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.
Which of the following is equal to 3 * 9?
  • A. 6 * 6
  • B. 9 * 3
  • C. 3 * 3 * 6
  • D. 3 * 3 * 3 * 3
Correct Answer & Rationale
Correct Answer: B

Option B, 9 * 3, is equal to 3 * 9 due to the commutative property of multiplication, which states that changing the order of factors does not change the product. Option A, 6 * 6, equals 36, which does not match 27 (the product of 3 * 9). Option C, 3 * 3 * 6, calculates to 54, also not equal to 27. Option D, 3 * 3 * 3 * 3, equals 81, further confirming it is not equivalent to 27. Thus, only option B accurately represents the value of 3 * 9.

Other Related Questions

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.
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.
1,500 / (15 + 5) =
  • A. 75
  • B. 130
  • C. 315
  • D. 400
Correct Answer & Rationale
Correct Answer: A

To solve the expression 1,500 / (15 + 5), first calculate the sum in the parentheses: 15 + 5 equals 20. Next, divide 1,500 by 20. Performing the division gives 1,500 ÷ 20 = 75, confirming option A as the correct answer. Option B (130) results from an incorrect division or miscalculation. Option C (315) likely stems from misunderstanding the order of operations, possibly miscalculating the sum before division. Option D (400) may arise from mistakenly multiplying instead of dividing. Understanding the correct order of operations is crucial for accurate calculations.
If 40 is 20 percent of a number, then the number is what percent of 40?
  • A. 500%
  • B. 200%
  • C. 80%
  • D. 20%
Correct Answer & Rationale
Correct Answer: A

To determine what percent a number (let's call it X) is of 40, we first establish that 40 is 20% of X. This can be represented as the equation: 40 = 0.2X. Solving for X gives us X = 200. Now, to find out what percent 200 is of 40, we use the formula (part/whole) × 100, which results in (200/40) × 100 = 500%. Option B (200%) is incorrect as it mistakenly uses X instead of calculating the percentage of 40. Option C (80%) and Option D (20%) are also incorrect for similar reasons; they do not accurately reflect the relationship between 200 and 40.