ACCUPLACER Next Generation Arithmetic Exams — Next Generation Arithmetic ACCUPLACER
1. Of the following, which best expresses 52 as a percent of 170?
Answer: A
52 is best expressed as 30% of 170.
To find what percentage 52 is of 170, we can use the formula: (part/whole) x 100. In this case, (52/170) x 100 equals approximately 30.59%, which rounds to 30%.
A) 30% of 170
This option is correct as it represents the closest approximation of 52 as a percentage of 170. Calculating 30% of 170 gives us 51, which is quite close to 52, validating that 52 can be expressed as approximately 30% of 170.
B) 33% of 170
This option is incorrect because 33% of 170 equals 56.1, which is higher than 52. Therefore, it does not accurately express 52 as a percentage of 170.
C) 35% of 170
This option is also incorrect since 35% of 170 equals 59.5, which again is greater than 52. Thus, it fails to represent 52 as a percentage of 170 accurately.
D) 40% of 170
This option is incorrect as well. Calculating 40% of 170 gives us 68, which significantly exceeds 52. Hence, it does not reflect the correct percentage representation of 52 in relation to 170.
Conclusion
The correct answer is A because it most closely represents 52 as a percentage of 170, yielding an approximate value of 30%. The other options fail as they represent percentages that exceed or do not meet the value of 52, demonstrating that they are not suitable representations for this question.
Answer: D
The cost of a plain bagel increased by 20% from last year to this year.
To determine the percentage increase in the cost of a plain bagel, we compare the difference in price to the original price. The increase from $0.75 to $0.90 represents a $0.15 increase, which is 20% of the original price.
A) 10%
This option is incorrect because a 10% increase on $0.75 would result in an increase of only $0.075, leading to a new price of $0.825, which does not match the current price of $0.90.
B) 15%
This option is also incorrect as a 15% increase on $0.75 would lead to an increase of $0.1125, resulting in a total price of $0.8625, which is not equal to the current price of $0.90.
C) 17%
Choosing 17% is incorrect since a 17% increase on $0.75 amounts to approximately $0.1275, bringing the total price to about $0.8775, which again does not match the current price of $0.90.
D) 20%
This option is correct as it accurately reflects the calculation of the percentage increase. The increase of $0.15 from the original price of $0.75 is indeed 20% of the original price, resulting in the new price of $0.90.
Conclusion
The correct answer is 20% because it accurately represents the calculation of the increase in price relative to the original cost. All other options fail to reflect the true percentage increase based on the provided prices. Thus, D is the only valid answer based on the given data.
3. 1 is 5 percent of what number?
Answer: B
1 is 5 percent of 20.
To determine what number 1 is 5 percent of, we can set up the equation 1 = 0.05 * x, where x is the number we want to find. Solving this gives us x = 20, confirming that 1 is indeed 5 percent of 20.
A) 5
Option A is incorrect because 5 cannot be the number from which 1 is 5 percent. If we calculate 5 percent of 5, we get 0.25, not 1.
B) 20
Option B is correct as it accurately reflects that 1 is 5 percent of 20. This can be easily verified by calculating 5 percent of 20, which equals 1, thus satisfying the condition of the question.
C) 25
Option C is incorrect because if we take 5 percent of 25, we obtain 1.25, which is greater than 1. Therefore, 1 cannot be 5 percent of 25.
D) 50
Option D is also incorrect as 5 percent of 50 equals 2.5, which is significantly higher than 1. Thus, 1 cannot be 5 percent of 50.
Conclusion
The correct answer is 20 because it directly satisfies the condition that 1 is 5 percent of that number. All other options fail to meet this criterion, as they either yield results greater than or less than 1 when calculating their respective 5 percent values.
Answer: B
Susan has borrowed 26 books from the school library.
To determine how many books Susan has borrowed, we can first find out how many books Linda has borrowed. Since Richard has borrowed 17 books and he has borrowed half as many as Linda, we can conclude that Linda has borrowed 34 books. Given that Linda has borrowed 8 more books than Susan, we can deduce that Susan has borrowed 26 books.
A) 25
This option is incorrect because if Susan had borrowed 25 books, then Linda would have borrowed 33 books (25 + 8). However, that would mean Richard borrowed 16.5 books, which is not possible as he has borrowed 17 books.
B) 26
This option is correct. If Susan borrowed 26 books, then Linda has borrowed 34 books (26 + 8). Since Richard has borrowed half as many as Linda, he would have borrowed 17 books (34 ÷ 2), which aligns perfectly with the given information.
C) 34
This option is incorrect because if Susan borrowed 34 books, Linda would have borrowed 42 books (34 + 8). This would imply that Richard borrowed 21 books (42 ÷ 2), which contradicts the fact that he has borrowed only 17 books.
D) 42
This option is incorrect. If Susan borrowed 42 books, then Linda would have borrowed 50 books (42 + 8). Consequently, Richard would have borrowed 25 books (50 ÷ 2), which again does not match the 17 books he actually borrowed.
Conclusion
The correct answer is 26 books, as it accurately reflects the relationships established in the problem. All other options fail to provide a consistent solution with the number of books that Richard has actually borrowed, reinforcing that option B is the only viable answer.
5. 3/8 expressed as a percent is
Answer: B
3/8 expressed as a percent is 37.50%.
To convert the fraction 3/8 into a percentage, you multiply it by 100, resulting in 37.50%. This calculation shows that 3/8 is equivalent to 37.50% when expressed in percentage form.
A) 3.75%
This option is incorrect because 3.75% represents a much smaller fraction (specifically, 3.75 out of 100) compared to 3/8. The correct conversion of 3/8 to a percentage yields a significantly higher value.
B) 37.50%
This option is correct as it accurately reflects the conversion of the fraction 3/8 into a percentage. By multiplying 3/8 by 100, we arrive at 37.50%, which is the proper representation of the fraction in percentage form.
C) 38%
This option is inaccurate because 38% does not accurately represent the value of 3/8. While it is close, it is not exact, as the precise conversion yields 37.50%.
D) 38,1/3%
This option is also incorrect as it suggests a value that is not equivalent to 3/8. The notation 38,1/3% implies a value greater than 38%, which does not align with the actual conversion of 3/8, which is 37.50%.
Conclusion
The correct answer is 37.50%, as it accurately represents the fraction 3/8 when converted to a percentage. All other options either significantly undervalue or overvalue the fraction, demonstrating a misunderstanding of the conversion process. Thus, B is the only option that correctly reflects the mathematical relationship of the original fraction.
6. ½% of 20 is?
Answer: A
½% of 20 is 1/10.
Calculating ½% of 20 yields 0.1, which can be expressed as 1/10.
A) 1/10
This option is correct because ½% of 20 is indeed 0.1, which equals 1/10. The calculation involves converting the percentage into a decimal (0.5% = 0.005) and multiplying it by 20, resulting in 0.1.
B) 1/4
This option is incorrect because 1/4 equals 0.25. Since ½% of 20 is 0.1, which is significantly less than 0.25, this choice does not reflect the correct calculation.
C) 5
This option is incorrect as 5 does not represent ½% of 20. In fact, 5 is 25% of 20, which is far greater than the 0.1 calculated from ½%.
D) 10
This option is also incorrect because 10 is 50% of 20. It overshoots the value of ½% significantly, which, as calculated, is only 0.1.
Conclusion
The correct answer is 1/10, as it accurately represents the calculation of ½% of 20. All other options fail to represent the outcome of the percentage calculation, either being too high or misrepresenting the fraction entirely. Thus, A is the only valid response.
Answer: D
Sienna has 256 DVDs.
To determine how many DVDs Sienna has, we first need to calculate how many DVDs Teri has. Since Robert has half as many DVDs as Teri and he has 32 DVDs, Teri must have 64 DVDs. Given that Sienna has four times as many DVDs as Teri, she has 256 DVDs.
A) 4
This option is incorrect as it significantly underestimates the number of DVDs Sienna possesses. Based on the calculations, Sienna's DVD count derived from Teri's is far greater than 4.
B) 16
This option is also incorrect. Although it is a higher number than 4, it still does not reflect the accurate count derived from the relationship between Sienna's and Teri's DVDs.
C) 64
This choice is incorrect as well. While it matches Teri's DVD count, Sienna has four times as many DVDs as Teri, which should lead to a much larger total.
D) 256
This option is correct. Since Teri has 64 DVDs and Sienna has four times that amount, the correct calculation is 4 x 64, which equals 256 DVDs.
Conclusion
The correct answer is 256 DVDs, as derived from the relationships between the quantities of DVDs owned by Sienna, Teri, and Robert. The other options fail to account for the multiplication factor indicated in the problem and do not align with the correct calculations.
8. Which of the following is equal to 3 * 9?
Answer: B
9 * 3 is equal to 3 * 9.
9 multiplied by 3 yields the same result as 3 multiplied by 9, both equating to 27.
A) 6 * 6
6 multiplied by 6 equals 36, which does not match the product of 3 * 9. Thus, this option is incorrect.
B) 9 * 3
This option is correct because 9 multiplied by 3 is indeed equal to 27, which is the same as 3 multiplied by 9.
C) 3 * 3 * 6
This expression calculates to 54, as 3 * 3 equals 9 and then 9 * 6 equals 54. Therefore, this option is incorrect.
D) 3 * 3 * 3 * 3
This option represents 3 raised to the fourth power, equating to 81. Since its value does not match 27, it is incorrect.
Conclusion
The answer B) 9 * 3 is definitively correct as it directly matches the product of 3 * 9, both equating to 27. The other options fail because their products do not equal 27, demonstrating the importance of understanding multiplication commutativity in this context.
9. If 3 < a < 7 < b, which of the following must be greater than 20?
Answer: C
ab must be greater than 20.
Given that 3 < a < 7 and 7 < b, we can establish that the minimum value for a is just above 3 and the minimum value for b is just above 7. Therefore, when we calculate the product ab, it will yield a value that is greater than 3 * 7, which equals 21.
A) a²
The expression a² ranges from just above 9 (since a is slightly more than 3) to just below 49 (since a is slightly less than 7). Therefore, a² can be less than 20 when a is close to 3, which disqualifies this option as a must.
B) 2b
The expression 2b starts from just above 14 (since b is slightly more than 7) and can go higher. However, since 2b could be less than 20 if b is just over 7, this option does not necessarily satisfy the condition.
C) ab
This expression is determined to be greater than 21 since the minimum values for a and b are just above 3 and 7, respectively. Therefore, ab is definitely greater than 20, making this the only option that must be greater than 20.
D) b + a
The sum b + a starts from just above 10 (since a is slightly more than 3 and b is slightly more than 7). Thus, it can be less than 20 if a is close to 3, which makes this option incorrect.
Conclusion
The expression ab is the only option that must be greater than 20, as it consistently exceeds the product of the minimum values of a and b. All other options can potentially yield values less than 20 depending on the specific values of a and b within their defined ranges. Thus, option C is definitively correct.
Answer: A
Harriet rode 1/4 of the total distance in the first 12 minutes.
Since Harriet took 48 minutes to cover the entire distance to the library, in the first 12 minutes, she would have covered a fraction of the total distance. Specifically, 12 minutes is one-fourth of 48 minutes, indicating she rode 1/4 of the total distance.
A) 1/4
This option is correct because 12 minutes represents one-fourth of the total 48 minutes it took Harriet to reach the library. Therefore, the distance covered in the first 12 minutes is indeed 1/4 of the total distance.
B) 1/3
Option B is incorrect because 1/3 of the total distance would imply that in 16 minutes, Harriet would have reached that fraction of the total distance. Since she only traveled for 12 minutes, this does not accurately reflect the time taken.
C) 1/2
This option is also incorrect. If Harriet had ridden half of the total distance, she would have taken 24 minutes (half of 48 minutes) to cover that distance. Since she only rode for 12 minutes, she did not cover half of the distance.
D) 3/4
Option D is incorrect as well. Riding 3/4 of the distance would have required Harriet to ride for 36 minutes (3/4 of 48 minutes). Since she only rode for 12 minutes, this option does not reflect the actual distance traveled.
Conclusion
In conclusion, the correct answer, 1/4, accurately represents the fraction of the total distance Harriet rode in the first 12 minutes. All other options fail to correspond to the time she spent riding relative to the total time, making them incorrect. Thus, understanding the relationship between time and distance is essential to solving this problem accurately.