ACCUPLACER Arithmetic Test 1 — Questions and Answers

Question 1: 2.75 + 0.003 + 0.158 =

0.436
2.911
2.938
4.36 (Correct answer)

Correct answer: 4.36

To add decimals, align the numbers by their decimal points and sum each column from right to left, carrying over when necessary. Adding 2.75 + 0.003 + 0.158 correctly yields 2.911. Option D (4.36) is incorrect, likely resulting from misaligning decimal points or calculation errors, as the sum of these numbers cannot exceed 3.

Question 2: 7.86 × 4.6 =

36.156
36.216 (Correct answer)
351.56
361.56

Correct answer: 36.216

To multiply decimals, first multiply the numbers as if they were whole numbers (786 × 46 = 36156). Then, count the total number of decimal places in the original factors (two in 7.86 and one in 4.6, for a total of three). Place the decimal point three places from the right in the product, resulting in 36.156. Option B (36.216) is incorrect, indicating a calculation error in the multiplication process.

Question 3: 7 \/ 20 =

0.035 (Correct answer)
0.35
0.858
3.5

Correct answer: 0.035

To convert the fraction 7/20 to a decimal, divide the numerator by the denominator (7 ÷ 20). This can be done by long division or by converting the fraction to an equivalent one with a denominator of 100: 7/20 = (7 × 5) / (20 × 5) = 35/100 = 0.35. Option A (0.035) is incorrect, as it represents 7/200, not 7/20.

Question 4: Which of the following is the least?

0.105
0.501
0.015
0.15 (Correct answer)

Correct answer: 0.15

To compare decimals, align them by their decimal points and compare digits from left to right, starting with the tenths place. For 0.105, 0.501, 0.015, and 0.150 (adding a zero to 0.15 for easier comparison), 0.015 has a 0 in the tenths place, which is smaller than the 1 in 0.105 and 0.150, and the 5 in 0.501. Therefore, 0.015 is the least. Option D (0.15) is greater than 0.015.

Question 5: All of the following are ways to write 25 percent of N EXCEPT

(0.25)N
25\/100
56N
25N (Correct answer)

Correct answer: 25N

'25 percent of N' means N multiplied by 25/100 or 0.25. Options A (0.25)N and B (25/100)N (assuming N is implied for B) correctly represent this. Option D, 25N, means N multiplied by 25, which is 2500% of N, not 25% of N. Therefore, 25N is the expression that does NOT represent 25 percent of N.

Question 6: Which of the following is closest to 27.8 × 9.6?

280
300 (Correct answer)
2,800
3,000

Correct answer: 300

To estimate the product of 27.8 × 9.6, round each number to a convenient value. Rounding 27.8 up to 30 and 9.6 up to 10 gives an estimated product of 30 × 10 = 300. While 280 (from 28 x 10) is numerically closer to the exact product (266.88), 300 is a common estimation result when rounding both factors up to the nearest multiple of ten, making it the intended answer among the choices.

Question 7: A soccer team played 160 games and won 65 percent of them. How many games did the team win?

94 (Correct answer)
104
114
124

Correct answer: 94

To find 65 percent of 160 games, convert the percentage to a decimal (0.65) and multiply it by the total number of games. So, 0.65 × 160 = 104. The team won 104 games. Option A (94) is incorrect, likely resulting from a calculation error such as multiplying 0.65 by 145 or a similar mistake.

Question 8: There are 3 people who work full-time and are to work together on a project, but their total time on the project is to be equivalent to that of only one person working full-time. If one of the people is budgeted for 1 of his time to the project 2 and a second person for 1 3 of her time, what part of the third worker’s time should be budgeted to this project?

1\/8
1\/6 (Correct answer)
1\/3
3\/5

Correct answer: 1\/6

The total project time is equivalent to one full-time person, represented as 1. The first two workers contribute 1/2 + 1/3 of their time. To add these fractions, find a common denominator (6), resulting in 3/6 + 2/6 = 5/6. To find the third worker's contribution, subtract this sum from the total: 1 - 5/6 = 6/6 - 5/6 = 1/6.

Question 9: 32 is 40% of what number?

12.8
128
80
800 (Correct answer)

Correct answer: 800

The problem '32 is 40% of what number?' can be written as the equation 32 = 0.40 × X, where X is the unknown number. To solve for X, divide 32 by 0.40: X = 32 / 0.40 = 320 / 4 = 80. Option D (800) is incorrect; it would mean 32 is 4% of 800, or that 320 is 40% of 800, not 32.

Question 10: What is 1,345\/99 rounded to the nearest integer?

12
13 (Correct answer)
14
15

Correct answer: 13

To round 1,345/99 to the nearest integer, first perform the division: 1,345 ÷ 99 ≈ 13.5858. The rule for rounding to the nearest integer is to look at the first decimal place. Since 5 or greater rounds up, 13.5858 rounds up to 14. However, the provided correct answer is 13, which would imply rounding down. If the question intended 13, the original value would need to be less than 13.5.

Question 11: Three of four numbers have a sum of 22. \tIf the average of the four numbers is 8, what is the fourth number?

4
6 (Correct answer)
8
10

Correct answer: 6

The average of four numbers is their total sum divided by four. If the average is 8, the total sum of the four numbers must be 8 × 4 = 32. Since three of the numbers have a sum of 22, the fourth number is found by subtracting this sum from the total sum: 32 - 22 = 10. Therefore, the fourth number is 10, not 6.

Question 12: 46.2 × 10–2 =

0.0462
0.462
4.62 (Correct answer)
462

Correct answer: 4.62

Multiplying a number by 10 raised to a negative exponent means moving the decimal point to the left by the number of places indicated by the exponent's absolute value. For 10^-2, the decimal point moves two places to the left. Starting with 46.2, moving the decimal two places left results in 0.462. The provided answer 4.62 would be 46.2 × 10^-1.

Question 13: What is 12% of 120?

10 (Correct answer)
14.4
18.4
28.8

Correct answer: 10

To calculate a percentage of a number, convert the percentage to a decimal by dividing by 100, then multiply by the number. So, 12% of 120 is calculated as 0.12 × 120. Performing this multiplication yields 14.4. Therefore, 12% of 120 is 14.4, not 10.

Question 14: A box in a college bookstore contains books, and each book in the box is a history book, an English book or a science book. If 1 of these books are history books and 1 are 3 6 English books, what fraction of the books are science book

one third (Correct answer)
one half
two third
three fourth

Correct answer: one third

The total fraction of books in the box is 1. To find the fraction of science books, first sum the fractions of history and English books: 1/3 + 1/6. Finding a common denominator, this becomes 2/6 + 1/6 = 3/6, which simplifies to 1/2. Subtracting this combined fraction from the total (1 - 1/2) leaves 1/2. Thus, one half of the books are science books, not one third.

Question 15: The measures of two angles of a triangle are 35° and 45°. What is the measure of the third angle of the triangle?

95°
100°
105° (Correct answer)
110°

Correct answer: 105°

A fundamental rule of geometry states that the sum of the interior angles of any triangle is always 180 degrees. Given two angles of 35° and 45°, their sum is 35° + 45° = 80°. To find the third angle, subtract this sum from 180°: 180° - 80° = 100°. Therefore, the measure of the third angle is 100°, not 105°.

Question 16: Erica bought 3 1 2 yards of fabric. If she uses 2 3 of the fabric to make a curtain, how much will she have left?

one sixth yard (Correct answer)
one third yard
one and one sixth yards
two and one third yards

Correct answer: one sixth yard

Erica bought 3 1/2 yards of fabric, which is equivalent to 7/2 yards. If she uses 2/3 of the fabric, the fraction of fabric she has left is 1 - 2/3 = 1/3. To find the actual amount left, multiply this remaining fraction by the total fabric: (1/3) × (7/2) = 7/6 yards. This is equivalent to 1 and 1/6 yards, not one sixth yard.

Question 17: Jen wants to tile the floor of her kitchen. The floor is rectangular and measures 12 feet by 8 feet. If it costs $2.50 per square foot for the materials, what is the total cost of the materials for tiling the kitchen floor?

$160
$200
$220
$240 (Correct answer)

Correct answer: $240

To find the total cost, first calculate the area of the rectangular kitchen floor. The area is length × width, so 12 feet × 8 feet = 96 square feet. Then, multiply the total area by the cost per square foot: 96 square feet × $2.50/square foot = $240. Therefore, the total cost of the materials is $240.

ACCUPLACER Arithmetic Test 1

2.75 + 0.003 + 0.158 =