GACE Exam Questions

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1.

Read the passage then answer the question that follows.

Which of the following best describes the author’s attitude toward the link between fast food and obesity?

  • Unconvinced

  • Amazed

  • Angry

  • Frustrated

Correct answer: Unconvinced

The author is not convinced that obesity is caused by fast food, as he then suggests that the link could be the increased use of technology.

2.

Consider the following statement: To join the U.S. Military, all members need to be at least 18 years of age.

Which of the following statements must be true?

  • Individuals who are not at least 18 years old are not in the military

  • Everyone in the U.S. is at least 18 years old

  • All individuals in the U.S. who are at least 18 years old are members of the military

  • Some members of the military are not 18 years old

Correct answer: Individuals who are not at least 18 years old are not in the military

You are told that all members of the military are at least 18 years of age. With an "all" quantifier, find the contrapositive. The contrapositive tells you that if an individual is not at least 18 years old, he or she is not a member of the military.

3.

Read the passage then answer the question that follows.

Which of the following provides the best outline for the passage?

  • A question is asked, then answered

  • A theory is stated, then refuted

  • A statement is made, then supported

  • An argument is made, then refuted

Correct answer: A question is asked, then answered

The passage starts with the question of how much fantasy football costs employers. Then, that question is answered by stating the actual dollar amount that it costs.

4.

Angie scored in the 87th percentile on the algebra exam. Brooke scored in the 79th percentile. The exam contained 175 questions, and Angie answered 148 questions correctly. Which of the following statements must be true?

  • Brooke answered fewer than 148 questions correctly

  • Brooke answered 79 questions correctly

  • Brooke answered 138 questions correctly

  • Eight students received scores between Angie's and Brooke's

Correct answer: Brooke answered fewer than 148 questions correctly

Brooke scored in a lower percentile than Angie, so she must have answered fewer questions correctly than Angie did. Thus, she answered fewer than 148 questions correctly. 

You do not know how many questions Brooke answered correctly. Therefore, you can eliminate the answer choices that state that Brooke answered 79 or 138 questions correctly. Next, you do not know how many test takers there were. Therefore, you should not assume that there were 100 students taking the test, which is what the other answer choice does.

5.

65 less than 2 times a number is 53. What is the number?

  • 59

  • -6

  • 28

  • 89

Correct answer: 59

The algebraic equation is 2x - 65 = 53. 

To solve the equation, add 65 to both sides of the equation, giving you 2x = 118. 

Then, divide both sides by 2 to get x = 59.

6.

Find z when x equals 3 and y equals -2.

z = 6x2 + 2y2 - 2xy + 3

  • 77

  • -24

  • 32

  • -18

  • 12

Correct answer: 77

1. Insert 3 for x and -2 for y.

z = 6x2 + 2y2 - 2xy + 3

z = 6(3)2 + 2(-2)2 - 2(3)(-2) + 3

2. Simplify.

z = 6(9) + 2(4) - 2(-6) + 3

z = 54 + 8 + 12 + 3

z = 77

7.

There are 15 yellow balls and 17 red balls in a bag. What is the probability of picking a yellow ball from the bag?

  • 15/32

  • 1/2

  • 13/16

  • 7/8

  • 17/32

Correct answer: 15/32

1. Find the total number of balls in the bag.

15 + 17 = 32 balls

2. Set up a proportion representing the number of yellow balls in the bag.

There are 15 yellow balls, so the chance of picking out a yellow ball is 15/32.

8.

Read the passage then answer the question that follows.

What is the best definition for the author’s use of the word “competent”?

  • Skilled

  • Qualified

  • Adequate

  • Suitable

Correct answer: Skilled

The author uses the word competent to describe how one will become skilled at thinking.

9.

View the supporting details to answer the following question.

Which of the following types of beverages saw the smallest percent increase in sales from 2011 to 2012?

  • Root Beer

  • Soda

  • Ginger Ale

  • Diet Coke

Correct answer: Root Beer

Calculate the percent increase using the percent change formula (difference / original). The total for Root Beer in 2011 is 25,000 and 25,500 in 2012. The percent change fraction is 500/25,000, thus giving you the smallest percent increase at 2.0%.

10.

Read the passage then answer the question that follows. 

Which of the following sentences is a sentence fragment?

  • Sentence 6

  • Sentence 2

  • Sentence 4

  • Sentence 7

Correct answer: Sentence 6

Sentence 6 is a sentence fragment. The phrase “As the historian Widukind of Crovey” should be linked to Sentence 7, as it completes the entire thought: “The historian Widukind of Crovey recorded that King Gnupasson, who is mentioned in both carvings, was forced to pay tribute to the German king in that year.” 

Sentences 2, 4, and 7 are all standard sentences.

11.

Solve the following equation:

x2+ 6x + 5 = 0

  • -5, -1

  • 1, 2

  • -3, 2

  • 0, 4

  • 0, 0

Correct answer: -5, -1

1. Factor the quadratic equation.

x2+ 6x + 5 = 0

(x + 5)(x + 1) = 0 

2. Set each factor equal to 0 and solve for x.

x + 5 = 0

x = -5

x + 1 = 0 

x = -1

The solution is -5, -1.

12.

Solve for b if a is equal to -2:

b = a3 – 5a2 + 7a - 1

  • -43

  • 16

  • -27

  • 8

  • 2

Correct answer: -43

1. Insert the value of a.

b = a3 – 5a2 + 7a - 1

b = (-2)3 – 5(-2)2 + 7(-2) - 1

2. Simplify.

b = -8 – 5(4) + -14 - 1

b = -8 - 20 - 15

b = -43

13.

Read the passage then answer the question that follows. 

Which of the following sentences, when inserted into the blank, would best complete the meaning of the passage?

  • Scientists believe that this technology could be the answer to the energy crisis.

  • This technology will cost a lot of money to develop.

  • This technology will not benefit the environment.

  • This technology will make the inventor extremely rich.

Correct answer: Scientists believe that this technology could be the answer to the energy crisis.

The previous sentence states that with the new miniaturizing technology they could possibly build new applications that do not require external power sources. Thus, this technology could be the answer to the energy crisis. 

The other answer choices would be out of place for the author to suddenly state his own views.

14.

The figure is composed of a cylinder with a height of 50 inches and a cone with a height of 30 inches. The cylinder and the cone share a base that has a radius of 40 inches. What is the volume of the figure the cylinder and cone compose?

  • 96000π in³

  • 80000π in³

  • 16000π in³

  • 24000π in³

  • 22000π in³

Correct answer: 96000π in³

1. Find the volume of the cylinder.

Volume of a cylinder = πr²h

V = π(40in²)(50in) = 80000π in³

2. Find the volume of the cone.

Volume of a cone = (1/3)(πr²h)

V = (1/3)(π)(40in²)(30in) = 16000π in³

3. Add the volumes together.

80000π + 16000π = 96000π in³

15.

If 1/4p - 3 = 9, what is twice the value of p?

  • 96

  • 24

  • 12

  • 48

Correct answer: 96

First, add 3 to each side of the equation: 1/4p = 12

Now, divide each side of the equation by 1/4: p = 48

The question asks for twice the value of p: 48 x 2 = 96

16.

Read the passage then answer the question that follows. 

Which of the following sentences, if inserted as Sentence 6, would be most consistent with the passage?

  • The cattle used to be transported to the island by swimming the shallow, mile-wide straight.

  • The Scottish Government wanted to use Fuday Island as a tourist attraction.

  • Fuday Island did not have many areas with water that was drinkable.

  • The Scottish used cattle as a source of meat, and they also used the cows for dairy products.

Correct answer: The cattle used to be transported to the island by swimming the shallow, mile-wide straight.

Sentence 5 mentions that the island is used for cattle grazing and Sentence 7 mentions that the first cattle to be introduced to the island were all killed. Therefore, Sentence 6 would need to state something about cattle and how they arrived at the island. The best answer choice is: “The cattle used to be transported to the island by swimming the shallow, mile-wide straight. 

The other sentence choices do not directly relate to Sentences 5 and 7, and should not be inserted as Sentence 6.

17.

If a coin is flipped three times, what is the probability that it will land on heads all three times?

  • 1/8

  • 1/2

  • 1/4

  • 1/16

  • 1/32

Correct answer: 1/8

Since the probability of a coin landing on heads one time is 1/2, multiply 1/2 three times to find the answer.

1/2 × 1/2 × 1/2 = 1/8

18.

Brandon's math average is based on five tests. Brandon's test scores were 75, 83, 94, 85, and 98. What is Brandon's math average for the five tests?

  • 87

  • 77

  • 80

  • 85

Correct answer: 87

To find the average, take the sum of the scores and divide it by the number of tests.

435 / 5 = 87

19.

Read the passage then answer the question that follows. 

Which of the following sentences in the passage is an unnecessary shift in the point of view?

  • Sentence 9

  • Sentence 2

  • Sentence 5

  • Sentence 7

Correct answer: Sentence 9

Sentence 9 of the passage contains an unnecessary shift in the point of view. Sentence 9 is written using the first person point of view and the other sentences are written using the third person point of view.

20.

All whole numbers are divisible by:

  • 1

  • 0

  • -1

  • 100

  • 10

Correct answer: 1

All whole numbers (0, 1, 2, 3, etc.) are divisible by 1. Every whole number is an example of this rule.

No number other than 0 is divisible by 0. Only negative whole numbers are divisible by -1. Only certain whole numbers that are multiples of 100 are divisible by 100.