ASVAB Arithmetic Reasoning

Jenny's test grades are 93, 89, 96, and 98. If she wishes to raise her average to 95, what does she need to score on her next test?

B) To determine Jenny's average, add the test scores and divide the sum by the number of tests she took. You want to know what she needs on the next test to achieve an average of 95, so let x equal the unknown score. Set up the equation as (93+89+96+98+x)/5=95. Combine the like terms: (376+x)/5=95. Multiplying both sides by 5 results in 376+x=475, so x-99

The high school track measure one-quarter of a mile around. How many laps would you have to run in order to run three and a half miles?

B) Recognize that if the track is a quarter mile long, then 1 mile equals four laps. Therefore, multiply 4 x 3.5 miles. The answer is 14 laps.

Miriam bought five cases of motor oil on sale A case of motor oil normally costs $24.00, but she was able to purchase the oil for $22.50 a case. How much money did Miriam save on her entire purchase?

A) Subtract the sale price from the regular price to find out how much she saves on each case: $24.00-$22.50=$1.50. Multiply the answer by the total number of cases to get your final answer: $1.50 x 5=$7.50

Karl is driving in Austria, where the speed limit is posted in kilometers per hour. The car's speedometer shows that he's traveling at a rate of 75 kilometers per hour. Karl knows that a kilometer is about 5/8 of a mile. Approximately how many miles per hour is Karl traveling?

A) One kilometer is approximately 5/8 of 1 mile, so you can multiply 75x5/8:75x5=375, and 375/8= about 46.8 miles. Therefore, Karl was traveling at 47 miles per hour.

Kiya had only one coupon for 10% off one frozen turkey breast. The turkey breasts cost $8.50 each, and Kiya wanted to buy two. How much did she pay?

A) One turkey breast costs $8.50 minus 10% of $8.50 (which is $0.85) or $8.50-$0.85=$7.65. The other turkey breast is full price, so add the two costs: $8.50+$7.65=$16.15.

An office building has 30 employees and provides 42 square feet of work space per employee. If five more employees are hired, how much less work space will each employee have?

A) The office has 1260 square feet of space (multiply 45 square feet by 30 square employees) . With 35 employees, each employee will have 36 square feet of work space (1260/35). Which is 6 square feet less than originally.

A carpenter earns $12.30 an hour for a 40-hour week. His overtime pays 1.5 times his base pay. If he puts in a 46-hour week, how much is his weekly pay?

A) You need to add the carpenter's base pay and over time pay to find his total pay for the week. First find his base pay per week: $12.30/hr.x40 hr.=$492. Then find his overtime rate per hour, which is 1.5 times his base pay: $12.30/hr.x1.5=$18.45. Multiply this rate by the number of hours of overtime to find his overtime pay:$18.45/hr.x6 hr.=$110.70. Finally, add his base pay and his overtime pay to find his total pay for the week: $492.00+$110.70=$602.70

A carpenter needs to cut four sections, each 3 feet, 8 inches long, from a piece of molding. If the board is only sold by the foot, what's the shortest length of board she can buy?

A) Convert the mixed number to inches: 3 feet, 8 inches equal 44 inches (12 in./ft.x3 ft.=36 in. and 36 in.+8 in.=44 in.) Each section needs to be 44 inches long, and you need four sections. So 44 in. x 4=176 in. The total amount of molding needed is 176 inches. To find the amount of molding needed in feet, convert 176 inches into feet by dividing 176 by 12 in. You get 14 2/3 feet, so the shortest board length is 15 feet.

The sum of two numbers is 70. One number is 8 more than the other. What's the smaller number?

A) 31 Let X equal the smaller number and x + 8 equal the larger number. Because the sum of the two numbers is 70, you can express this mathematically as x+x+8=70. Now all you have to do is solve. Combine the like terms: 2x+8=70. Then subtract 8 from 70 and divide by 2x. You find x= 31

As a member of FEMA, you're required to set up a contingency plan to supply meals to residents of a town devastated by a tornado A breakfast ration weighs 12 ounces, and the lunch and dinner rations weigh 18 ounces each. Assuming a food truck can carry 3 tons, and that each resident will receive 3 meals per day, how many residents can you feed from one truck during a 10-day period?

B) First find how many ounces of rations each truck can hold. One ton is 2,000 pounds, so one truck can carry three times that, or 6,000 pounds. There are 16 ounces in a pound, so one truck can carry 96,000 ounces: 6,000 lbsx16 oz.=96,000 oz. Then figure out how many daily rations are in a truckload. The total daily ration for each resident is 12 ounces+18 ounces+18 ounces, or 48 ounces. You can express the number of daily rations supplied as 96,000 oz./48 oz./daily ration=2,000 by 10 days results in 200 residents who can be fed by one truck during this 10-day period.

A waitress earns an average tip of 12% of the cost of the food she serves. If she serves $375 worth of food in one evening, how much money in tips will she earn on average?

B) Multiply the total amount spent on food, $375, by 12% (or 0.12) to determine the amount of tips: $375*0.12=$45

Stan bought a monster truck for $2,000 down and payments of $450 a month for five years .What's the total cost of the monster truck?

B) The total cost is the down payment plus 5 years' worth of monthly payments. Five years contain 60 months, so multiply $450 (monthly payment)x60=$27,000 (total payment). Then, add $27,000 +$2,000(down payment)=$29,000(total cost)

Your car uses gasoline at the rate of 21 miles per gallon. if gasoline costs $2.82 per gallon and you drive for 7 hours at a speed of 48 miles per hour, how much will you pay for gasoline for the trip?

B) Your first step is to determine the number of miles traveled. Multiply the rate of travel by the time: 48x7=336 miles. The amount of gas used is the total miles driven divided by the number of miles per gallon: 336/21=16 gal. used. At the price of $2.82 per gallon, you spent $45.12 for gas: $2.82x16=$45.12

The population of Grand Island, Nebraska, grew by 600,000 people between 1995 and 2005. 1/5 more than the town council predicted. The town council originally predicted the city's population would grow by

B) B) Let x equal the original number of how much Grand Island would grow. An additional 1/5 would make the population grow 6/5, or 120%, of x. You can express the equation as 1.2x=600,000. To solve for x, divide both sides of the equation by 1.2, which give you x=500,000.

Michael needs 55 gallons of paint to paint an apartment building. He would like to purchase the paint or the least amount of money possible. Which of the following should he buy?

B) Choice (A) doesn't provide enough paint (2x25 gal.=50 gal), so it's wrong. Now determine the cost of each of the other options: Choice (B): 11X$108= $1,188 Choice (C)= 6x$215=$1,290 Choice (D)= 55x$23= $1,265 The lowest price is $1,188, Choice (B)

A printing plant that produces baseball cards has a monthly overhead of $6,000. It costs 18 cents to print each card, and the cards sell for 30 cents each. How many cards must the printing plant sell each month in order to make a profit?

C) Let x equal the number of cards printed and sold each month. Each card costs $0.18 to print and sells for $0.30. Therefore, the cost is equal to 6,000+0.18x, and revenue is equal to 0.30x. You're looking for the point where revenue is greater than the cost. The inequality is 0.30x>6,000+0.18x, Now solve for x: 0.12X>6,000 x>50,000

Keith is driving from Reno to Kansas City to meet his girlfriend. The distance between the two cities is 1,650 miles. If Keith can average 50 miles per hour, how many hours will it take him to complete his trip?

C) Distance equals speed times time, so divide the total distance by Keith's average speed to find how long the trip took: 1,650 mi./50 mph=33 hr.

A security guard walks the equivalent of six city blocks when he makes a circuit around the building. If he walks at a pace of eight city blocks every 30 minutes, how long will it take him to complete a circuit around the building, assuming he doesn't run into any thieves?

C) Divide 30 by 8 to determine how long the security guard takes to walk one city block: 30/8=3.75 minutes. Then multiply 3.75 by 6, the number of blocks it takes to complete the circuit. The answer is 22.50 minutes.

A recruiter travels 1,100 miles during a 40-hour workweek. If she spends 2/5 of her time travelling, how many hours does she spend traveling?

C) Don't let the number of miles traveled confuse you. You don't use them to solve the problem. Finding 2/5 of a 40 hour workweek is the same thing as multiplying 40 times 2, which is 80, and then dividing 80 by 5, which equals 16 hours the recruiter travels weekly.

Carpet stain protector costs $0.65 per square yard. How much will it cost to apply the protector to a 16-foot-x-18-foot carpet?

C) First, determine the number of square feet of carpet you want to protect: 16 ft.*18 ft.=288ftsquared. The carpet stain protector is priced by the square yard, so divide 288 by 9 to convert square feet ot square yards (because 1 ydsquared=3 ft*3 ft=9 ftsquared). 288ftsquared/9ftsquared/yd=32 ydsquared.

Joe received an hourly wage of $8.15. Hos boss gave him a 7% raise. How much does Joe make per hour now?

C) Joe gets a 7% raise. To calculate the new wage, start off by multiplying $8.15*0.07=$0.57. Then add that number (the amount of Joe's raise) to his original hourly wage. Joe's new hourly wage is $8.15+$0.57=$8.72.

A teacher deposits $3,000 i a retirement fund. If she doesn't add an more money to the fund, which earns an annual interest rate of 6%, how much money will she have in 1 year?

C) The interest formula says that interest equals principal times rate times time, or _I_=_Prt_. To determine the amount of interest earned, multiply the principal ($3,000) by the interest rate (6%) and the number of years interest accrues (1 year): $3,000x0.06x1=$180. Add the interest earned to the principal to show how much total money the teacher would have:$180+$3,000=$3,180.

Alice leaves her house, driving east at 45 miles per hour (mph). Thirty minutes later, her husband Dave notices she forgot her cellphone and sets off after her. How fast must Dave travel in order to catch up with Alice 3 hours after he leaves?

C) To find distance, you multiply speed by time. First find how far Alice travels before Dave catches up with her. By the time Dave leaves, Alice has already been traveling for half an hour. There hours later, she wouldn't been traveling for 3.5 hours at 45 miles per hour, or 157.5 miles: 3.5 hr.*45mph=157.5 mi. Dave has three hours to cover this distance. Now find his speed. To travel 157.5 miles in 3 hours, Dave would have to travel as 52.5 mph: 157.5 mi/3 hr. = 52.5 mph.

If a car is towed 12 miles to the repair shop and the tow charge is $3.50 per mile, how much does the tow cost?

C) $42.00 Multiply 12 miles by $3.50 per mile: 12 * $3.50=$42.00

Darla spent $120.37 on groceries in January, $108.45 in February, and $114.86 in March. What was the average monthly cost of Darla's groceries?

D) Add the three monthly amounts to determine the total amount Darla spent on groceries: $120.30+$108.45+$114.86=$343.68. Divide the total amount by 3 to determine the average monthly cost: $114.56.

Joan is taking an admissions examination. If she has to get at least 40 of the 60 questions right to pass, what percent of the questions does she need to answer correctly?

D) Divide the number of questions she has to get right (40) by the total number of questions (60) to reach 66 2/3%.

A train headed south for Wichita left the station at the same time a train headed north for Des Moines left the same station. The train headed for Wichita traveled at 55 miles per hour. The train headed for Des Moines traveled at 70 miles per hour. How many miles apart are the trains at the end of 3 hours?

D) The train headed for Wichita traveled 55 miles/hourx3 hours=165 total miles. The train headed to Des Moines traveled 70 miles/hourx3 hours=210 total miles. Adding the distances together gives you the number of miles apart the two trains are after three hours: 210+165=375. Another option: you can add the two rates of speed (55+70) and multiply the sum by 3 hours (125x3 hours: 375)

A baker makes 20 pies, A Boy Scout troop buys 1/4 of his pies, a preschool teacher buys 1/3 of his pies, and a caterer buys 1/6 of hos pies. How many pies does the baker have left?

D) To find the amount of pie purchased (which, by the way, does not give you the final answer), you have to add the fractions. But first the fractions need to have a common denominator. The denominators (4, 3, and 6) all divide evenly into 12, so use 12 as the common denominator. To convert the fractions to the least common denominator of 12, do the following: 1/4*3/3- 3/12 1/3*4/4=4/12 1/6*2/2=6/12 Now you can add the fractions together: 3/12+4/12+6/12=3+4+2/12=9/12 Nine-twelfths of 20 pies is the same thing as 3/4, or 75%, of the 20 pies. That equals 15 pies. But that's not what the question asks. One more step: subtract the pies sold (15) from the original 20, leaving 5 pies.

A sales manager buys antacid in bottles by the gross. If he goes through 3 bottles of antacid every day, how long will the gross last?

D) 144 bottles are in a gross, and 144/3 (bottles per day) =48 days.

How many square feet of carpeting are needed to carpet a 12-foot-x-12-foot room?

D) You determine square footage by multiplying length by width: 12*12=144