Accuplacer Practice Test 2 Section III: Arithmetic

1. How many numbers are on the complete number line?

7

100

1,000,000

None of the above

D. The correct solution is none of the above. The complete number line comprises all possible numbers, including fraction/decimal numbers. This is an infinite number of numbers. See Lesson: Basic Addition and Subtraction.

Explanation

D. The correct solution is none of the above. The complete number line comprises all possible numbers, including fraction/decimal numbers. This is an infinite number of numbers. See Lesson: Basic Addition and Subtraction.

2. The histogram below shows the number of text messages between a group of friends in a week. Which statement is true for the histogram?

There are 30 friends in the group.

The highest frequency is 8 friends.

The bin size is 1,000 text messages.

Two bins have the same frequency.

D. The correct solution is two bins have the same frequency. The bins 400–600 and 800–1,000 have three friends. See Lesson: Interpreting Categorical and Quantitative Data.

Explanation

D. The correct solution is two bins have the same frequency. The bins 400–600 and 800–1,000 have three friends. See Lesson: Interpreting Categorical and Quantitative Data.

3. If a certain widget sells for $5 each and Linda has $321, how many widgets can she buy?

1

64

65

1,605

B. Use division, ignoring the remainder (which is how much Linda has left after paying $5 per widget). In this case, 321 ÷ 5 = 64 with a remainder of 1. She can buy 64 widgets. See Lesson: Basic Multiplication and Division.

Explanation

B. Use division, ignoring the remainder (which is how much Linda has left after paying $5 per widget). In this case, 321 ÷ 5 = 64 with a remainder of 1. She can buy 64 widgets. See Lesson: Basic Multiplication and Division.

4. Write 145.5% as a decimal.

1.455

14.55

145.5

1455

A. The correct answer is 1.455 because 145.5% as a decimal is 145.5 ÷ 100 = 1.455. See Lesson: Decimals and Fractions.

Explanation

A. The correct answer is 1.455 because 145.5% as a decimal is 145.5 ÷ 100 = 1.455. See Lesson: Decimals and Fractions.

5. Which statement is true?

The sum of a positive number and a negative number is always negative.

The sum of a positive number and a negative number is always positive.

The sum of a positive number and a negative number is always zero.

None of the above.

D. The correct solution is none of the above. Try some test cases. For example, –1 + 5 = 4, but –5 + 1 = –4. Also, –5 + 5 = 0. Counterexamples therefore show that statements A, B, and C are false. See Lesson: Basic Addition and Subtraction.

Explanation

D. The correct solution is none of the above. Try some test cases. For example, –1 + 5 = 4, but –5 + 1 = –4. Also, –5 + 5 = 0. Counterexamples therefore show that statements A, B, and C are false. See Lesson: Basic Addition and Subtraction.

6. Three bands on a tour have documented their ticket sales. Band 1: Mean: 13,500, Standard Deviation: 1,000 Band 2: Mean: 14,250, Standard Deviation: 500 Band 3: Mean 12,500, Standard Deviation: 1,500 Which statement best describes the mean and standard deviation?

Band 1 had the greater average, but Band 3 had a higher standard deviation.

Band 2 had the greater average, but Band 3 had a higher standard deviation.

Band 1 had the greater average, but Band 2 had a higher standard deviation.

Band 2 had the greater average, but Band 1 had a higher standard deviation.

B. The correct solution is Band 2 had the greater average, but Band 3 had a higher standard deviation. The largest mean is Band 2. Although Band 1 had a higher deviation than Band 2, option B is the best answer because Band 3 had the largest standard deviation, which means the data are more spread out from the mean. See Lesson: Interpreting Categorical and Quantitative Data.

Explanation

B. The correct solution is Band 2 had the greater average, but Band 3 had a higher standard deviation. The largest mean is Band 2. Although Band 1 had a higher deviation than Band 2, option B is the best answer because Band 3 had the largest standard deviation, which means the data are more spread out from the mean. See Lesson: Interpreting Categorical and Quantitative Data.

7. How many times can 5 go into –255?

51

-5

0

-51

D. This question involves another way to express division. In this case, it is –255 ÷ 5. When dividing signed numbers, remember that if the dividend and divisor have different signs, the quotient is negative. Otherwise, the process is the same as dividing whole numbers. The division algorithm yields –51. See Lesson: Basic Multiplication and Division.

Explanation

D. This question involves another way to express division. In this case, it is –255 ÷ 5. When dividing signed numbers, remember that if the dividend and divisor have different signs, the quotient is negative. Otherwise, the process is the same as dividing whole numbers. The division algorithm yields –51. See Lesson: Basic Multiplication and Division.

8. How many dogs are necessary to make a cat-to-dog ratio of 3:2 in an area with 1,425 cats?

285

950

2,138

2,375

B. The correct answer is B. Set up the proportion of dogs to cats (or vice versa):

Since 1,425 ÷ 3 = 475, the number of dogs is the product of 2 and 475, or 950. See Lesson: Ratios, Proportions, and Percentages.

Explanation

B. The correct answer is B. Set up the proportion of dogs to cats (or vice versa):

Since 1,425 ÷ 3 = 475, the number of dogs is the product of 2 and 475, or 950. See Lesson: Ratios, Proportions, and Percentages.

9.

Explanation

10. Write 1.5 as a percent.

0.15%

1.5%

15%

150%

D. The correct answer is 150% because 1.5 as a percent is 1.5 × 100 = 150%. See Lesson: Decimals and Fractions.

Explanation

D. The correct answer is 150% because 1.5 as a percent is 1.5 × 100 = 150%. See Lesson: Decimals and Fractions.

11. Which expression is different from the others?

4:9

0.44

44%

D. The correct answer is D. Converting answers A and D to decimals yields (approximately) 0.44 and 2.25, respectively. Answers B and C are both equal to 0.44, so answer D differs from the others. See Lesson: Ratios, Proportions, and Percentages.

Explanation

D. The correct answer is D. Converting answers A and D to decimals yields (approximately) 0.44 and 2.25, respectively. Answers B and C are both equal to 0.44, so answer D differs from the others. See Lesson: Ratios, Proportions, and Percentages.

12. Multiply.

See Lesson: Multiplication and Division of Fractions.

Explanation

See Lesson: Multiplication and Division of Fractions.

13.

See Lesson: Multiplication and Division of Fractions.

Explanation

See Lesson: Multiplication and Division of Fractions.

14.

See Lesson: Decimals and Fractions.

Explanation

See Lesson: Decimals and Fractions.

15.

See Lesson: Multiplication and Division of Fractions.

Explanation

See Lesson: Multiplication and Division of Fractions.

16. How many whole numbers are less than 3 but greater than –3?

2

3

4

5

B. The correct solution is 3. The whole numbers include 0, 1, 2, 3,…. All whole numbers are greater than –3, but only 0, 1, and 2 are less than 3. See Lesson: Basic Addition and Subtraction.

Explanation

B. The correct solution is 3. The whole numbers include 0, 1, 2, 3,…. All whole numbers are greater than –3, but only 0, 1, and 2 are less than 3. See Lesson: Basic Addition and Subtraction.

17. If a survey finds that 120 people are in group X and 230 people are in group Y, what is the ratio of people in group Y to people in group X or group Y?

12:35

12:23

23:35

35:23

C. The ratio is 23:35. The first part of the ratio is the number of people in group Y, which is 230. The second part is the number of people in either group, which is the sum 120 + 230 = 350. The ratio is therefore 230:350 = 23:35. See Lesson: Ratios, Proportions, and Percentages.

Explanation

C. The ratio is 23:35. The first part of the ratio is the number of people in group Y, which is 230. The second part is the number of people in either group, which is the sum 120 + 230 = 350. The ratio is therefore 230:350 = 23:35. See Lesson: Ratios, Proportions, and Percentages.

18. The high temperatures in degrees Fahrenheit for the beginning of April are 45, 48, 53, 57, 52, 60, 58. The last temperature is 28. Compare the standard deviation and interquartile range before and after the last temperature.

The standard deviation and interquartile range increase.

The standard deviation and interquartile range decrease.

The standard deviation increases, and the interquartile range decreases.

The standard deviation decreases, but the interquartile range increases.

A. The correct solution is the standard deviation and interquartile range increase. The standard deviation increases from 5.06 to 9.61, and the interquartile range increases from 9.5 to 11. See Lesson: Interpreting Categorical and Quantitative Data.

Explanation

A. The correct solution is the standard deviation and interquartile range increase. The standard deviation increases from 5.06 to 9.61, and the interquartile range increases from 9.5 to 11. See Lesson: Interpreting Categorical and Quantitative Data.

19. If the captain of a search party evenly assigns 242 people into 11 groups, how many people are in each group?

11

22

24

37

B. Because the question indicates that the 11 groups have the same number of people, division is appropriate. The 242 people are divided evenly among 11 groups. This can be expressed as 242 ÷ 11 = 22 people in each group. The division algorithm is helpful here. See Lesson: Basic Multiplication and Division.

Explanation

B. Because the question indicates that the 11 groups have the same number of people, division is appropriate. The 242 people are divided evenly among 11 groups. This can be expressed as 242 ÷ 11 = 22 people in each group. The division algorithm is helpful here. See Lesson: Basic Multiplication and Division.

20. The box plot below shows the amount three families spent each week on groceries. Which statement describes the median and interquartile range?

The median is the greatest for Family 2, but the interquartile range is greater for Family 3.

The median is the greatest for Family 2, but the interquartile range is the same for all families.

The median is the greatest for Family 1, but the interquartile range is greater for Family 3.

The median is the greatest for Family 1, but the interquartile range is the same for all families.

D. The correct solution is the median is the greatest for Family 2, but the interquartile range is the same for all families. The median is $110 for Family 2, but the interquartile range is $35 for each family. See Lesson: Interpreting Categorical and Quantitative Data.

Explanation

D. The correct solution is the median is the greatest for Family 2, but the interquartile range is the same for all families. The median is $110 for Family 2, but the interquartile range is $35 for each family. See Lesson: Interpreting Categorical and Quantitative Data.