Arithmetic Reasoning ASVAB

Brian works for five hours and is paid $24. Christina works for three hours and is paid $10.95. How much more per hour does Brian make than Christina?

A. $1.15 (A) Brian's hourly wage is 24÷5 ($4.80). Christina's hourly wage is 10.95÷3 ($3.65). $4.80 − $3.65 = $1.15.

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

A. $16.15 NOTE: ONLY ONE ITEM HAS DISCOUNT (A) One turkey breast costs $8.50 minus 10% of $8.50, or $8.50 − $0.85 = $7.65. The other turkey breast is full price. $7.65 + $8.50 = $16.15.

Junior has saved money in his piggybank over the winter. He wants to buy a $30 computer game. If he has 14 one-dollar bills, 16 half dollars, 12 quarters, 8 dimes, 25 nickels, and 10 pennies, how much more does he need to borrow from Dad to buy the game?

A. $27.15 B. $2.85 C. $2.95 D. $1.85 (B) Convert the change to dollars or fractions of dollars and add: 14 dollars = $14.00 16 half dollars = $8.00 12 quarters = $3.00 8 dimes = $0.80 25 nickels = $1.25 10 pennies = $0.10 Total = $27.15 Subtract the total from $30.00 to determine how much money Junior has to borrow: $30.00 − $27.15 = $2.85.

A 2-ton truck is taxed at a rate of $0.12 per pound. How much is the total tax bill?

A. $480 (A) 2 tons = 4,000 pounds. 4,000 × $0.12 = $480.00.

10: A bin of bolts at the hardware store contains 7-dozen bolts when full. The stock clerk is supposed to reorder bolts when the bin is 1⁄6 full. How many bolts are in the bin when it's time to reorder?

A. 14 bolts B. 1 bolt C. 84 bolts D. 12 bolts (A) First find how many bolts a full bin contains: 7 ×12 = 84 bolts. Then multiply the total number of bolts in a full bin by 1⁄6 to find how many bolts are in the bin when it's 1⁄6 full: 84⁄1 × 1⁄6 = 84⁄6 = 14 bolts.

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. 15 feet B. 14 feet C. 16 feet D. 12 feet (A) Convert the mixed number to inches. 3 feet 8 inches equals 44 inches (12 inches per foot × 3 feet = 36 inches + 8 inches = 44 inches). 44 inches (length each section needs to be) × 4 (number of sections needed) = 176 inches (total molding needed). To determine the amount of molding needed in feet, convert 176 inches into feet by dividing 176 inches by 12 inches. You get 142⁄3 feet, so the shortest board length is 15 feet.

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?

A. 150 residents B. 200 residents C. 250 residents D. 300 residents (B) One ton = 2,000 pounds, so one truck can carry 6,000 pounds. There are 16 ounces in a pound, so one truck can carry 96,000 ounces. The total daily ration for each resident is 12 ounces + 18 ounces + 18 ounces, or 48 ounces. The number of daily rations supplied can be expressed as 96,000 ÷ 48 = 2,000. Dividing 2,000 by 10 days results in 200 residents who can be fed by one truck during this 10-day period.

The product of two consecutive odd numbers is 399. What are the numbers?

A. 17 and 19 B. 19 and 21 C. 21 and 23 D. 25 and 27 The fastest way to solve this would be to simply multiply the possible choices together (19 × 21 = 399). You can also solve this with algebra. Let x equal the first number and x + 2 the second number. x(x + 2) = 399 x^2 + 2x = 399 (Note: This is a quadratic equation that can be solved by setting it equal to zero and factoring.) x^2 + 2x - 399 = 0 (x - 19)(x + 21) = 0 x - 19 = 0 x + 21 = 0 x = 19 x = -21 x + 2 = 21 x + 2 = -19 (B) Two solutions are possible: 19 and 21, and -21 and -19. Because the latter pair isn't one of the answer choices, the first pair is the correct answer.

Your piggy bank contains $19.75 in dimes and quarters. There are 100 coins in all. How many dimes are there?

A. 25 B. 30 C. 35 D. 40 (C) Let x equal the number of dimes. Then 100 - x represents the number of quarters. There is $0.10x in dimes and $0.25(100 - x) in quarters. 0.10x + 0.25(100 - x) = 19.75 0.10x + 25 - 0.25x = 19.75 -0.15x = -5.25 x = -5.25/-0.15 x = 35 NOTE: .25(100-X) TO LOOK FOR DIMES

A house contains one 12-foot-×-14-foot bedroom, one 12-foot-×-10-foot bedroom, and one 8-foot-×-12-foot bedroom. What's the total amount of carpeting needed to carpet all three bedrooms?

A. 384 square yards B. 42 2/3 square yards C. 216 square yards D. 88 square yards (B) Find the area of each bedroom and add them together: 12 × 14 = 168; 12 × 10 = 120; 8 × 12 = 96. 168 + 120 + 96 = 384 square feet. Then, because 9 square feet make up a square yard, divide the total area in square feet by 9 to determine the number of square yards needed: 384 ÷ 9 = 42 2/3 square yards. CONVERTED TO YARDS BCOZ OF THE MEASUREMENT IS IN YARDS

A student buys a science textbook for $18.00, a math textbook for $14.50, and a dictionary for $9.95. What is the total cost of the books?

B. $42.45 (B) Simply add the cost of all the books: $18.00 + $14.50 + $9.95 = $42.45.

150 centimeters is equivalent to:

B. 1 1⁄2 meters (B) 100 centimeters equal 1 meter, so 150 centimeters equal 1 1⁄2 meters.

A treasure map is drawn to a scale of 2 inches = 3 miles. On the map, the distance between Point A and X-marks-the-spot is 9 1/2 inches. How many actual miles does this represent.

B. 141/4 miles NOTE: PAY ATTENTION TO PROPORTION GIVEN... (B) If 2 inches = 3 miles, then 1 inch equals 11⁄2 miles: 3 ÷ 2 = 1.5. Multiply 11⁄2 miles × 91⁄2 inches to determine the actual distance: 1.5 × 9.5 = 14.25 or 141⁄4 miles.

Jack loaned Bob $1,500 at an annual interest rate of 7%. After one year, how much will Bob owe Jack?

C. $1,605 I= PxRxT (in year) (C) First determine the amount of interest owed. Multiply the principal ($1,500) by the interest rate (7%) by the number of years (1): $1,500 × 0.07 × 1 = $105. Then add the interest owed and the principal to determine the total amount owed.

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

C. $20.80 NOTE: 9 SQ FEET= 1 SQ YARD (C) To determine the number of square yards to be protected, multiply 16 feet by 18 feet to determine the number of square feet, 288. Then divide 288 by 9 to convert square feet to square yards (1 square yard = 3 feet × 3 feet = 9 square feet). Multiply the quotient, 32 square yards, by the cost of protection per square yard, $0.65, to get the correct answer, $20.80. Remember to perform all the steps in a calculation.

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

C. $8.72 (C) 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.

In a manufacturing plant that produces new computers, a 0.15 probability exists that a computer will be defective. If five computers are manufactured, what's the probability that all of them will be defective?

C. 0.000076 (C) The probability that all five computers will be defective is 0.15 × 0.15 × 0.15 × 0.15 × 0.15 = 0.0000759 (round up to 0.000076).

A half-pint of cream is what part of a gallon?

C. 1 ⁄ 16 (C) 8 pints make up a gallon, so a gallon contains 16 half-pints. One half-pint equals 1⁄16 of a gallon.

How many quart cans can be filled from a 25-gallon bucket of paint?

C. 100 (C) A gallon consists of 4 quarts. 4 × 25 = 100.

If 4 people can run 8 machines, how many machines can 2 people run?

C. 4 (C) Two people is 1⁄2 as many as 4 people: 2 ÷ 4 = 1⁄2. Multiply the number of machines 4 people can run by 1⁄2 to determine how many machines 2 people can run: 8 × 1⁄2 = 4.

An aircraft flies over Boondock Air Force Base at 10:20 a.m. At 10:32 a.m., the plane passes over Sea Side Naval Air Station, 120 miles away. How fast is the aircraft traveling?

C. 600 mph NOTE: CONVERT MINS TO HOUR (C) The aircraft travels 120 miles in 12 minutes, which is 1⁄5 of an hour. Therefore, in 5⁄5 (one) hour, it would travel 5 × 120, or 600 miles. The aircraft is traveling 600 miles per hour.

A bricklayer charges $8 per square foot to lay a patio. How much would it cost for the bricklayer to lay a 12-foot-×-16-foot patio?

D. $1536 (D) First determine the square footage of the patio: 12 feet × 16 feet = 192 square feet. Then multiply this number by the cost per square foot to determine what the brick layer charges: 192 × $8 = $1,536

The cost of a protein bar increased from $2.50 to $2.80. The percent increase in the $2.80 rate was how much?

D. 12% (D) First subtract the old cost from the new cost: $2.80 - $2.50 = $0.30. Then divide the difference by the old cost to find the percent difference: $0.30 ÷ $2.50 = 0.12 = 12%.

Last year, Margot grew 50 bushels of corn in her backyard. This year, the yield has increased 8%. How many bushels of corn did Margot grow this year?

D. 54 (D) Multiply 50 bushels by 8% to find the yield increase in bushels: 50 × 0.08 = 4. Add 4 bushels (the amount of the increase) to 50 bushels (the original yield) to determine that an 8% increase equals 54 bushels.