Arithmetic Reasoning

On a scaled drawing of an office building floor, 1/2 inch represents 3 feet of actual floor dimension. A floor, which is actually 75 feet wide and 132 feet long, would have which of the following dimensions on the scaled drawing? a. 12.5 inches wide and 22 inches long b. 17 inches wide and 32 inches long c. 25 inches wide and 44 inches long d. 29.5 inches wide and 52 inches long e. none of these

A. 12.5 inches wide and 22 inches long The scaled drawing shows 1/2 inch for every 3 feet of actual floor dimension. Therefore: 75 feet/3 feet = 25 feet, and 25 multiplied by 1/2 equals 12.5 inches and 132 feet/3 feet = 44 feet, and 44 multiplied by 1/2 equals 22 inches.

A crate containing a tool weighs 12 pounds. If the tool weighs 9 pounds, 9 ounces, how much does the crate weigh? a. 2 pounds, 7 ounces b. 2 pounds, 9 ounces c. 3 pounds, 3 ounces d. 3 pounds, 7 ounces e. 3 pounds, 9 ounces

A. 2 pounds, 7 ounces We know the crate weighs 12 pounds and that 12 pounds equals 11 pounds, 16 ounces. The weight of the tool is 9 pounds, 9 ounces. So 11 pounds, 16 ounces minus 9 pounds, 9 ounces equals 2 pounds, 7 ounces.

A passenger airplane can carry two tons of cargo. A freight airplane can carry six tons of cargo. If an equal number of both kinds of airplanes are used to ship 160 tons of cargo and each airplane carries its maximum cargo load, how many tons of cargo are shipped on the passenger airplanes? a. 40 tons b. 60 tons c. 80 tons d. 100 tons e. 120 tons

A. 40 tons Together, one passenger airplane and one freight airplane carry 8 tons (2 + 6 = 8). To carry 160 tons 160/8, 20 pairs of airplanes are needed. The 20 passenger airplanes carry 2 tons each, so 40 tons of cargo are being shipped on the passenger airplanes.

Two office workers have been assigned to address 750 envelopes. One addresses twice as many envelopes per hour as the other. If it takes 5 hours for them to complete the job, what was the rate of the slower worker? a. 50 envelopes per hour b. 75 envelopes per hour c. 100 envelopes per hour d. 125 envelopes per hour e. 150 envelopes per hour

A. 50 envelopes per hour Let x equal the number of envelopes addressed in 1 hour by the slower worker, and let 2x equal the number of envelopes addressed in 1 hour by the faster worker. Together, they address 3x envelopes in an hour. 3x x 5 = 750 15x = 750 x - 50 The slower worker addresses 50 envelopes each hour.

In order to check on a shipment of 500 articles, a sampling of 50 articles was carefully inspected. Of the sample, 4 articles were found to be defective. On this basis, what is the probable percentage of defective articles in the original shipment? a. 8% b. 4% c. 0.8% d. 0.4% e. 0.04%

A. 8% The sample size is 50. Four defects were found in the sample. The number of defective articles divided by the sample size 4/50 tells us how much of the sample was defective (0.08, or 8%). If 8% of the sample was defective, it is probable that the percentage of defective articles in the complete original shipment is also 8%.

The arithmetic mean of the salaries paid to five employees earning $18,400, $19,300, $18,450, $18,550, and $17,600 respectively is: a. $18,450 b. $18,460 c. $18,470 d. $18,475 e. $18,500

B. $18,460 The "arithmetic mean" is also known as the "average." First add the five salaries together: $18,400 + $19,300 + $18,450 + $18,550 + $17,600 = $92,300. Then divide the total by the number of items being averaged: $92,300 ÷ 5 = $18,460.

A pound carton of margarine contains four equal sticks of margarine. The wrapper of each stick has markings that indicate how to divide the stick into eight sections, each section measuring one tablespoon. If a recipe calls for four tablespoons of margarine, the amount to use is: a. 1/16 lb. b. 1/8 lb. c. 1/4 lb. d. 1/2 lb. e. 3/4 lb.

B. 1/8 lb. Each stick of margarine is 1/4 lb. Each stick consists of eight sections or tablespoons. Four sections or tablespoons are 1/2 of 1/4, or 1/8 lb.

It takes a runner 9 seconds to run a distance of 132 feet. What is the runner's speed in miles per hour? (5,280 feet equal 1 mile) a. 5 b. 10 c. 12 d. 15 e. 16

B. 10 The distance is 1/40 of a mile (132 feet/5,280 feet) and 9 seconds equals 1/400 of an hour (9/3,600). Traveling 1/40 mile in 1/400 hour, the runner moves 1 mile in 1/10 hour, or 10 miles in 1 hour, or 10 miles per hour.

If an aircraft is traveling at 630 miles per hour, how many miles does it cover in 1,200 seconds? a. 180 miles b. 210 miles c. 240 miles d. 280 miles e. 310 miles

B. 210 miles Since 1,200 seconds equals 20 minutes (1,200 seconds/60 seconds) and 20 minutes equals 1/3 hour, 1/3 of 630 miles equals 210 miles.

An Air Force recruiting station enlisted 560 people. Of these, 25% were under 20 years old and 35% were 20 to 22 years old. How many of the recruits were over 22 years old? a. 196 b. 224 c. 244 d. 280 e. 336

B. 224 25% + 35% = 60%. 60% were 22 years old or under 22 years of age. 40% were over 22 years old. 560 × 0.40 = 224.

If your watch gains 20 minutes per day, and you set it to the correct time at 7:00 a.m., the correct time when the watch indicates 1:00 p.m. is: a. 12:45 p.m. b. 12:50 p.m. c. 12:55 p.m. d. 1:05 p.m. e. 1:10 p.m.

C. 12:55 PM The interval between 7:00 a.m. and 1:00 p.m. is 6 hours, or 1/4 of a day, and 1/4 of 20 minutes equals 5 minutes. Subtracting 5 minutes from a watch reading of 1:00 p.m. equals 12:55 p.m.

If the weight of water is 62.4 pounds per cubic foot, the weight of the water that fills a rectangular container that is 6 inches by 6 inches by 1 foot is: a. 3.9 pounds. b. 7.8 pounds. c. 15.6 pounds. d. 31.2 pounds. e. 62.4 pounds.

C. 15.6 pounds 1/2 foot x 1/2 foot x 1 foot = 1/4 cubic foot and 1/4 of 62.4 pounds = 15.6 pounds

There are 20 cigarettes in one pack and 10 packs of cigarettes in a carton. A certain brand of cigarette contains 12 mg of tar per cigarette. How many grams of tar are contained in one carton of these cigarettes? (1 gram = 1,000 milligrams) a. 0.024 grams b. 0.24 grams c. 2.4 grams d. 24 grams e. 240 grams

C. 2.4 grams If there are 200 cigarettes in a carton (20 cigarettes × 10 packs), a full carton of 200 cigarettes contains 2,400 mg of tar (12 mg × 200 cigarettes). 2,400 mg equals 2.4 grams.

The length of a rectangle is 4 times its width. If the area of the rectangle is 324 square feet, the dimensions of the rectangle are: a. 8 feet × 32 feet. b. 8 feet × 33 feet. c. 9 feet × 36 feet. d. 9 feet × 40 feet. e. 9 feet × 46 feet.

C. 9 feet x 36 feet Let x equal the width of rectangle, making the length equal to 4x. The area of the rectangle is equal to its length times its width, so 324 = x(4x). Solve the equation for x to find the width, and then use that measurement to find the length. x(4x) = 324 4x^2 = 324 x^2 = 81 x = 9

The price of a $100 item after successive discounts of 10% and 15% is: a. $75.00 b. $75.50 c. $76.00 d. $76.50 e. $77.00

D. $76.50 $100 × 0.10 = $10.00, and $100 - $10 = $90, the price after the initial 10% discount. Then: $90 × 0.15 = $13.50, and $90.00 - $13.50 = $76.50, the price after the additional 15% discount.

When 550 gallons of oil are added to an oil tank that is 1/8 full, the tank becomes 1/2 full. The capacity of the oil tank is most nearly: a. 1,350 gallons. b. 1,390 gallons. c. 1,430 gallons. d. 1,470 gallons. e. 1,510 gallons.

D. 1,470 gallons 1/8x + 550 = 1/2x 550 = x/2 - x/8 550 = 3x/8 550 x 8/3 = x 1,467 = x

Assume that it takes an average of 3 man-hours to stack 1 ton of a particular item. In order to stack 36 tons of that item in 6 hours, the number of persons required is: a. 9 b. 12 c. 15 d. 18 e. 21

D. 18 To stack 36 tons of the item, it takes 108 man-hours (36 × 3). It takes 18 persons to get that much work done in 6 hours 108/6 = 18.

An athlete jogs 15 laps around a circular track. If the total distance jogged is 3 kilometers, what is the distance around the track? a. 0.2 meters b. 2 meters c. 20 meters d. 200 meters e. 2,000 meters

D. 200 meters We know 3 kilometers equals 3,000 meters, so 3000 meters/15 laps = 200 meters per lap.

About how many meters will a point on the rim of a wheel travel if the wheel makes 35 rotations and its radius is one meter? a. 110 b. 120 c. 210 d. 220 e. 240

D. 220 If the radius of the wheel is one meter, its diameter is 2 meters. The circumference of the wheel is equal to π (pi = 3.14) multiplied by the diameter (2). The circumference is multiplied by the number of rotations to get the distance traveled. circumference = (Pi x 2) x 35 = 6.28 x 35 = 219.8

A certain governmental agency had a budget last year of $1,100,500. Its budget this year was 7% higher than that of last year. The budget for next year is 8% higher than this year's budget. Which of the following is the agency's approximate budget next year? a. $1,117,600 b. $1,161,600 c. $1,261,700 d. $1,265,600 e. $1,271,700

E. $1,271,700 $1,100,500 × 0.07 = $77,035, and $1,100,500 + $77,035 = $1,177,535, this year's budget. For next year: $1,177,535 × 0.08 = $94,203, and $1,177,535 + $94,203 = $1,271,738, which is closest to choice E, $1,271,700.

Assume that the United States Mint produces one million nickels a month. The total value of the nickels produced during a year is: a. $50,000 b. $60,000 c. $250,000 d. $500,000 e. $600,000

E. $600,000 One million nickels per month for 12 months equals 12 million nickels each year, and 12,000,000 × 0.05 = $600,000.

The floor area in an Air Force warehouse measures 200 feet by 200 feet. What is the maximum safe floor load if the maximum weight the floor area can hold is 4,000 tons? a. 100 pounds per square foot b. 120 pounds per square foot c. 140 pounds per square foot d. 160 pounds per square foot e. 200 pounds per square foot

E. 200 pounds per square foot The floor area is 40,000 square feet (200 feet × 200 feet). The floor's maximum safe load is 4,000 tons, or 8,000,000 pounds (4,000 tons × 2,000 pounds). So 8,000,000 pounds/40,000 square feet = 200 pounds per square foot.

If there are red, green, and yellow marbles in a jar and 20% of these marbles are either red or green, what are the chances of blindly picking a yellow marble out of the jar? a. 1 out of 3 b. 1 out of 5 c. 2 out of 3 d. 2 out of 5 e. 4 out of 5

E. 4 out of 5 If 20% are either red or green, 80% are yellow. The chance of blindly picking a yellow marble is 4 out of 5 (80%).

The area of a square is 36 square inches. If the side of this square is doubled, the area of the new square will be: a. 72 square inches. b. 108 square inches. c. 216 square inches. d. 244 square inches. e. none of these.

E. None of These The square root of 36 equals 6, so each side of the square equals 6 inches. Doubling the length of a side (6 × 2) makes the sides 12 inches long, and 12 × 12 = 144 square inches.

A room measuring 15 feet wide, 25 feet long, and 12 feet high is scheduled to be painted shortly. If there are two windows in the room, each 7 feet by 5 feet, and a glass door, 6 feet by 4 feet, then the area of wall space to be painted measures: a. 842 square feet b. 866 square feet c. 901 square feet d. 925 square feet e. 4,406 square feet

We can assume the room is rectangular and has two long walls and two short walls. To answer this question, we must find the total area of the walls, and then subtract the area taken by the windows and door. First, let's find the area of one of the long walls: 25 ft. × 12 ft. = 300 sq. ft. Since there are two long walls, the total area of the long walls is 300 × 2 = 600 sq. ft. Next, let's find the area of the shorter walls: 15 ft. × 12 ft. = 180 sq. ft. There are two short walls, so the total area of both short walls is 2 × 180, which is 360 sq. ft. The total wall space, including the windows and door, is 600 sq. ft. + 360 sq. ft., which equals 960 sq. ft. The windows take up 35 sq. ft. each (7 ft. × 5 ft.), and the door takes up 24 sq. ft. (6 ft. × 4 ft.). So, the total area that does not need to be painted is: 35 + 35 + 24 = 94 sq. ft. The total area of wall space that does need to be painted is 960 - 94, or 866 sq. ft.