ACT Exam Questions

Page 9 of 26

161.

Find the values of t that satisfy the inequality below:

-t² + 6t < 0

  • t < 0 and t > 6

  • t > 6

  • t > 0

  • t > 0 and t < 6

Correct answer: t < 0 and t > 6

-t² + 6t < 0

Upon factoring, we have:

t(-t + 6) < 0

Thus, t < 0 or -t + 6 < 0; t > 6.

We test each inequality for validity:

For t < 0, let t = -1, -t² + 6t = -1 − 6 = -7 < 0.

For t > 6, let t = 7, -t² + 6t = -49 + 42 = -7 < 0.

Therefore, t < 0 and t > 6.

162.

Choose the option that represents the best way to write the underlined portion of the sentence below.

Neither Cass nor Alex met the deadline for the scholarship application.

  • No change

  • Neither Cass or Alex

  • Neither Cass and Alex

  • Neither Cass but Alex

Neither Cass nor Alex met the deadline for the scholarship application.

"Neither" is paired with "nor," and "either" is paired with "or."

163.

Express v in terms of x and y.

x = (vy)²

  • v = (√x)/y

  • v = y√x

  • v = x/y²

  • v =√(x/y)

Correct answer: v = (√x)/y

x = (vy)² = v²y²

x = v²y²

Dividing both sides by y², we have v² = x/y².

Taking the square root of both sides, we have:

v = √(x/y²) = √(x)/y.

164.

A cars travels at a speed of 60 miles per hour over 3 hours and then 55 miles per hour over 5 hours. Determine its average speed, rounding to the nearest whole number.

  • 57 miles per hour

  • 59 miles per hour

  • 58 miles per hour

  • 56 miles per hour

Correct answer: 57 miles per hour

Distance = speed × time

Total time taken = 3 + 5 = 8 hours.

Total distance = (60 × 3) + (55 × 5) = 455 miles.

Average speed = (total distance)/(total time)

455/8 = 56.875.  

56.875 rounds up to 57 miles per hour.

165.

Read the passage then answer the following question.

The author's father did which of the following with his seat belt?

  • Buckled it behind his back

  • Buckled it across his chest

  • Nothing

  • Tied it in a knot

The first paragraph states that the author's father buckled the seat belt behind his back.

From the passage: Instead of actually putting on his seat belt, he buckled it behind him, so that he was sitting on top of the seat belt.

166.

Determine the value of m if 4 = 32^m

  • 2/5

  • 5

  • 2 1/2

  • 2

Correct answer: 2/5

Since 4 = 2 × 2 = 2² and 32 = 2 × 2 × 2 × 2 × 2 = 2⁵.

We have 4 = 32^m equivalent to 2² = 2^(5m).

Since the bases are equal, we must have 2 = 5m; thus, m = 2/5.

167.

Find the smallest number in the following set of numbers:

0.0123, 0.0200, 0.009, 0.0078, 0.01200

  • 0.0078

  • 0.0123

  • 0.009

  • 0.01200

Correct answer: 0.0078

The smallest number has the first figure (between 1 and 9) from the decimal place in the smallest position.

Considering the above, among 0.0123, 0.0200, 0.009, 0.0078, 0.01200, we have 0.009 and 0.0078 whose first figures (between 1 and 9) are in the thousandths position.

Comparing the figures in that decimal place, we know that 7 < 9. So the smallest value is 0.0078.

168.

Identify the smallest number if:

a = 1/0.001

b = 2/0.0021

c = 5/0.05

d = 1/0.00009

e = 1/0.00801

  • 1/d

  • 1/b

  • 1/c

  • 1/e

Correct answer: 1/d

a = 1/0.001; b = 2/0.0021; c = 5/0.0500; d = 1/0.00009; e = 1/0.00801

c = 5/0.0500 = 1/0.0100; and b = 2/0.0021 = 1/0.00105

Using place values, we have 0.00009 < 0.001 < 0.00105 < 0.00801 < 0.0100.

When a < b, 1/a > 1/b (As an example: 2 < 3 and 1/2 > 1/3).

Thus we have:

1/0.00009 > 1/0.001 > 1/0.00105 > 1/0.00801 > 1/0.0100

Therefore, d > a >b > e > c, and 1/d < 1/a < 1/b < 1/e < 1/c

1/d is the smallest.

169.

Choose the option that represents the best way to write the underlined portion of the sentence below.

Most people recognize Dr. King as a civil rights leader, but he was also an opponent of the war in Vietnam.

  • No change

  • leader; but he

  • leader but he

  • leader but, he

Most people recognize Dr. King as a civil rights leader, but he was also an opponent of the war in Vietnam.

This sentence consists of two independent clauses, which are joined by a coordinator. When a coordinator (in this case, "but") is used to join two independent clauses, it is always preceded by a comma.

170.

Choose the option that represents the best way to write the underlined portion of the sentence below.

Dinah Washington, a famous jazz singer; had a very distinct voice.

  • a famous jazz singer,

  • No change

  • a famous, jazz singer

  • a famous jazz singer:

Dinah Washington, a famous jazz singer, had a very distinct voice.

The phrase "a famous jazz singer" is an appositive phrase, and should be set off by commas.

171.

Read the passage then answer the following question.

The more expensive golf clubs are made of:

  • 1025-carbon steel

  • Titanium

  • Platinum

  • Lead

The author states in the first paragraph that the clubs are made from 1025-carbon steel.

From the passage: Last week I went shopping for golf clubs, and came home with a set that cost around $2,000. The set had a lot of cool features and was made out of soft 1025-carbon steel for precise impact.

172.

Find the input of the function f(x) = x² − x − 1 if the output is -1.

  • 1

  • -2

  • -1

  • 2

Correct answer: 1

If the output is -1, then we find x such that x² − x − 1 = -1; x² − x = 0.

Upon factoring, we have x(x − 1) = 0.

x = 0 and x − 1 = 0; x = 1.

From the answer choices given, x = 1.

173.

Jane can mow a lawn in 2 hours. Henry can mow the same lawn in 1.5 hours. About how long will it take to mow the lawn if Jane and Henry work together?  Round your answer to the nearest whole minute.

  • 51 minutes

  • 42 minutes

  • 72 minutes

  • 90 minutes

  • 28 minutes

Correct answer: 51 minutes

To solve this equation, change the hours to minutes and set up the following equation:

x/120 + x/90 = 1

Multiply by 360. 

3x + 4x = 360

7x = 360

x = 51.43

This answer rounds to 51 minutes.

174.

Read the passage then answer the following question.

It can reasonably be inferred from the passage that cardiovascular disease and type II diabetes:

  • Have become problems for children in recent years

  • Have been health problems for children for hundreds of years

  • Only affect the middle aged and the elderly

  • Are health problems found primarily among women

The author clearly states in the first two sentences that these are health problems faced by children that previously only affected the middle-aged and the elderly.

From the passage: These conditions were previously health problems found mostly in the middle-aged and elderly population.

175.

View the supporting details to answer the following question.

How many more Shumard Oak trees are there than the sum of Bald Cypress and Hackberry trees?

  • 199 trees

  • 569 trees

  • 405 trees

  • 363 trees

Correct answer: 199 trees

Add the number of Bald Cypress and Hackberry trees:

206 + 164 = 370

Shumard Oak trees = 569

569 − 370 = 199 trees.

176.

Choose the option that represents the best way to write the underlined portion of the sentence below.

The car, which was my mother's birthday present, and it is something she's wanted her entire life.

  • is something

  • No change

  • and is something

  • it is something

The car, which was my mother's birthday present, is something she's wanted her entire life.

A verb follows a non-essential clause. Thus, the correct usage should be "is something."

177.

Read the passage then answer the following question.

How are the employees responding to the changes taking place at work?

  • They are joining forces to try and stop the changes

  • They have resigned their positions

  • They are on strike

  • They have filed a class-action lawsuit against their employer

In the last sentence, the author states that the employees are joining forces to resist the changes.

From the passage: Employees are joining forces to stop the continuous unwanted changes that they are being forced to accept.

178.

Choose the option that represents the best way to write the underlined portion of the sentence below.

David, along with his students, is going to the museum.

  • No change

  • are going

  • be going

  • am going

David, along with his students, is going to the museum.

The subject, David, is singular. Therefore, to ensure subject-verb agreement, the verb must also be singular, in this case, "is going."

179.

Read the passage then answer the following question.

In addition to online classes, many universities also offer which of the following to accommodate working students?

  • One-day-a-week classes

  • Classes at multiple locations

  • Courses that meet every other week

  • Accelerated degree programs

The third paragraph states that universities are offering more online classes, as well as classes that meet once a week.

From the passage: Universities have noticed the need for online classes and the need for one-day-a-week classes...

180.

Read the passage, and then answer the following question.

According to the passage, the Cahaba River has suffered extinctions because of:

  • Pollution

  • A large dam that was constructed upriver

  • An invasive species of fish

  • Algae that is toxic to the lilies

In a state which leads the nation in extinctions, the Cahaba River has also suffered losses, largely due to pollution. 

In the first sentence of the fourth paragraph, the author of the passage states that the Cahaba River has experienced extinctions mostly due to pollution. The Cahaba River lily, however, continues to flourish.