COUNTY OF
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STUDY GUIDE
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BASIC ARITHMETIC
& SAMPLE TEST QUESTIONS
YOUR CAREER STARTS HERE.
Human Resources
Los Angeles
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County Examination Guide: Preparing for Basic Arithmetic Multiple Choice Items, Exams of Elementary Mathematics
This guide assists in preparing for County examinations containing multiple choice basic arithmetic items. It provides sample questions and instructions on how to solve basic arithmetic problems. The guide emphasizes the importance of job-related exam content and the benefits of thorough preparation.
Typology: Exams
2021/2022
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COUNTY OF
LOS ANGELES
out
ob
STUDY GUIDE
VERSION 3
BASIC ARITHMETIC
& SAMPLE TEST QUESTIONS
YOUR CAREER STARTS HERE.
Human Resources
Los Angeles County
WELCOME
Thank you for your interest in employment with the County of Los Angeles. This guide is designed to familiarize and assist you with preparing for examinations containing multiple- choice basic arithmetic items. The sample questions provided in this study guide are intended to give you an idea of the kinds of basic arithmetic items you may encounter in County tests. However, it is important to note that actual test questions will vary in format, content, and level of difficulty, depending on the job class being tested.
ABOUT THE COUNTY’S EXAMINATIONS
As an Equal Opportunity Employer, the County of Los Angeles takes steps to ensure that our exam content is job-related. We conduct studies to determine the knowledge, skills, abilities and personal characteristics that are essential to satisfactorily perform the duties of the job. These studies assist us in developing the content of our examinations. Testing applicants for jobs provides us with an objective and cost-effective means to assess the qualifications of our applicants.
HOW SHOULD I PREPARE FOR THE WRITTEN TEST?
To prepare for the written test, you should study the concepts assessed in each section. It is likely that there will be several sections to the written test in addition to arithmetic; thus, it is to your benefit to carefully read the job bulletin to determine the knowledge, skill, and ability areas the written test will cover. In addition, it is important that you read the entire written test notice for the location and time of the written test as well as for parking instructions and other important information. Pay special attention to whether testing aids/materials such as handheld calculators are allowed in the written test. If the test notice indicates that testing aids/materials are allowed, then you are strongly advised to bring these with you, as they will not be provided. On the test day, it is recommended that you arrive 15 minutes prior to the test’s starting time, wear comfortable clothes, bring an accurate watch, and make sure you are well-rested. Also, remember to bring your test notice and a picture I.D. such as a driver license, or you may not be admitted into the test!
NOTE: Applicants who require special testing arrangements such as readers or interpreters must provide seven (7) days advance notice of their disability and requested accommodation. Check the front side of the job bulletin for telephone numbers to call and make disability accommodation requests. The County will attempt to meet reasonable accommodation requests whenever possible.
TEST-TAKING TIPS
Most County examinations have a set time limit, so it is important that you work quickly, but not so fast as to become careless. Always read all the possible choices before selecting your answer. If you do not know the answer to a problem, it is usually best to skip it and move on to the others. Note that on most County examinations, your score is based on the number of correct responses. If you are not sure of the answer to a problem, eliminate the answers you believe are wrong, and mark the choice that is your best response. Above all, budget your time, pace yourself, and avoid getting bogged down on any single question.
- 9 days, 5 hours, 48 minutes 7 days, 15 hours, 9 minutes
- 3 days, 13 hours, 13 minutes
A. 19 days, 13 hours, 40 minutes B. 19 days, 12 hours, 30 minutes C. 20 days, 11 hours, 20 minutes D. 20 days, 10 hours, 10 minutes
- 80% of 35 =
A. 26
B. 27
C. 28
D. 29
- A local city applies a 5.5% tax to utility usage charges when issuing residential utility bills. What is the amount of tax that is applied to a $178.00 utility usage charge?
A. $5. B. $9. C. $14. D. $15.
- A pallet shipment has been received in a warehouse. If six boxes fit into one crate and ten crates fit onto one pallet, how many boxes are on one pallet?
A. 60 B. 66 C. 600 D. 660
- The mailroom’s automatic folding machine can fold 7,500 pages per hour. How long will it take for the machine to fold a 6-page letter for a mass mailing to 625 individuals?
A. 20 minutes B. 30 minutes C. 45 minutes D. 50 minutes
- An employee’s monthly income is $3,509.00. If the employee receives a salary increase of 4%, what is her new monthly salary?
A. $2,649. B. $2,694. C. $3,649. D. $3,694.
- In a Social Services Agency, each of the 9 employees on a team is required to process 12 cases per day. On a particular day, one employee calls in sick and two others are on vacation. Provided the cases are distributed equally among the remaining team members, how many cases will each team member have to process to meet the daily required number of cases?
A. 12 B. 18 C. 20 D. 24
- Last year, a department spent $8,300 for office equipment. This year, it will spend 5 percent less. How much will it spend this year?
A. $6,
B. $6,
C. $7,
D. $7,
- A room that was originally 12’ x 14’ was increased to 15’ x 20’. How many square feet of floor space were added?
A. 112 B. 118 C. 128 D. 132
- An employee’s gross salary is $950.00 per week. From his salary, 12% is deducted for federal taxes; 9% for state taxes; and 4% for health insurance premiums. If all of these deductions are taken as a percent of his salary, what is his net income for a four-week period?
A. $2,600.
B. $2,825.
C. $2,850.
D. $2,950.
- 2,125 employees work in a department. Each employee works 40 hours per week. What is the total number of hours worked by these employees in a 4-week period?
A. 260, B. 280, C. 310, D. 340,
GLOSSARY OF MATHEMATICAL TERMS
Area: The number of square units that covers a shape or figure.
Denominator: The bottom part of a fraction. (Example: in the fraction ¾, 4 is the denominator.)
Digit: The ten numerals 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The number 14 has two digits: 1 and 4.
Difference: The result of subtracting one number from another.
Divisor: In a division problem, the number that is divided into another (For example when dividing 4 into 20, the 4 would be the divisor, as it is used to divide the number 20 into five parts).
Factor: One of two or more numerical values that are multiplied together to yield a product.
Fraction: A number expressed in terms of a numerator and denominator.
Least Common Multiple:
The smallest, non-zero multiple of the denominators of two or more fractions.
Numerator: The top part of a fraction. (Example, in the fraction ¾ 3 is the numerator).
Operation: Any one of the basic arithmetic functions of addition, subtraction, multiplication, or division.
Product: The result of two numbers being multiplied together.
Quotient: The result of dividing one number into another.
Sum: The result of adding together two or more numbers.
ANSWERS AND EXPLANATIONS TO ARITHMETIC SAMPLE QUESTIONS
NOTE : Typically, there are multiple ways of obtaining the correct answer to each question, only one of which is provided as the answer explanation. Use the glossary on page 7 to help you define any terms with which you may be unfamiliar.
- Correct Answer: B Set up the problem by lining up numbers vertically, aligning all decimal points (Step # 1). Working right to left, set up the problem for solving by carrying values over only when the top value for a column is less than its bottom value (Step #2). Subtract all values to determine the difference (Step #3).
STEP #1 STEP #2 STEP
6 9 10 6 9 10
- 70 0 10. 70 0 10. 70 0
- 27 8 – 5. 27 8 – 5. 27 8
- 422
- Correct Answer: A Working from right to left, multiply 526 by each digit in the factor “213” separately. You may wish to add zero placeholders (shown in bold) to help ensure that columns are aligned correctly (Step #1). Add the products from Step #1 to arrive at the correct answer (Step #2).
STEP #1 STEP #
526 526 x 213 x 213 1578 1578 526 0 526 0 1052 00 + 1052 00 112038
- Correct Answer: D Add the measurements in the minutes column for a total of 70 minutes (Step #1). Since 60 minutes equals 1 hour, convert the 70 minutes into 1 hour, 10 minutes; carry the 1 hour into the hours measurement column; and sum for a total of 34 hours, 10 minutes (Step #2). Since 24 hours equals 1 day, convert the 34 hours into 1 day, 10 hours; carry the 1 day into the days measurement column; and sum for a total of 20 days (Step #3).
- Correct Answer: C Multiply 35 by the decimal equivalent of 80% (.8) and insert the decimal point in the product one place from the right, as the factors 35 and .8 have a total of one decimal place (Step #1).
STEP
x.
Correct Answer: B Multiply $178.00 by the decimal equivalent of 5.5% (.055) to determine the amount of tax that will be applied. Insert the decimal point in the product three places from the right, as the factors 178 and .055 have a total of three decimal places (Step #1).
STEP #
x. 055 890 890
- 000 9790
$9.
STEP #1 STEP #2 STEP # 3
9 days, 5 hours, 48 minutes 7 days, 15 hours, 9 minutes
- 3 days, 13 hours, 13 minutes 70 minutes
1 hour 9 days, 5 hours, 48 minutes 7 days, 15 hours, 9 minutes
- 3 days, 13 hours, 13 minutes 34 hours, 10 minutes
1 day 1 hour 9 days, 5 hours, 48 minutes 7 days, 15 hours, 9 minutes
- 3 days, 13 hours, 13 minutes 20 days, 10 hours, 10 minutes
- Correct Answer: A Multiply the number of boxes in a crate (6) by the number of crates on the pallet (10) to determine that there are 60 boxes on one pallet (Step #1).
STEP #
x 6 60
- Correct Answer: B Multiply the number of individuals who will receive the letter (625) by the number of pages in the letter (6) to determine that 3,750 sheets need to be folded (Step #1). Divide the number of pages that can be folded per hour (7,500) by the number of minutes in one hour (60) to determine that 125 sheets can be folded per minute (Step #2). Divide the number of sheets that need to be folded (3,750) by the number of sheets that can be folded per minute (125) to determine that it will take the machine 30 minutes to fold the letters (Step #3).
STEP #1 STEP #2 STEP
x 6 3750
- Correct Answer: C Multiply $3509 by the decimal equivalent of 4% (.04). Insert the decimal point in the product two places from the right, as the factors 3509 and .04 have a total of two decimal places (Step #1). Add the product from Step #1 to the employee’s previous salary to determine the new salary (Step #2).
STEP #1 STEP
x. 0 4 14 03 6
- 00 00 14 03 6
- Correct Answer: D Find the total area of both the original room and the enlarged room (Step #1). The formula for area is A = L x W, where A = area; L = length; and W = width. The product is expressed in square feet. Subtract the area of the original room from the area of the enlarged room to determine the amount of floor space that was added (Step #2).
STEP # Original room measurement: 12’ x 14’ = 168 Enlarged room measurement: 15’ x 20’ = 300
STEP # 300 - 168 = 132 square feet
- Correct Answer: C Add the decimal equivalent of the federal tax, state tax, and insurance deductions to determine the total percent deduction (Step #1). Multiply the employee’s gross weekly salary by 4 to determine his gross salary for a four- week period. Insert the decimal point in the product two places from the right, as the factors 950.00 and 4 have a total of two decimal places (Step #2). Multiply the product from above by the decimal equivalent of the total percent deduction to determine the amount that is deducted for a four-week period. Insert the decimal point in the product two places from the right, as the factors 3800 and .25 have a total of two decimal places (Step #3). Subtract the product from above from the employee’s gross four-week income to determine his net income for a four-week period (Step #4).
STEP #1 STEP #2 STEP #3 STEP
x 4 $ 3800. 00
x. 25 1 90 00
- 7 60 0 9 50 00
$950.
- Correct Answer: D Multiply the total number of employees (2,125) by the weekly number of hours each employee works (40) to determine that there are 85,000 hours worked in one week (Step #1). Multiply 85,000 by 4 to determine that there are 340,000 hours worked in a 4-week period (Step #2).
STEP #1 STEP #
x 40 0000
- 8500 85000
x 4 340000
- Correct Answer: C Multiply the weight of one case (17.3) by 6 to determine the weight of 6 cases. Insert the decimal point in the product one place from the right, as the factors 17.3 and 6 have a total of one decimal place (Step #1).
STEP #
x 6
8
Correct Answer: A Divide the employee’s original weekly earnings by 36 to determine his hourly salary before the promotion (Step #1). Multiply the hourly salary before the promotion by the decimal equivalent of 2% to determine the amount of the salary increase. Insert the decimal point in the product four places from the right, as the factors 21.50 and .02 have a total of four decimal places (Step #2). Add the product from Step #2 to the hourly salary before the raise to determine the new hourly salary after the raise (Step #3). Multiply the new hourly salary by 34 to determine the employee’s weekly salary if he reduces his hours. Insert the decimal point in the product two places from the right, as the factors 24.08 and 34 have a total of two decimal places (Step #4).
STEP #1 STEP #2 STEP #3 STEP #
- 5 36 774. 00
- 72 54
- 36
- 0
- 0 0
x .0 2 43 0 0
- 000 0 043 0 0
$0.
x 34 87 7 2
- 657 9 745 6 2
$745.