Civil Service Study Notice: These questions are original educational practice materials designed to mirror the formats, cognitive standards, and administrative reasoning tested in NYC civil service competitions. They are not actual past DCAS examination questions. NYCExam is an independent educational prep resource not affiliated with DCAS or the City of New York.
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Mathematical Reasoning Practice Questions & Explanations
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Question 1 of 10
Multiple Choice (Single Answer)
The NYC Department of Transportation plans to resurface a straight municipal parking lot measuring 180 feet in length and 90 feet in width. Asphalt sealant covers 120 square feet per gallon and is sold only in full 5-gallon buckets costing $85 per bucket. What is the total minimum expenditure required for the sealant?
Question 2 of 10
Multiple Choice (Single Answer)
A Department of Environmental Protection inspector earns a base salary of $32.00 per hour for a standard 35-hour workweek. Hours worked in excess of 35 hours in a single week are compensated at 1.5 times the base rate (time-and-a-half). During an emergency water main repair week, the inspector logs 47 total hours. What are the inspector's gross earnings for that week?
Question 3 of 10
Multiple Choice (Single Answer)
A municipal agency fleet contains 45 hybrid sedans and 30 light utility vans. Hybrid sedans average 36 miles per gallon (MPG) and light utility vans average 18 MPG. Over the course of one month, each sedan is driven 1,080 miles and each van is driven 720 miles. Fuel costs an average of $3.50 per gallon. What is the total combined fuel cost for the fleet that month?
Question 4 of 10
Multiple Choice (Single Answer)
The NYC Administration for Children's Services maintains a strict staffing policy requiring 1 supervising caseworker for every 6 field caseworkers, and each field caseworker can handle a maximum active caseload of 15 family cases. If an agency district office is assigned 540 active family cases, what is the minimum total number of casework staff (field caseworkers plus supervising caseworkers) required?
Question 5 of 10
Multiple Choice (Single Answer)
A municipal water tariff charges commercial facilities a base account charge of $45.00 per month plus $3.80 per 100 cubic feet (HCF) for the first 50 HCF used, and $4.60 per HCF for any volume consumed beyond 50 HCF. If a public maintenance depot uses 75 HCF in October, what is the total water utility charge?
Question 6 of 10
Multiple Choice (Single Answer)
In fiscal year 2024, the Department of Buildings issued 12,500 electrical permits at $160 each. For fiscal year 2025, the permit fee was increased by 15%, but due to economic conditions, the total volume of permits issued decreased by 8%. What was the total revenue generated from electrical permits in fiscal year 2025?
Question 7 of 10
Multiple Choice (Single Answer)
Three intake clerks work together to process food vendor permit renewals. Clerk A can process 24 applications per hour, Clerk B processes 18 per hour, and Clerk C processes 30 per hour. If all three work continuously without interruption, how many hours will it take them to process a combined backlog of 504 applications?
Question 8 of 10
Multiple Choice (Single Answer)
A municipal IT department purchased 240 tablet computers for field inspectors at an initial cost of $650 per unit. City accounting rules dictate straight-line depreciation over a 5-year useful life with an expected salvage value of $50 per unit at the end of year 5. What is the total book value of all 240 tablets combined at the end of year 3?
Question 9 of 10
Multiple Choice (Single Answer)
A city courier van leaves the central municipal depot in Queens at 8:15 AM to deliver supplies to an office in Staten Island, traveling 28 miles at an average speed of 35 miles per hour. The driver spends 25 minutes unloading boxes and then drives 18 miles to a second site in Brooklyn at an average speed of 24 miles per hour. At what time does the courier arrive at the Brooklyn facility?
Question 10 of 10
Multiple Choice (Single Answer)
A city capital project has a total budget of $1,800,000. It is funded by three entities: the federal government provides 45% of the funds, New York State provides 35%, and New York City covers the remaining balance. During construction, cost overruns increase total expenditures by 12%. If NYC agreed to absorb 100% of all cost overruns, what is NYC's final total financial contribution to the project?
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About Mathematical Reasoning
Mathematical Reasoning is the ability to choose the right mathematical methods or formulas to solve a problem. Unlike basic arithmetic computation (Number Facility), Mathematical Reasoning requires candidates to analyze complex workplace scenarios, determine which mathematical operations are needed, formulate equations or models, and interpret quantitative results in municipal administrative contexts—such as cost-benefit analyses, staffing ratios, overtime allocations, rate-of-work projections, and public expenditure audits.
Exam Day Strategies
Rely solely on provided facts: Do not use outside assumptions or personal experience. If a rule is stated in the prompt, treat it as absolute.
Watch for qualifying words: Pay close attention to words like always, never, unless, mandatory, and except.
Pace yourself evenly: Civil service tests allocate approximately 1.5 to 2 minutes per question. Flag difficult questions and return later.
Verify all answer choices: Eliminate clearly contradicted options first before making your final selection.
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