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.
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 รท 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.

Other Related Questions

2(1/2 + 1/3) =
  • A. 1(2/3)
  • B. 1(5/6)
  • C. 2(1/6)
  • D. 2(5/6)
Correct Answer & Rationale
Correct Answer: A

To solve 2(1/2 + 1/3), first find a common denominator for the fractions 1/2 and 1/3, which is 6. Rewrite the fractions: 1/2 becomes 3/6 and 1/3 becomes 2/6. Adding these gives 5/6. Now, multiply by 2: 2 * 5/6 equals 10/6, which simplifies to 1(2/3). Option B, 1(5/6), results from miscalculating the addition. Option C, 2(1/6), misinterprets the multiplication step. Option D, 2(5/6), incorrectly applies the multiplication to the wrong sum. Each incorrect option reflects a misunderstanding of the operations involved.
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.
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.
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.