Arithmetic Reasoning Exam Flashcards

Richard drives from his home to work at an average speed of 50 miles per hour. Later he drives from his work to home at a speed of 60 miles per hour. What is his average speed over the two trips?

Answer: 54.5 miles per hour

To calculate the average speed for a round trip, you must use the formula Total Distance / Total Time. Let 'd' be the distance one way. The time for the first trip is d/50 hours, and for the return trip is d/60 hours. The total distance is 2d, and the total time is (d/50 + d/60) = (6d/300 + 5d/300) = 11d/300 hours. Dividing total distance by total time (2d / (11d/300)) gives 600/11, which is approximately 54.54 miles per hour, rounded to 54.5 mph.

On a map of the Pacific Northwest, the scale is such that 1 inch equals 6 miles. Using the map, the distance from Seattle to San Francisco is 113 1\/3 inches. How far is the round trip from Seattle to San Francisco in miles, rounded to the nearest mile?

Answer: 1,360 mi.

First, calculate the one-way distance from Seattle to San Francisco using the map scale. Given 1 inch equals 6 miles, a map distance of 113 1/3 inches translates to (113 + 1/3) * 6 miles, which is (340/3) * 6 = 680 miles. For a round trip, this distance must be doubled: 680 miles * 2 = 1,360 miles.

What is the fifth number in the series 3, 6, 12, 24?

Answer: 48

Observe the pattern in the given series: each number is obtained by multiplying the previous number by 2. Following this rule, 3 * 2 = 6, 6 * 2 = 12, and 12 * 2 = 24. To find the fifth number, multiply the fourth number (24) by 2, which gives 48.

How many hours are there in one week?

Answer: 168

To find the total number of hours in one week, you need to know that there are 7 days in a week and 24 hours in a day. Multiply these two values together: 7 days * 24 hours/day = 168 hours.

Amanda's bank account has a balance of $928.16. She deposits a check for $412.83 and then uses her bank card to pay fro a $17.22 lunch, get $36.59 worth of gas and buy a new pair of shoes for $67.90. How much money does she have in the bank account at the end of the day?

Answer: $1,219.28

Start with Amanda's initial bank balance of $928.16. Add the deposited check of $412.83 to get $1,340.99. Then, subtract each of her expenses: $17.22 for lunch, $36.59 for gas, and $67.90 for shoes. Performing these subtractions sequentially ($1340.99 - $17.22 - $36.59 - $67.90) results in a final balance of $1,219.28.

A plane takes off from New York with 72 of the 90 seats occupied. What percentage of seats are not occupied?

Answer: 20%

First, determine the number of unoccupied seats by subtracting the occupied seats from the total seats: 90 - 72 = 18 seats. To find the percentage of unoccupied seats, divide the number of unoccupied seats by the total number of seats and multiply by 100. So, (18 / 90) * 100% = 0.20 * 100% = 20%.

If 25 percent of x is 80, what is 90 percent of x?

Answer: 288

First, use the given information that 25 percent of x is 80 to find the value of x. This can be written as 0.25x = 80, so x = 80 / 0.25 = 320. Next, calculate 90 percent of x by multiplying 0.90 by 320. This calculation yields 288.

Tara earns twice as much per hour as Kayte. Kayte earns $3 more per hour than Austin. As a group, they earn $41 pr hour. What is Austin's hourly wage?

Answer: $8.00

Let Austin's hourly wage be 'A'. Kayte earns $3 more than Austin, so her wage is A + 3. Tara earns twice as much as Kayte, so her wage is 2 * (A + 3) = 2A + 6. The sum of their wages is $41, so A + (A + 3) + (2A + 6) = 41. Combining like terms gives 4A + 9 = 41. Subtracting 9 from both sides yields 4A = 32, so Austin's hourly wage (A) is $8.00.

A 55 pound bag of soil holds 1\/2 cubic of soil. In order to fill a square flower box measuring 4-feet long and 1-foot high, how many bags of soil must be used?

Answer: 32 bags

First, calculate the volume of the square flower box. Since it's a square box 4-feet long and 1-foot high, its dimensions are 4 feet x 4 feet x 1 foot, giving a volume of 16 cubic feet. Each bag of soil holds 1/2 cubic foot. To find out how many bags are needed, divide the total volume of the box by the volume of one bag: 16 cubic feet / (1/2 cubic foot/bag) = 32 bags.

A shopkeeper buys 12 boxes of apples for $90. If two boxes were lost, what price would the shopkeeper need to sell each remaining box of apples for to make a 20% profit?

Answer: $10.80

The shopkeeper paid $90 for 12 boxes. After losing 2 boxes, 10 boxes remain. To make a 20% profit, the total selling price for the remaining boxes must be $90 * 1.20 = $108. To find the price per remaining box, divide this total desired revenue by the number of remaining boxes: $108 / 10 = $10.80.

A machine prints 30 newspapers in 20 minutes. At this rate how many hours would it take to print 900 newspapers?

Answer: 10

First, determine the machine's printing rate. It prints 30 newspapers in 20 minutes, which means it prints 1.5 newspapers per minute (30/20). To find out how long it takes to print 900 newspapers, divide the total number of newspapers by the rate per minute: 900 / 1.5 = 600 minutes. Finally, convert minutes to hours by dividing by 60: 600 minutes / 60 minutes/hour = 10 hours.

The average of two numbers is equal to double the positive difference between them. If the smaller number is 9, what is the larger number?

Answer: 15

Let the smaller number be S and the larger number be L. We are given S = 9. The average of the two numbers is (S + L) / 2, and their positive difference is L - S. The problem states that the average is equal to double the positive difference, so (S + L) / 2 = 2(L - S). Substituting S=9 gives (9 + L) / 2 = 2(L - 9). Multiplying both sides by 2 yields 9 + L = 4(L - 9), which simplifies to 9 + L = 4L - 36. Rearranging the terms to solve for L gives 45 = 3L, so L = 15.

Harry takes four math exams. His scores are 87, 94, 89, and 86. What is his average over the four exams?

Answer: 89

To find the average of Harry's four math exam scores, first sum all the scores: 87 + 94 + 89 + 86 = 356. Then, divide this total sum by the number of exams, which is 4. So, 356 / 4 = 89.

The day that the Wilson family arrived to their vacation destination the temperature reached 100 degrees in the day and 20 degrees at night. What was the average temperature for the day?

Answer: 60

To calculate the average temperature for the day, sum the highest and lowest temperatures recorded and then divide by two. The day temperature was 100 degrees and the night temperature was 20 degrees. Therefore, (100 + 20) / 2 = 120 / 2 = 60 degrees.

Grace takes out a $3,000 home insurance policy at a yearly rate of $34.65 for every $1.000. What is the yearly premium?

Answer: $103.95

To find the yearly premium, first determine how many $1,000 units are in the $3,000 home insurance policy. This is $3,000 / $1,000 = 3 units. Then, multiply this number of units by the rate per $1,000: 3 * $34.65 = $103.95.