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ACCUPLACER Next-Generation Quantitative Reasoning, Algebra, and Statistics

Next-Generation Quantitative Reasoning, Algebra, and Statistics – Question 11 of 20

Question: Every month Tanesha pays a fixed fee of $10 to use the parking lot at her workplace. She must also pay $2 each day that she parks her car in the lot. If she parks there $x$ days in one month, which of the following represents the amount, in dollars, that she must pay for using the parking lot that month? Options:

• $2x$
• $12x$
• 12x\frac{12}{x}x12​
• $10+2x$

Answer: The correct answer is $10+2x$. This represents the fixed monthly fee of $10 plus $2 for each day $x$ that she parks.

Next-Generation Quantitative Reasoning, Algebra, and Statistics – Question 12 of 20

Question: The figure above is a semicircle of radius $x$. What is the perimeter of the figure? Options:

• $(\pi +1)x$
• $(\pi +2)x$
• $(2\pi +1)x$
• $(2\pi +2)x$

Answer: The correct answer is $(\pi +2)x$. The perimeter of a semicircle is the sum of the curved part of the semicircle (half the circumference) and the diameter. The formula is $\pi r+2r$, where $r=x$. This simplifies to $(\pi +2)x$.

Quantitative Reasoning, Algebra, and Statistics- Question 13 of 20

Question: A hose can fill a cubical tank of edge length 1 meter in 15 minutes. At this rate, how long would it take for the hose to fill a cubical tank of edge length 2 meters? Options:

• 12\frac{1}{2}21​ hour
• 1 hour
• 1121\frac{1}{2}121​ hours
• 2 hours

Answer: The correct answer is 2 hours. The volume of the tank increases with the cube of the edge length. The volume of the larger tank is 8 times the smaller one (since 23=82^3 = 823=8), so it would take 8 times longer to fill. Since 15 minutes is 14\frac{1}{4}41​ of an hour, 8×148 \times \frac{1}{4}8×41​ hour = 2 hours.