Arithmetic Reasoning Flashcards

How long will it take for both Sarah and John to paint a house if Sarah takes four hours and Johnny takes six?

Answer: 2 hours and 24 minutes

To solve this, calculate the individual work rates: Sarah paints 1/4 house per hour, and John paints 1/6 house per hour. Their combined rate is 1/4 + 1/6 = 3/12 + 2/12 = 5/12 house per hour. To find the total time, take the reciprocal of the combined rate: 1 / (5/12) = 12/5 hours, which is 2.4 hours. Converting 0.4 hours to minutes (0.4 * 60) gives 24 minutes, so the total time is 2 hours and 24 minutes.

Employees of a discount appliance retailer get an extra 20% off the item's lowest price. How much will an employee pay if he buys a dishwasher during a 15% off sale when the dishwasher originally cost $450?

Answer: $306.00

First, calculate the price after the 15% off sale: $450 * (1 - 0.15) = $450 * 0.85 = $382.50. Then, apply the employee's additional 20% discount to this sale price: $382.50 * (1 - 0.20) = $382.50 * 0.80 = $306.00. The employee will pay $306.00 after both discounts are applied sequentially.

According to the manager of a weaving mill, ten machines could create 1450 meters of cloth if they operated at 100% efficiency for eight hours. Four machines operate at a 95% efficiency due to technical issues, while the remaining six operate at a 90% efficiency. In an eight-hour period, how many meters of cloth can these machines produce?

Answer: 1334 meters

First, determine the production rate per machine at 100% efficiency: 1450 meters / 10 machines = 145 meters per machine. Next, calculate the production for the four machines at 95% efficiency: 4 machines * (145 meters/machine * 0.95) = 4 * 137.75 = 551 meters. Then, calculate the production for the six machines at 90% efficiency: 6 machines * (145 meters/machine * 0.90) = 6 * 130.5 = 783 meters. Finally, sum these amounts: 551 + 783 = 1334 meters.

A worker put in 11 hours a day. Her typical workday is 7.5 hours, with the additional time being overtime for which she was compensated at 1.5 times her standard hourly rate. What was her standard hourly rate for that day if she was paid $112 for the day?

Answer: $8.78

Let 'x' be the standard hourly rate. The worker put in 7.5 regular hours and 11 - 7.5 = 3.5 overtime hours. Overtime is paid at 1.5 times the standard rate, so the overtime pay is 3.5 * 1.5x = 5.25x. The total pay is 7.5x (regular) + 5.25x (overtime) = 12.75x. Since the total pay was $112, we have 12.75x = $112. Solving for x, $112 / 12.75 = $8.7843, which rounds to $8.78.

There are 28 blue pencils and 7 black pencils in a box. How many black pens are there compared to blue pens?

Answer: 1:4

To find the ratio of black pens to blue pens, we compare the number of black pencils (7) to the number of blue pencils (28). This gives a ratio of 7:28. To simplify, divide both numbers by their greatest common divisor, which is 7. This results in a simplified ratio of 1:4.

What percentage of the page can Kate type if she can type a page in p minutes?

Answer: 5/p

If Kate can type one page in 'p' minutes, her typing rate is 1/p pages per minute. To find out what percentage (or fraction) of the page she can type in 5 minutes, multiply her rate by 5 minutes. This calculation is (1/p) * 5 = 5/p. Therefore, she can type 5/p of the page in 5 minutes.

A automobile is being sold for $12,590, which is a 20% discount from the original cost. What was the initial cost?

Answer: $15,737.50

The selling price of $12,590 represents a 20% discount from the original cost, meaning it is 80% of the original cost. To find the original cost, divide the discounted price by 0.80 (which represents 80%). So, $12,590 / 0.80 = $15,737.50. This is the initial cost before the discount.