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Quiz Session - Attempts With Random Questions

GACE Exam Questions

Page 9 of 27

161.

What is the midpoint between (0, 8) and (6, -4)?

  • (3, 2)

  • (0, 0)

  • (-1, 3)

  • (4, -2)

  • (1, -1)

Correct answer: (3, 2)

1. Find the midpoint of the x axis.

(0 + 6)/2 = 6/2 = 3

2. Find the midpoint of the y axis.

(8 + -4)/2 = 4/2 = 2

Therefore, the midpoint is (3, 2).

162.

Brady can grade 5 essays per hour. If he starts grading essays at 4:30 p.m., which of the following is the best estimate as to when he will be finished grading 29 essays?

  • 10:30 p.m.

  • 9:30 p.m.

  • 10:00 p.m.

  • 11:00 p.m.

Correct answer: 10:30 p.m.

Brady must grade 29 essays, which you can estimate at 30 essays. It takes 6 hours to grade 30 essays (30/5), so Brady will finish shortly before 10:30 p.m.

163.

Read the passage then answer the question that follows. 

Which of the following sentences draws attention away from the main idea of the passage?

  • Sentence 7

  • Sentence 4

  • Sentence 10

  • Sentence 12

Correct answer: Sentence 7

Sentence 7 draws attention away from the main idea of the passage. The passage is written to discuss Abraham Lincoln’s career. The mentioning of how happy his wife was to move to the White House draws attention away from the passage. 

The other sentence choices flow with their placement within the passage.

164.

Read the passage then answer the question that follows. 

Which of the following best summarizes the overall meaning of the passage?

  • New methods in science may allow for the design of smaller technology

  • Scientists are now able to precisely control photons

  • Scientists are focused on making things tinier

  • Photons function similar to optical fibers

Correct answer: New methods in science may allow for the design of smaller technology

The other answer choices are all true, but not central to the overall theme of the message.

165.

You gave three students a make-up exam, and the scores were 90, 88, and 74. What was the average score for the three make-up exams?

  • 84

  • 78

  • 82

  • 86

Correct answer: 84

To find the average of the three exams, divide the sum of the three exams by the number of exams: 

252 / 3 = 84

166.

Find all the factors of 45.

  • 1, 3, 5, 9, 15, and 45

  • 3, 5, 9, and 15

  • 0, 1, 3, 5, 9, 15, and 45

  • 5 and 9

  • 3, 5, and 9

Correct answer: 1, 3, 5, 9, 15, and 45

To determine all the factors of a number, first determine one factor and what it has to be multiplied by to get the number.

  • 1 is the first factor (0 is never a factor of any number other than 0). Since 1 × 45 = 45, 45 is also a factor.
  • The next number that can be divided evenly into 45 is 3. Since 3 × 15 is 45, 15 is also a factor.
  • The next number that can be divided evenly into 45 is 5. Since 5 × 9 is 45, 9 is also a factor.

There are no other numbers that can be divided evenly into 45, so all the factors of 45 are 1, 3, 5, 9, 15, and 45.

167.

Find the area of the shaded region.

  • 168.56 cm2

  • 152.08 cm2

  • 96.60 cm2

  • 180.08 cm2

  • 160.35 cm2

Correct answer: 168.56 cm2

1. Find the area of the square.

Area = (length)(width)

A = (28)(28) = 784 cm2

2. Since the shapes within the square form a complete circle, find the area of the circle.

Area of a circle = πr2

A = π(142)

A = 3.14(196) cm2

A = 615.44 cm2

3. Subtract the area of the circle from the area of the square.

784 - 615.44 = 168.56 cm2

168.

If 8n - t + h = z - x, what is the value of n when t = 5, h = 3, z = 3, and x = 1?

  • 1/2

  • 2

  • -1

  • 3

Correct answer: 1/2

Here is the equation you are given: 8n - t + h = z - x

Now, substitute the values you are given for t, h, z, and x: 8n - 5 + 3 = 3 - 1

8n - 2 = 2

8n = 4

n = 1/2

169.

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

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.

170.

Read the passage then answer the question that follows. 

Which of the following changes is needed in the first paragraph?

  • Sentence 4: Move the period at the end inside the quotation mark

  • Sentence 3: Change “a” to “an”

  • Sentence 5: Insert a comma after “Water”

  • Sentence 6: Insert a comma after “vapor”

Correct answer: Sentence 4: Move the period at the end inside the quotation mark

The period after the quotation mark of Sentence 4 should be moved inside the quotation mark. According to Standard American English, periods and commas are always placed inside of quotation marks, except in certain technical copy. 

The other answer choices do not need changed.

171.

If 1/3(z) - 2 = 5, what is three times the value of z?

  • 63

  • 21

  • 7

  • 3

Correct answer: 63

First, add 2 to each side of the equation: 1/3(z) = 7

Now, divide each side of the equation by 1/3: z = 21

The question asks for three times the value of z: 21 x 3 = 63

172.

What is the sum of 10 1/3, -9 2/9, and 5 2/3?

  • 6 7/9

  • 7 2/9

  • 25 2/9

  • 24 7/9

Correct answer: 6 7/9

Add the three fractional amounts. In order to get the same denominator for each fraction, change 1/3 to 3/9, and 2/3 to 6/9. Then, add the numbers, remembering that 9 2/9 is negative. The result is 6 7/9.

10 3/9 - 9 2/9 + 5 6/9 = 6 7/9

173.

Alisha is selling candy bars for the school fundraiser. She starts with a box of 30 candy bars and sells 4 on Monday, 5 on Tuesday, and 8 on Wednesday. How many candy bars does Alisha still need to sell?

  • 13

  • 15

  • 21

  • 17

Correct answer: 13

You need to subtract the total number of candy bars that Alisha has sold from the initial quantity: 

30 - 4 - 5 - 8 = 13.

174.

Read the passage then answer the question that follows. 

Which of the following sentences is a run-on sentence?

  • Sentence 2

  • Sentence 4

  • Sentence 6

  • Sentence 10

Correct answer: Sentence 2

Sentence 2 is a run-on sentence. The sentence contains two distinct sentences contained in a single sentence. A period should be placed between “storm” and “no.” 

Sentences 4, 6, and 10 are all single ideas represented in single sentences.

175.

Solve for m if n = -4:

n = 4m2 - 10m + 2

  • 3/2, 1

  • 1, 0

  • -3/2, 0

  • -1, 1

  • 0, 4

Correct answer: 3/2, 1

1. Insert the value for n into the equation.

-4 = 4m2 - 10m + 2

2. Add 4 to both sides.

-4 + 4 = 4m2 - 10m + 2 + 4

0 = 4m2 - 10m + 6

3. Factor.

(2m - 3)(2m - 2) = 0

4. Set each factor equivalent to 0 and solve for m.

2m - 3 = 0

2m = 3

m = 3/2

2m - 2 = 0

2m = 2

m = 1

176.

Read the passage then answer the question that follows. 

Which of the following sentences contains a nonstandard use of a comparative form?

  • Sentence 7

  • Sentence 4

  • Sentence 5

  • Sentence 6

Correct answer: Sentence 7

Sentence 7 contains a nonstandard use of a comparative form. The word “thicker” should be “thickest,” as the writer is comparing an individual’s fingers and toes to all of the other parts of the body. 

Sentences 4, 5, and 6 all contain standard use of a comparative form.

177.

Read the passage then answer the question that follows. 

Which of the following sentences contains a nonstandard pronoun use?

  • Sentence 3

  • Sentence 1

  • Sentence 5

  • Sentence 8

Correct answer: Sentence 3

Sentence 3 contains the indirect pronoun “who” when referring to the noun “water.” Standard American English requires the use of the pronoun “that” when referring to objects. 

Sentences 1, 5, and 8 contain standard pronoun use.

178.

Which statement about the set of numbers is false?

62 17 18 24 32 17 83 74 58

  • The median is greater than the mean

  • The mean is greater than the mode

  • The mean is greater than the median

  • The median is less than the mean

  • The range is greater than the mean

Correct answer: The median is greater than the mean

1. Find the mean by adding all the numbers together and dividing by the number of items (9).

62 + 17 + 18 + 24 + 32 + 17 + 83 + 74 + 58 = 385

385 ÷ 9 = 42.8

2. Determine the mode.

The mode is the number that is the most common in a list of numbers. Because 17 appears twice and all the other numbers appear only once, 17 is the mode.

3. Find the range.

The range is the difference between the largest and smallest numbers.

83 - 17 = 66

4. Order the numbers from least to greatest to find the median, the middle value in a list of numbers.

17 17 18 24 32 58 62 74 83

Because 32 is the middle value, it is the median. 32 is less than the mean, 42.8, so the statement "the median is greater than the mean" is false.

  • "The mode is less than the median" is true because 17 is less than 32.
  • "The mean is greater than the mode" is true because 42.8 is greater than 17.
  • "The mean is greater than the median" is true because 42.8 is greater than 32.
  • "The range is greater than the mean" is true because 66 is greater than 42.8.

179.

Read the passage then answer the question that follows. 

Which one of the following statements would the author most likely agree with regarding wearing your seat belt?

  • Wearing a seat belt could save your life if you are involved in a vehicle accident

  • Wearing a seat belt is harmful to your spinal cord

  • Parents always listen to the advice of their children

  • Wearing your seat belt during a vehicle accident increases your risk of being injured

Correct answer: Wearing a seat belt could save your life if you are involved in a vehicle accident

This statement is supported by the statistical data that is presented in the second paragraph.

180.

View the supporting details to answer the following question.

Which type of beverage saw the largest percent increase in sales from 2011 to 2012?

  • Diet Soda

  • Grape

  • Ginger Ale

  • Soda

Correct answer: Diet Soda

First, eliminate any answer choice that does not increase. Grape did not see an increase.

Next, calculate the percent increase using the percent change formula (difference / original). The total for Diet Soda in 2011 was 30,000 and 34,000 in 2012. The percent change fraction is 4,000/30,000, which equals the largest percent increase at 13.33%.

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