(Refer to the passage with Question 63.) In the passage, the sentence about the tile saw mainly serves to

illustrate why sharing a rarely used item is more practical than buying or renting it

explain why power tools are the items most frequently damaged by library patrons

argue that hardware stores charge unfairly high prices when renting out their equipment

show that most households cannot afford to buy groceries and tools in the same week

Hoping to reduce traffic on the crowded highway, the new light-rail line was approved by the city council. Construction is scheduled to begin next year. Which choice correctly revises the bolded portion?

Hoping to reduce traffic on the crowded highway, the city council approved the new light-rail line.

Hoping to reduce traffic on the crowded highway, the approval of the new light-rail line was given by the council.

Hoping to reduce traffic on the crowded highway, the new light-rail line gained the approval of the city council.

Hoping to reduce traffic on the crowded highway, it was the new light-rail line that the city council approved.

(Refer to the passage with Question 63.) In the passage, the author mentions the economist's view mainly to

raise an apparent puzzle that the members' explanation then resolves

show that economists invented the idea of rotating savings groups

prove that rotating savings groups are less efficient than banks

suggest that members misunderstand how their own groups operate

ACCUPLACER

Free ACCUPLACER Practice Questions

10 sample questions for the ACCUPLACER, with the correct answer and an explanation for each. No account needed. Try each one before you open the answer.

Sections covered on the exam: Arithmetic, Advanced Algebra & Functions, Quantitative Reasoning, Algebra & Statistics, Reading, Writing.

Question 1 · Arithmetic
What is the value of 48 ÷ 6 × 2 − 3² + 5?
- A.12
- B.15
- C.2
- D.0
Show answer and explanation
Answer: A. 12
Division and multiplication are done left to right: 48 ÷ 6 = 8, then 8 × 2 = 16. Next 3² = 9, so 16 − 9 + 5 = 12. Getting 0 comes from multiplying 6 × 2 before dividing, and 15 comes from treating 3² as 3 × 2.
Question 2 · Arithmetic
A diver is 42 feet below the water's surface. She ascends two-thirds of the way to the surface, pauses, and then descends 9 feet. What is her position now, relative to the surface?
- A.−37 feet
- B.−51 feet
- C.−5 feet
- D.−23 feet
Show answer and explanation
Answer: D. −23 feet
Two-thirds of 42 is 28, so she rises from −42 to −42 + 28 = −14 feet. Descending 9 more feet gives −14 − 9 = −23 feet. The value −37 comes from ascending only one-third of the distance (14 feet), and −5 comes from adding the 9 feet instead of subtracting it.
Question 3 · Advanced Algebra & Functions
Which of the following is the factored form of 6x² − 7x − 20?
- A.(3x + 4)(2x − 5)
- B.(6x + 5)(x − 4)
- C.(2x + 4)(3x − 5)
- D.(3x − 4)(2x + 5)
Show answer and explanation
Answer: A. (3x + 4)(2x − 5)
Look for two numbers whose product is 6(−20) = −120 and whose sum is −7: they are −15 and 8. Then 6x² − 15x + 8x − 20 = 3x(2x − 5) + 4(2x − 5) = (3x + 4)(2x − 5). The form (3x − 4)(2x + 5) expands to 6x² + 7x − 20, which has the wrong middle sign.
Question 4 · Reading
(Refer to the passage with Question 63.) In the passage, the sentence about the tile saw mainly serves to
- A.explain why power tools are the items most frequently damaged by library patrons
- B.argue that hardware stores charge unfairly high prices when renting out their equipment
- C.show that most households cannot afford to buy groceries and tools in the same week
- D.illustrate why sharing a rarely used item is more practical than buying or renting it
Show answer and explanation
Answer: D. illustrate why sharing a rarely used item is more practical than buying or renting it
The tile saw is a concrete example supporting the claim that libraries give access to things few can afford to own: it is used rarely, costly to buy, and costly to rent. The passage makes no accusation of unfair pricing, and the grocery comparison only measures cost. Damage to tools is a separate point raised later.
Question 5 · Reading
Hoping to reduce traffic on the crowded highway, the new light-rail line was approved by the city council. Construction is scheduled to begin next year.
Which choice correctly revises the bolded portion?
- A.Hoping to reduce traffic on the crowded highway, the city council approved the new light-rail line.
- B.Hoping to reduce traffic on the crowded highway, the approval of the new light-rail line was given by the council.
- C.Hoping to reduce traffic on the crowded highway, the new light-rail line gained the approval of the city council.
- D.Hoping to reduce traffic on the crowded highway, it was the new light-rail line that the city council approved.
Show answer and explanation
Answer: A. Hoping to reduce traffic on the crowded highway, the city council approved the new light-rail line.
The introductory phrase "Hoping to reduce traffic" must describe the noun that immediately follows it, and only the city council can hope. The other versions place "the approval," "the new light-rail line," or "it" right after the phrase, creating a dangling modifier that suggests a rail line or an approval was doing the hoping.
Question 6 · Arithmetic
What is the value of 72 − 4 × (15 − 3²) ÷ 3 ?
- A.136
- B.64
- C.60
- D.48
Show answer and explanation
Answer: B. 64
Start inside the parentheses: 15 − 9 = 6. Then 4 × 6 ÷ 3 = 8, so 72 − 8 = 64. The answer 136 comes from subtracting 72 − 4 first, and 48 comes from forgetting to divide by 3.
Question 7 · Arithmetic
A checking account is overdrawn, with a balance of −$48.60. The owner deposits three checks of $125.40 each and then makes four withdrawals of $62.75 each. What is the new balance?
- A.−$76.60
- B.$76.60
- C.$173.80
- D.−$174.20
Show answer and explanation
Answer: B. $76.60
The deposits total 3 × $125.40 = $376.20 and the withdrawals total 4 × $62.75 = $251.00. The balance is −$48.60 + $376.20 − $251.00 = $76.60. Treating the starting balance as positive gives $173.80, and counting only one deposit gives −$174.20.
Question 8 · Advanced Algebra & Functions
Which of the following is the complete factorization of 3x⁴ − 48?
- A.3(x − 2)²(x² + 4)
- B.3(x + 2)²(x − 2)²
- C.3(x² + 2)(x + 2)(x − 2)
- D.3(x² + 4)(x + 2)(x − 2)
Show answer and explanation
Answer: D. 3(x² + 4)(x + 2)(x − 2)
Factor out 3 to get 3(x⁴ − 16), then use the difference of squares twice: x⁴ − 16 = (x² + 4)(x² − 4) = (x² + 4)(x + 2)(x − 2). The form 3(x − 2)²(x² + 4) repeats the factor x − 2 instead of using x + 2 and x − 2. The sum x² + 4 does not factor over the real numbers.
Question 9 · Reading
(Refer to the passage with Question 63.) In the passage, the author mentions the economist's view mainly to
- A.raise an apparent puzzle that the members' explanation then resolves
- B.show that economists invented the idea of rotating savings groups
- C.prove that rotating savings groups are less efficient than banks
- D.suggest that members misunderstand how their own groups operate
Show answer and explanation
Answer: A. raise an apparent puzzle that the members' explanation then resolves
The author notes the system 'can seem puzzling' to an economist because no interest is paid, then uses members' own reasoning about spending temptation to explain its value. The author does not endorse the economist's view as proof of inefficiency, and nothing credits economists with inventing the groups.
Question 10 · Writing
The engineers who designed the prototype battery, claimed that it could hold a charge twice as long as current models, but independent testers have not yet confirmed the result.
Which choice correctly revises the bolded portion?
- A.battery claimed
- B.battery: claimed
- C.battery, claimed
- D.battery; claimed
Show answer and explanation
Answer: A. battery claimed
The subject is "The engineers who designed the prototype battery," and its verb is "claimed." No punctuation should separate a subject from its verb, even when the subject is long. A comma, semicolon, or colon at that point wrongly splits the sentence's core.

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