Mathematical Reasoning Flashcards

A city ordinance requires a ratio of at least 3 sanitation workers for every 2 collection trucks. If a depot has 18 collection trucks in operation, what is the minimum number of sanitation workers required to meet the ordinance?

Answer: 27

The problem requires setting up a proportion to find the unknown number of workers. The ratio is 3 workers to 2 trucks. Let 'x' be the required number of workers for 18 trucks. The proportion is 3/2 = x/18. To solve for x, cross-multiply: 2 * x = 3 * 18, which simplifies to 2x = 54. Dividing both sides by 2 gives x = 27.

A Parks Department crew can mow a large field in 8 hours. A second crew can mow the same field in 12 hours. If both crews work together, how long will it take them to mow the field?

Answer: 4.8 hours

This is a work-rate problem. Crew 1's rate is 1/8 of the field per hour. Crew 2's rate is 1/12 of the field per hour. Their combined rate is (1/8) + (1/12). To add these fractions, find a common denominator, which is 24. So, (3/24) + (2/24) = 5/24 of the field per hour. To find the total time, take the reciprocal of the combined rate: 24/5 = 4.8 hours.

The city's IT department has an annual budget of $4,200,000. If 40% is allocated for salaries, 25% for hardware upgrades, and 15% for software licenses, how much money remains for other expenses?

Answer: $840,000

First, calculate the total percentage of the budget that has been allocated: 40% + 25% + 15% = 80%. The remaining percentage is 100% - 80% = 20%. To find the remaining dollar amount, calculate 20% of the total budget: 0.20 * $4,200,000 = $840,000.

A city clerk's office processed the following number of permit applications per day over a four-day period: 164, 178, 155, and 167. To achieve a five-day average of 170 applications per day, how many applications must be processed on the fifth day?

Answer: 186

To have an average of 170 over 5 days, the total number of applications must be 170 * 5 = 850. The sum of the applications from the first four days is 164 + 178 + 155 + 167 = 664. To find the number needed on the fifth day, subtract the four-day total from the required five-day total: 850 - 664 = 186.

The city plans to resurface a rectangular parking lot that is 150 feet long and 100 feet wide. The cost of resurfacing is $18 per square yard. What is the total cost to resurface the parking lot?

Answer: $30,000

The problem requires calculating area and includes a unit conversion. First, convert the dimensions from feet to yards (1 yard = 3 feet). Length = 150 ft / 3 = 50 yards. Width = 100 ft / 3 = 33.33... yards. However, it's easier to calculate the area in square feet first: 150 ft * 100 ft = 15,000 square feet. Then, convert square feet to square yards (1 square yard = 9 square feet): 15,000 sq ft / 9 = 1,666.67 sq yards. Finally, calculate the cost: 1,666.67 sq yds * $18/sq yd ≈ $30,000. A more precise way without early rounding: (150/3) * (100/3) * 18 = 50 * (100/3) * 18 = 5000/3 * 18 = 5000 * 6 = $30,000.

A city's water consumption was 2.5 million gallons in May. In June, consumption increased to 3.2 million gallons due to a heatwave. What was the percentage increase in water consumption from May to June?

Answer: 28%

To find the percentage increase, use the formula: [(New Value - Original Value) / Original Value] * 100. First, find the difference in consumption: 3.2 million - 2.5 million = 0.7 million gallons. Next, divide the difference by the original consumption: 0.7 / 2.5 = 0.28. Finally, convert this decimal to a percentage by multiplying by 100: 0.28 * 100 = 28%.