Civil Service Exam Numerical Word Problem Solving — Questions and Answers

Question 1: A city department mails 4,800 notices. If 12.5% are returned as undeliverable, how many were successfully delivered?

4,000
4,200 (Correct answer)
4,400
4,600

Correct answer: 4,200

Returned: 12.5% of 4,800 = 600. Delivered: 4,800 - 600 = 4,200.

Undeliverable: 12.5% x 4,800 = 600. Delivered: 4,800 - 600 = 4,200. Tip: 12.5% = 1/8, so 4,800/8 = 600.

Question 2: A public works crew paves 0.3 miles of road per day. A project requires 7.2 miles, and the crew works 5 days per week. How many complete weeks will it take?

4 weeks
5 weeks (Correct answer)
6 weeks
7 weeks

Correct answer: 5 weeks

Days needed: 7.2 / 0.3 = 24 days. Weeks: 24 / 5 = 4.8, rounded up to 5 weeks.

Daily rate: 0.3 miles. Total: 7.2 miles. Days: 7.2 / 0.3 = 24 working days. Weeks: 24 / 5 = 4.8. Since partial weeks count, it takes 5 complete weeks.

Question 3: A department has $18,750 for office supplies. They spent $6,340 on paper and $4,215 on technology. What percentage of the budget remains?

43.7% (Correct answer)
46.2%
56.3%
53.8%

Correct answer: 43.7%

Spent: $10,555. Remaining: $8,195. Percentage: ($8,195 / $18,750) x 100 = 43.7%.

Total spent: $6,340 + $4,215 = $10,555. Remaining: $18,750 - $10,555 = $8,195. Percentage: $8,195 / $18,750 x 100 = 43.7%.

Question 4: Two water plants serve a city. Plant A processes 2.4 million gallons/day and Plant B 1.8 million. How many days to meet 150 million gallon demand?

32 days
34 days
36 days (Correct answer)
38 days

Correct answer: 36 days

Combined: 4.2 million/day. Days: 150 / 4.2 = 35.71, rounded up to 36 days.

Combined rate: 2.4 + 1.8 = 4.2 million gallons/day. Days: 150 / 4.2 = 35.714. Round up to 36. After 35 days: 147M gallons (3M short).

Question 5: A government agency hires 24 seasonal workers at $16.75/hour for 35 hours/week over a 13-week project. What is the total labor cost?

$182,910 (Correct answer)
$181,545
$183,750
$188,370

Correct answer: $182,910

Weekly per worker: $16.75 x 35 = $586.25. Weekly total: $586.25 x 24 = $14,070. Project total: $14,070 x 13 = $182,910.

Per worker per week: $16.75 x 35 = $586.25. All workers per week: $586.25 x 24 = $14,070. Total project: $14,070 x 13 = $182,910.

Question 6: A filing cabinet holds 450 folders. It is currently 3/5 full and 30 more folders are added. What fraction of capacity is now used?

2/3 (Correct answer)
7/10
11/15
3/4

Correct answer: 2/3

Current: 3/5 x 450 = 270. After adding 30: 300. Fraction: 300/450 = 2/3.

Current: 270 folders. After adding 30: 300 folders. Fraction: 300/450 = 2/3 (about 66.7%). Room for 150 more.

Question 7: A county collects property taxes from 12,500 properties at an average of $3,240 per bill with a 94% collection rate. How much revenue is collected?

$38,070,000 (Correct answer)
$38,750,000
$40,500,000
$40,030,000

Correct answer: $38,070,000

Total billed: 12,500 x $3,240 = $40,500,000. At 94%: $40,500,000 x 0.94 = $38,070,000.

Total potential: 12,500 x $3,240 = $40,500,000. Collected: $40,500,000 x 0.94 = $38,070,000. Uncollected: $2,430,000.

Question 8: An office uses 45 kWh/day on weekdays and 20 kWh/day on weekends at $0.14/kWh. What is the monthly bill for 22 weekdays and 8 weekend days?

$138.60
$160.44
$161.00 (Correct answer)
$172.20

Correct answer: $161.00

Weekday: 22 x 45 = 990 kWh. Weekend: 8 x 20 = 160 kWh. Total: 1,150 kWh x $0.14 = $161.00.

Weekday: 990 kWh. Weekend: 160 kWh. Total: 1,150 kWh. Cost: 1,150 x $0.14 = $161.00.

Question 9: A training session has 36 participants divided into equal groups of 4 to 6 members. How many possible group sizes are there?

1
2 (Correct answer)
3
4

Correct answer: 2

36/4 = 9 groups (works). 36/5 = 7.2 (doesn't divide evenly). 36/6 = 6 groups (works). Two possible sizes.

Testing: 36/4 = 9 (valid). 36/5 = 7.2 (invalid). 36/6 = 6 (valid). Two possible group sizes: 4 or 6.

Question 10: A fleet has 15 sedans (28 mpg) and 10 SUVs (18 mpg). Each vehicle travels 1,200 miles/month and fuel costs $3.60/gallon. What is the monthly fleet fuel cost?

$4,628.57
$4,800.00
$4,714.29 (Correct answer)
$5,400.00

Correct answer: $4,714.29

Sedans: 15 x (1200/28) = 642.86 gal. SUVs: 10 x (1200/18) = 666.67 gal. Total: 1,309.52 gal x $3.60 = $4,714.29.

Sedans: 15 x 42.857 = 642.86 gallons. SUVs: 10 x 66.667 = 666.67 gallons. Total: 1,309.52 gallons. Cost: 1,309.52 x $3.60 = $4,714.29.

Question 11: Benefits cost $850/employee/month. If the workforce grows from 340 to 385 employees, what is the additional ANNUAL cost?

$38,250
$382,500
$459,000 (Correct answer)
$3,927,000

Correct answer: $459,000

New employees: 45. Monthly additional: 45 x $850 = $38,250. Annual: $38,250 x 12 = $459,000.

Additional employees: 385 - 340 = 45. Monthly: 45 x $850 = $38,250. Annual: $38,250 x 12 = $459,000. Note: $38,250 (option A) is the monthly figure.

Question 12: A clerk mails 288 letters. Stamps cost $0.68 for standard and $1.05 for oversized. If 75% are standard, what is the total postage?

$195.84
$222.48 (Correct answer)
$223.20
$292.32

Correct answer: $222.48

Standard: 216 x $0.68 = $146.88. Oversized: 72 x $1.05 = $75.60. Total: $222.48.

Standard: 75% of 288 = 216. Oversized: 72. Standard postage: 216 x $0.68 = $146.88. Oversized: 72 x $1.05 = $75.60. Total: $222.48.

Civil Service Exam Numerical Word Problem Solving

A city department mails 4,800 notices.
If 12.5% are returned as undeliverable, how many were successfully delivered?

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