

Megan has exactly 23 weeks until she retires. How many hours does Megan have before she retires?

  • 3,864

  • 161

  • 892

  • 1,759

  • 4,254

Correct answer: 3,864

First, you will need to convert 23 weeks to days: 23 weeks * 7 days / 1 week = 161 days.

Then, convert 161 days to hours: 161 days * 24 hours / 1 day = 3,864 hours.

78.

Consider the following statement: If Darla orders lasagna for lunch, she will not eat the breadsticks.

Which of the following statements must be true?

  • If Darla ate breadsticks for lunch, she did not order lasagna

  • Darla ate lasagna with breadsticks for lunch

  • If Darla did not eat breadsticks, she must have ordered lasagna

  • Darla will not eat breadsticks for lunch

  • Darla does not like breadsticks

Correct answer: If Darla ate breadsticks for lunch, she did not order lasagna

The statement is an "If-Then" statement. Identify the contrapositive.

In this question, the contrapositive is: "If Darla ate breadsticks for lunch, she did not order lasagna."

The statement does not suggest that Darla does not like breadsticks, nor does it suggest what exactly Darla will order for her lunch.

79.

Read the passage, then answer the following question.

The author’s main point of the passage is:

  • To present what individuals do with their smartphones

  • To discuss the favorite gaming apps used on smartphones

  • To determine what apps should or should not be used on smartphones

  • To discuss how technology keeps getting tinier and smarter

  • To describe the nation's obsession with smartphones

Correct answer: To present what individuals do with their smartphones

The passage starts by stating that smartphone users were asked what they did with their smartphones and then discusses the variety of apps that they download and use on their smartphones.

80.

Wendy and Robin cut a total of 156 heads of hair this week. If Wendy cut 14 more heads of hair than Robin did, how many heads of hair did Robin cut?

  • 71

  • 48

  • 14

  • 64

Correct answer: 71

Backsolving is the easiest way to solve this problem. To backsolve, choose the answer choice that is the middle option to start with, and work toward the correct answer.

64 is the middle option in the answer bank. If Wendy and Robin cut a total of 156 heads of hair and Robin cut 64, that would leave Wendy cutting 92 heads of hair. Wendy's 92 heads of hair less Robin's 64 heads of hair equals 28 heads of hair. This answer choice proves to be too low, as you only want Wendy cutting 14 more heads of hair than Robin, so you need to choose the answer choice that is higher than 64.

The answer choice that is higher than 64 is 71. If Wendy and Robin cut a total of 156 heads of hair and Robin cut 71, that would leave Wendy cutting 85 heads of hair. Wendy's 85 heads of hair less Robin's 71 heads of hair equals 14 heads of hair. Thus, you can determine Wendy cut 14 more heads of hair than Robin did.

You can also solve this problem by setting up the algebraic equation:

(x + 14) + x = 156

14 + 2x = 156

2x = 142

x = 71