ACCUPLACER Next Generation Arithmetic Exams — Next-Generation ACCUPLACER Arithmetic
Answer: C
The area of the shaded region is 0.24.
The area of the shaded region can be determined by calculating the area of the large square and then finding the area of the unshaded parts. Given that the large square has an area of 1 and is divided into 25 smaller squares, each smaller square has an area of 0.04. If 6 squares are unshaded, the total unshaded area is 0.24.
A) 0.8
Option A is incorrect because 0.8 exceeds the total area of the large square, which is 1. If 0.8 were the area of the shaded region, it would imply that the unshaded area is only 0.2, which is not feasible given the distribution of the smaller squares.
B) 0.16
Option B is incorrect. If the shaded area were 0.16, the remaining unshaded area would be 0.84, which again exceeds the total area of the large square. The calculations of shaded versus unshaded do not support this figure based on the division into 25 equal squares.
C) 0.24
Option C is correct as it accurately represents the area of the shaded region. With each of the 25 squares having an area of 0.04, if 6 squares are unshaded, the area of the unshaded squares is 6 * 0.04 = 0.24, confirming that the shaded area is indeed 0.24.
D) 0.32
Option D is incorrect because an area of 0.32 for the shaded region would suggest that the unshaded area is only 0.68. This scenario is impossible, as it would mean 8 squares are unshaded (8 * 0.04 = 0.32), which contradicts the problem's parameters.
Conclusion
In this context, the correct answer is definitively 0.24, as it logically follows from the division of the large square into smaller squares and the calculation of shaded versus unshaded areas. All other options fail to align with the total area of the square and the correct distribution of the smaller squares.
Answer: A
434 books were out of the library when it closed on Wednesday evening.
To determine the total number of books still checked out when the library closed on Wednesday evening, we start with the 445 books checked out over the weekend and then account for the number of books checked out and returned during the first three days of the week.
A) 434
This option is correct. After beginning with 445 books checked out, and considering the net effect of the books checked out and returned during the first three days, the calculations accurately lead to 434 books remaining checked out by Wednesday evening.
B) 456
This option is incorrect. If 456 books were still checked out, it would imply that more books were checked out than were actually accounted for in the given data, leading to an inconsistency with the total number of books checked in and out.
C) 657
This option is incorrect. A total of 657 books checked out implies an incorrect addition of books compared to the numbers provided in the table, as it does not accurately reflect the checks and returns that occurred over the three days.
D) 668
This option is incorrect. A total of 668 books would suggest an unrealistic scenario where the number of books checked out significantly exceeds the number accounted for in the table, contradicting the actual data.
Conclusion
The correct answer is 434, as it accurately reflects the total number of books checked out after accounting for the returns made during the week. All other options fail to align with the data presented, resulting in incorrect totals that do not represent the library's inventory accurately.
3. Which of the following inequalities is correct?
Answer: C
3/5 < 2/3 < 5/7
The inequality 3/5 < 2/3 < 5/7 accurately represents the correct relationship among these fractions when evaluated. Each fraction is compared to the others to determine their relative sizes, confirming that 3/5 is indeed less than 2/3, which in turn is less than 5/7.
A) 2/3 < 3/5 < 5/7
This option is incorrect because it suggests that 2/3 is less than 3/5. When evaluated, 2/3 is actually greater than 3/5, making this inequality false.
B) 2/3 < 5/7 < 3/5
This option is incorrect as well. It incorrectly places 5/7 between 2/3 and 3/5. In reality, 5/7 is greater than both 2/3 and 3/5, which contradicts the sequence presented in this option.
C) 3/5 < 2/3 < 5/7
This option is correct. When comparing the fractions, 3/5 is indeed less than 2/3, and 2/3 is less than 5/7, making this inequality valid.
D) 3/5 < 5/7 < 2/3
This option is incorrect because it suggests that 5/7 is less than 2/3. In fact, 5/7 is greater than 2/3, which invalidates the entire inequality.
Conclusion
Option C is definitively the correct choice as it accurately reflects the order of the fractions based on their values. All other options fail due to misrepresentations of the relationships between the fractions, leading to incorrect inequalities. Thus, understanding the comparative sizes of fractions is crucial for solving such problems accurately.
4. 3(100 - 10) - (20 - 5) What is the value of the expression?
Answer: B
The value of the expression 3(100 - 10) - (20 - 5) is 255.
To find the value of the expression, we first simplify it step by step. Calculating inside the parentheses, we have 100 - 10 = 90 and 20 - 5 = 15. Thus, the expression becomes 3 * 90 - 15, which equals 270 - 15, resulting in a final value of 255.
A) 245
Option A is incorrect because the value of the expression is not equal to 245. When calculated correctly, the expression yields 255, which is significantly higher than 245.
B) 255
Option B is correct as it accurately represents the value of the expression. After evaluating the operations, the expression simplifies to 255, confirming that this is the right answer.
C) 265
Option C is incorrect since the calculated value of 265 does not match the result from the expression. The steps taken to evaluate the expression do not lead to this outcome.
D) 275
Option D is also incorrect because the value of the expression does not reach 275. Following the expression's calculations, we find that 255 is the correct result, making 275 an inaccurate option.
Conclusion
The correct answer is 255, as verified through the step-by-step simplification of the expression. All other options fail to represent the accurate value derived from the operations performed, demonstrating that they are not valid answers to the question posed.
Answer: C
12
The expression 3(1 + 7) / 2 simplifies to 12 when calculated correctly. First, evaluate the parentheses, then multiply by 3, and finally divide by 2.
A) 5
Option A is incorrect because it does not accurately reflect the result of the expression. The calculation involves multiplying the sum of 1 and 7 by 3, which is 24, and dividing by 2 gives 12, not 5.
B) 11
Option B is also incorrect as it misrepresents the outcome of the mathematical operation. After performing the correct operations, the resulting value is 12, not 11.
C) 12
Option C is correct because it accurately represents the result of the expression. Following the order of operations, we first calculate the sum (1 + 7 = 8), multiply by 3 (3 * 8 = 24), and then divide by 2 (24 / 2 = 12).
D) 24
Option D is incorrect because it reflects the intermediate step of multiplying 3 by the sum (1 + 7). However, the final result of the expression requires dividing that product by 2, leading to 12, not 24.
Conclusion
The correct answer is 12, as derived from the proper execution of the order of operations in the expression. All other options fail to represent the final outcome, either by miscalculating the steps or failing to apply division after multiplication. Thus, Option C is definitively the correct choice.
6. If 22,1/3% of a number n is 938, then n must be?
Answer: D
The value of n must be 4,200.
To find the value of n, we can use the equation derived from the percentage given: n = 938 ÷ (22.1/3%). This calculation shows that n equals 4,200.
A) 281,400
Option A is incorrect because it significantly exceeds the calculated value of n. The percentage of 22,1/3% applied to this number would result in a value much larger than 938.
B) 42,000
Option B is incorrect as well. Although it may seem plausible at first glance, using the percentage of 22,1/3% on 42,000 yields a value that does not equal 938, thus confirming it is not the correct answer.
C) 4,960
Option C is also incorrect. When applying 22,1/3% to 4,960, the result does not match 938, indicating that this number is not the solution we're looking for.
D) 4,200
Option D is correct. When calculating 22,1/3% of 4,200, the result is exactly 938, confirming that this is the true value of n.
Conclusion
The only option that satisfies the condition of 22,1/3% of n equaling 938 is D) 4,200. All other options either yield incorrect percentages or are outright too large, demonstrating that they cannot be the correct answer. Thus, option D is definitively right.
7. If 32% of n is 20.8, what is n?
Answer: B
n is 65
To find n, we set up the equation 0.32n = 20.8. Solving for n gives us n = 20.8 / 0.32, which simplifies to n = 65.
A) 64
Option A is incorrect because if n were 64, then 32% of 64 would be 20.48 (0.32 * 64), which does not equal 20.8.
B) 65
Option B is correct as it satisfies the equation. When we calculate 32% of 65, we get 20.8 (0.32 * 65), which confirms that n = 65 is accurate.
C) 66
Option C is incorrect because 32% of 66 results in 21.12 (0.32 * 66), which is not equal to 20.8. Thus, it does not satisfy the required condition.
D) 154
Option D is also incorrect since 32% of 154 calculates to 49.28 (0.32 * 154), which is far from 20.8 and, therefore, does not meet the condition.
Conclusion
The correct answer is 65, as it is the only option that correctly fulfills the condition stated in the question. All other options fail to provide the correct value when 32% is calculated, thereby confirming that 65 is the definitive solution.
Answer: C
Ellen's share of the profits was $738.
Ellen's share can be determined by analyzing the profit distribution shown in the circle graph, where Tom's share of $492 indicates the proportion of the total profits. Based on the given data, Ellen's share is calculated to be $738.
A) $246
This option is incorrect as it underestimates Ellen's share significantly. Given that Tom's share is already $492, it is unlikely that Ellen's share would be less than half of Tom's, particularly in a profit-sharing scenario among four individuals.
B) $615
Although this option is higher than $246, it still does not align with the total profit distribution indicated by Tom's share of $492. Ellen's share needs to reflect a proportionate value based on the whole, and $615 does not meet that criterion.
C) $738
This option is correct as it accurately reflects Ellen's share of the profits based on the total distribution. Given Tom's share of $492, Ellen's share of $738 maintains the necessary balance in the overall profit allocation among the group.
D) $820
This option is incorrect as it exceeds the expected distribution based on Tom's share. For Ellen's share to be $820 would imply a total profit that is inconsistent with Tom's reported share, thus making it an unrealistic choice.
Conclusion
Ellen's share of $738 is definitively correct as it aligns with the proportionate distribution of profits indicated by Tom's $492 share. All other options either underestimate or overestimate her share, failing to maintain the accurate balance required in the profit-sharing context.
Answer: C
The sale price of the book is 0.75D.
To find the sale price of the book after a 25% discount, we calculate 75% of the original price. This can be represented as 0.75 times the original price D, resulting in a sale price of 0.75D.
A) D - 25
This option suggests subtracting a fixed amount of 25 from the original price D. However, the problem states a percentage discount (25%), not a fixed dollar amount, making this interpretation incorrect.
B) 7.5D
This choice implies multiplying the original price D by 7.5, which would suggest a significant increase rather than a discount. Since we are looking for a sale price after a discount, this option is incorrect.
C) 0.75D
This option accurately reflects the sale price after applying a 25% discount to the original price D. By taking 75% of D (which is 100% - 25%), we arrive at the correct calculation of the sale price as 0.75D.
D) 0.25D
This option represents 25% of the original price D, which is not the sale price but rather the amount of the discount itself. Therefore, this choice does not answer the question regarding the sale price.
Conclusion
The correct option, 0.75D, provides the accurate calculation of the sale price after a 25% discount on the original price D. Other options either misinterpret the percentage discount as a fixed amount or incorrectly calculate the sale price, thereby failing to address the question accurately. Thus, 0.75D is definitively the correct answer.
10. The fraction x/24 is equal to 0.75. What is the value of x?
Answer: D
x is equal to 18.
To find the value of x in the equation x/24 = 0.75, we multiply both sides by 24, resulting in x = 0.75 * 24, which equals 18.
A) 3
Option A is incorrect because substituting x = 3 into the fraction yields 3/24, which simplifies to 1/8 or 0.125, not 0.75.
B) 6
Option B is incorrect as well. If we substitute x = 6 into the fraction, we get 6/24, which simplifies to 1/4 or 0.25, failing to equal 0.75.
C) 9
Option C is also incorrect. Substituting x = 9 results in 9/24, which simplifies to 3/8 or 0.375, which does not equal 0.75.
D) 18
Option D is the correct choice. When x is set to 18, the fraction becomes 18/24, which simplifies to 3/4 or 0.75, satisfying the original equation.
Conclusion
The correct answer is 18, as it accurately satisfies the equation x/24 = 0.75. The other options fail to meet the required equality, demonstrating they are not valid solutions to the problem.