# AFQT Arithmetic Reasoning Exam

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

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To calculate the average we must: (Score A + Score B + Score C + Score D)/(number of exams) = (87 + 94 + 89 + 86)/4 =356/4 = 89

#### 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?

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You may assume the answer is to take the average of the two journeys, which would require adding 50 plus 60 and dividing by 2. However, if a person is going at a slower speed then it takes more hours so the answer will be close to the lower speed. The best way to solve this is to setup a destination length and solve for x, which is the average speed. Assume the destination length is 300 miles. 300/50 = 6 hours and 300/60 = 5 hours. Therefore it takes 11 hours to travel the entire distance of 600 miles. 600/11 = 54.5 miles per hour.

#### 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?

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\$3,000/\$1,000 = 3. Therefore the yearly amount is: 3 x \$34.65 = \$103.95 Another method of solving this problem would be: \$3,000/x = \$1000/\$34.65 \$1000x = \$103.95

#### How many hours are there in one week?

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There are 7 days a week and 24 hours in a day. Therefore: 7 x 24 = 168

#### 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?

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To work this out we use the following equation: (highest temperature + lowest temperature)/2 = (100+20)/2 = 60 degrees

#### 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?

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If Austin’s hourly wage is x, then Kayte’s wage is (x+3), so Tara’s wage is 2(x+3). Together they earn \$41 per hour, so we can write the equation: x+(x+3)+2(x+3)=41 x+x+3+2x+6=41 4x+9=41 4x=32 x=8 Austin’s hourly wage is \$8 per hour

#### 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?

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To find the volume of the flower box you take l×w×h. Don't forget that the measurements are for a square flower box, so you can assume that if the box is 4-feet long, then it's also 4-feet wide. So 4×4×1=16 cubic feet. Each bag holds 1/2 cubic foot of soil. 16/(1/2) = 16 × 2 = 32.

#### 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?

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The shop keeper has lost 2 of his original 12 boxes. Therefore, the shopkeeper has 10 boxes left. Each box cost an average of: \$90/10 = \$9. If the shopkeeper wants a 20% profit he would need to sell each box at: \$9 + 20% = \$9 + (\$9 x 0.2) = \$9.00 + \$1.80 = \$10.80

#### 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?

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Multiply 113.33 x 6 to get the distance in miles and then double the answer to account for both legs of the trip. 113.33 x 6 ? 680, then 680 x 2 = 1,360 miles.

#### 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?

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Solving this question is requires using addition and subtraction. Start with the starting balance, add the deposit, and subtract the expenditures. \$928.16+\$412.83 =\$1,340.99. Now subtract the following from the new balance: \$1,340.99- \$17.22-\$36.59-\$67.90=\$1,219.28.

#### 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?

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Work this out using algebra with the larger number = x and lower number = y: 2(x-y) = (x+y)/2, 4(x – y) = x + y Sub in y = 9, 4(x – 9) =x + 9, 4x – 36 = x + 9, 3x = 45, x = 15

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

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If the machine prints 30 newspapers in 20 minutes, it prints: (30 newspapers)/(20 minutes) = 3/2 newspapers per minute. To calculate the time to print 900 newspapers: (900 newspapers)/(3/2 newspapers per minute) = 1800/3 = 600 minutes ÷ 60 minutes per hour = 10 hours

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

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The pattern is to double each number: 3 + 3 = 6; 6 + 6 = 12; 12 + 12 = 24; so 24 + 24 = 48.

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

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First set up the equation to determine x. 25% of x = 80 and 25% = 1/4. Similarly 90% = 9/10 Therefore, 1/4x= 80 so, x = (4/1) x 80 = 320 So, 9/10x = 9/10 x 320 = 288

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

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First we must identify the number of seats that were not occupied: Total – occupied = not occupied. 90 – 72 = 18. Then we can work out the percentage: Percentage = (Not Occupied Seats)/(Total Seats) X 100 = 18/90 x 100 = 20%

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