accuplacer arithmetic diagnostic practice test

Commonly used by colleges and universities to place students into appropriate courses.

Choose the best answer. If necessary, use the paper you were given.
3(1/2) * 2(1/3) =
  • A. 8(1/6)
  • B. 7(5/6)
  • C. 6(1/6)
  • D. 5(5/6)
Correct Answer & Rationale
Correct Answer: A

To solve 3(1/2) * 2(1/3), first convert the mixed numbers to improper fractions: 3(1/2) becomes 7/2 and 2(1/3) becomes 7/3. Multiplying these fractions yields (7/2) * (7/3) = 49/6. Converting 49/6 back to a mixed number gives 8(1/6). Option B, 7(5/6), results from incorrect multiplication. Option C, 6(1/6), miscalculates the product as well. Option D, 5(5/6), reflects a misunderstanding of fraction multiplication. The proper method confirms that 8(1/6) is indeed the accurate result.

Other Related Questions

Marisol has 5 times as many books as Jerry. Jerry has 15 books. How many books does Marisol have?
  • A. 10
  • B. 20
  • C. 75
  • D. 225
Correct Answer & Rationale
Correct Answer: C

To determine how many books Marisol has, multiply the number of books Jerry has (15) by 5, since Marisol has 5 times as many. This calculation yields 15 x 5 = 75. Option A (10) is incorrect as it underestimates the multiplication factor. Option B (20) also miscalculates, suggesting a much lower total. Option D (225) overestimates the number of books, resulting from an incorrect multiplication. Thus, the only accurate answer is 75, reflecting Marisol's total based on Jerry's count.
Maria worked 2 weeks, earning $435.50 the first week and $278.38 the second week. If she paid one-half of her two-week earnings for tuition, how much did she pay for tuition?
  • A. $713.88
  • B. $356.94
  • C. $217.75
  • D. $139.19
Correct Answer & Rationale
Correct Answer: B

To find the amount Maria paid for tuition, first calculate her total earnings for the two weeks. Adding her earnings from both weeks: $435.50 + $278.38 = $713.88. Since she paid one-half of her total earnings for tuition, divide this amount by 2: $713.88 / 2 = $356.94. Option A ($713.88) represents her total earnings, not the tuition amount. Option C ($217.75) and Option D ($139.19) do not correctly reflect half of her total earnings. Therefore, $356.94 accurately represents the amount she paid for tuition.
At the factory where he works, Mr. Lopez must make a minimum of 48 circuit boards per day. On Wednesday, he made 60 circuit boards. What percent of the required minimum did he make?
  • A. 125%
  • B. 112%
  • C. 80%
  • D. 25%
Correct Answer & Rationale
Correct Answer: A

To find the percentage of the required minimum that Mr. Lopez made, divide the number of circuit boards he produced (60) by the minimum required (48) and then multiply by 100. \[ \text{Percentage} = \left(\frac{60}{48}\right) \times 100 = 125\% \] Option A is correct as it reflects that he made 125% of the minimum requirement. Option B (112%) is incorrect because it underestimates his production relative to the minimum. Option C (80%) is also wrong, as it suggests he produced only a fraction of the required amount. Option D (25%) is far too low, indicating a misunderstanding of the basic calculation.
Of the following, which best expresses 52 as a percent of 170?
  • A. 30% of 170
  • B. 33% of 170
  • C. 35% of 170
  • D. 40% of 170
Correct Answer & Rationale
Correct Answer: A

To determine what percent 52 is of 170, divide 52 by 170 and multiply by 100. This calculation yields approximately 30.59%, which rounds to 30%. Option A (30% of 170) is correct, as it closely matches this percentage. Option B (33% of 170) results in 56.1, which is higher than 52. Option C (35% of 170) equals 59.5, also above 52. Option D (40% of 170) gives 68, significantly exceeding 52. Thus, only option A accurately reflects 52 as a percent of 170.