ASVAB Arithmetic Reasoning

Transcription

1 ASVAB Arithmetic Reasoning Number: Arithmetic Reasoning Passing Score: 800 Time Limit: 120 min File Version: 1.0

2 Arithmetic Reasoning QUESTION 1 If there are 3 quarts of gas in a gallon container, how full is the container? A. 50% B. 60% C. 75% D. 80% /Reference: QUESTION 2 If 12 workers are needed to run 4 machines, how many workers are needed to run 20 machines? A. 20 B. 48 C. 60 D. 80 /Reference: QUESTION 3 How many 36-passenger buses will it take to carry 144 people?

3 A. 3 B. 4 C. 5 D. 6 Correct Answer: B /Reference: QUESTION 4 If the tire of a car rotates at a constant speed of 552 times in one minute, how many times will the tire rotate in half-an-hour? A. 276 B. 5,520 C. 8,280 D. 16,560 Correct Answer: D /Reference: QUESTION 5 A motorcycle costs $7,250. If it depreciates by 12% per year, how much will it be worth after one year? A. $870 B. $1,250 C. $5,920 D. $6,380 Correct Answer: D

4 /Reference: QUESTION 6 It costs $0.50 per square yard to waterproof canvas. What will it cost to waterproof a canvas truck cover that is 15' x 24'? A. $6.67 B. $18.00 C. $20.00 D. $ /Reference: QUESTION 7 A faucet gives 20 gallons of water in 5 seconds. How many gallons does it give in 7 seconds? A. 24 B. 26 C. 28 D. 30 /Reference:

5 QUESTION 8 One in every 9 people in a town vote for party A. All others vote for party B. How many people vote for party B in a town of 810? A. 90 B. 720 C. 801 D. 819 Correct Answer: B /Reference: QUESTION 9 Find the average of the following numbers: 29, 15 A B C D /Reference: To find the average of these 2 numbers add them together then divide by 2: 44 / 2 = 22.0 QUESTION 10 A landscaping company charges 8 cents per square foot to apply fertilizer. How much would it cost for them to fertilize a 49 ft. x 26 ft. lawn? A. $10.19 B. $ C. $ D. $10,192

6 /Reference: The first step in solving this problem is to calculate the area of the lawn to find out how many square feet of lawn need fertilized. Area is width multiplied by height which, in this case, is 49 ft. x 26 ft. = 1274 ft22. The cost to apply fertilizer is 8 cents per square foot so the answer is 1274 ft22 * $0.08 = $ QUESTION 11 A 1 ton truck is taxed at a rate of $0.14 per pound. How much is owed in taxes? A. $140 B. $420 C. $0.14 D. $280 Correct Answer: D /Reference: The key to this question is remembering that a ton contains 2,000 pounds. Then, it's just a matter of multipling 2,000 by the number of tons the truck weighs to get the weight in pounds: 2,000 x 1 ton = 2,000 pounds then multiplying by the tax rate per pound. So, the answer is 2,000 x $0.14 = $280. QUESTION 12 A machine in a factory has an error rate of 2 parts per 100. The machine normally runs 24 hours a day and produces 60 parts per hour. Yesterday the machine was shut down for 2 hours for maintenance. How many error-free parts did it produce yesterday? A B C D. 1440

7 Correct Answer: A /Reference: The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour: (2/100) x 60 = 0.02 x 60 = 1.2 errors per hour So, in an average hour, the machine will produce = 58.8 error free parts. The machine ran for 24-2 = 22 hours yesterday so you would expect that 22 x 58.8 = error free parts were produced yesterday. QUESTION 13 9 members of a bridal party need transported to a wedding reception but there are only 2 4-passenger taxis available to take them. How many will need to find other transportation? A. 3 B. 1 C. 0 D. 2 Correct Answer: B /Reference: There are 2 4-passenger taxis available so that's 2 x 4 = 8 total seats. There are 9 members of the bridal party who need transporting so 9-8 = 1 person who will have to find other transportation. QUESTION 14 What's the quotient of / 0.63? A B C D Correct Answer: D /Reference:

8 The first step to solving this problem is that the word 'quotient' means the result of division. After that, it's simply a matter of dividing by by 0.63 to get QUESTION 15 What are the next two numbers in this series: {5, 15, 11, 33, 29,?,?} A. 5, 15 B. 87, 83 C. 87, 29 D. 75, 25 Correct Answer: B /Reference: This series is constructed by alternately multiplying the last number in the series by 3 and then subtracting 4 from the result: 5 15 = 5 x 3 11 = = 11 x 3 29 = 33-4 Making the next two numbers in the series: 87 = 29 x 3 83 = 87-4 QUESTION 16 Sam's sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 3 to 2 and the ratio of baseball to basketball cards is 3 to 1, what is the ratio of football to basketball cards? A. 9:2 B. 3:2 C. 12:3 D. 6:2

9 Correct Answer: A /Reference: The ratio of football cards to baseball cards is 3:2 and the ratio of baseball cards to basketball cards is 3:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 9:6 and the ratio of baseball cards to basketball cards as 6:2 so the ratio of football cards to baskeball cards is 9:2. QUESTION 17 A triathlon course includes a 800m swim, a 31.2km bike ride, and a 3.98km run. What is the total length of the race course? A m B m C km D km /Reference: This is a simple addition problem with the caveat that you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike ride and run distances. To convert 800 meters to kilometers divide it by 1000 to get 0.80 then add the remaining distances: = 35.98km. NOTE You could also convert the bike and run distances to meters and then add the swim distance but that requires two conversions instead of one. Not only does doing just one conversion save you time it also minimizes the steps needed to complete this problem and therefore reduces the chances for a calculation mistake. QUESTION 18 A 2 ton truck is taxed at a rate of $0.19 per pound. How much is owed in taxes? A. $380 B. $1,140 C. $760 D. $0.38 Correct Answer:

10 /Reference: The key to this question is remembering that a ton contains 2,000 pounds. Then, it's just a matter of multipling 2,000 by the number of tons the truck weighs to get the weight in pounds: 2,000 x 2 tons = 4,000 pounds then multiplying by the tax rate per pound. So, the answer is 4,000 x $0.19 = $760. QUESTION 19 On average, the center for a basketball team hits 44% of his shots while a guard on the same team hits 48% of his shots. If the guard takes 150 shots this year, how many shots will the center have to take to score as many points as the guard assuming each shot is worth the same number of points? A. 341 B. 164 C. 72 D. 66 Correct Answer: B /Reference: If the guard hits 48% of his shots and takes 150 shots he'll make /100= = 72 shots. The center makes 44% (0.44) of his shots so he'll have to take 72/0.44 = 164 shots to make the same number of shots as the guard and thus score the same number of points. QUESTION 20 A machine in a factory has an error rate of 4 parts per 100. The machine normally runs 24 hours a day and produces 40 parts per hour. Yesterday the machine was shut down for 6 hours for maintenance. How many error-free parts did it produce yesterday? A B C. 960 D Correct Answer: B /Reference:

11 The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour: (4/100) x 40 = 0.04 x 40 = 1.6 errors per hour So, in an average hour, the machine will produce = 38.4 error free parts. The machine ran for 24-6 = 18 hours yesterday so you would expect that 18 x 38.4 = error free parts were produced yesterday. QUESTION 21 If a problem asks you to find the quotient of two numbers, what operation would you perform? A. Divide B. Multiply C. Add D. Subtract Correct Answer: A /Reference: When finding the quotient of two numbers you would divide. QUESTION 22 Sam is having a birthday party for his son and is serving orange juice to the 6 children in attendance. If Sam has 1 liter of orange juice and wants to divide it equally among the children, how many liters does each child get? A. 1/6 liter B. 1/5 liter C. 1/3 liter D. 1/12 liter Correct Answer:

12 /Reference: 1 liter of orange juice divided among 6 children is 1/6 liter liter for each child QUESTION 23 Connie loaned Sam $1,500 at a yearly interest rate of 9%. After one year what is the interest owed on this loan? A. $1,635 B. $135 C. $9 D. $108 Correct Answer: B /Reference: The yearly interest charged on this loan is the annual interest rate (9%) multiplied by the amount borrowed ($1,500). To get the interest charged first convert the interest rate from a percentage to a decimal by dividing by 100 (9 / 100) to get 0.09 then multiply 0.09 by $1,500 to get $135. NOTE When you're dealing with percentages you'll always need to convert the percent to a decimal by dividing by 100 before doing any calculations with it. QUESTION 24 If a rectangle is twice as long as it is wide and has a perimeter of 6 inches, what is the area of the rectangle? A. 4 B. 6 C. 2 D. 0.5 /Reference: The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 6 inches so the equation becomes: 2w + 2h = 6. Putting these two equations together and solving for width (w): 2w + 2h = 6 w + h = 6 / 2 w + h = 3

13 w = 3 - h From the question we know that h = 2w so substituting 2w for h gives us: w = 3-2w 3w = 3 w = 3 / 3 w = 1 Since h = 2w that makes h = 2 and the area 1 x 2 = 2 QUESTION 25 Connie loaned Sam $1,000 at a yearly interest rate of 5%. After one year how much will Sam owe Connie? A. $950 B. $50 C. $1,005 D. $1,050 Correct Answer: D /Reference: The yearly interest charged on this loan is the annual interest rate (5%) multiplied by the amount borrowed ($1,000). To get the interest charged first convert the interest rate from a percentage to a decimal by dividing by 100 (5 / 100) to get 0.05 then multiply 0.05 by $1,000 to get $50. But, the question doesn't ask how much annual interest was charged it asks how much is owed at the end of the year. So, the answer is the loan amount of $1,000 + $50 interest charged which is $1,050. QUESTION 26 How many 11-passenger vans will it take to drive all 69 players and coaches on the football team to the away game? A. 5 B. 8 C. 6 D. 7 Correct Answer: D /Reference: Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van: 69 / 11 = 6 3/11 vans. Because

14 taking 3/11 of a van isn't possible one extra van is needed bringing the total to 7. QUESTION 27 A 3 ton truck is taxed at a rate of $0.15 per pound. How much is owed in taxes? A. $1,350 B. $900 C. $450 D. $0.45 Correct Answer: B /Reference: The key to this question is remembering that a ton contains 2,000 pounds. Then, it's just a matter of multipling 2,000 by the number of tons the truck weighs to get the weight in pounds: 2,000 x 3 tons = 6,000 pounds then multiplying by the tax rate per pound. So, the answer is 6,000 x $0.15 = $900. QUESTION members of a bridal party need transported to a wedding reception but there are only 2 4-passenger taxis available to take them. How many will need to find other transportation? A. 3 B. 1 C. 2 D. 4 /Reference: There are 2 4-passenger taxis available so that's 2 x 4 = 8 total seats. There are 10 members of the bridal party who need transporting so 10-8 = 2 people who will have to find other transportation. QUESTION 29 If an object travels at 0.6 cm per second, how many meters does it travel in 3 hours? A B

15 C. 6, D Correct Answer: B /Reference: Convert the object's speed from cm per second to m per hour: Then multiply by the number of hours: QUESTION 30 On average, the center for a basketball team hits 44% of his shots while a guard on the same team hits 45% of his shots. If the guard takes 160 shots this year, how many shots will the center have to take to score as many points as the guard assuming each shot is worth the same number of points? A. 356 B. 164 C. 364 D. 70 Correct Answer: B /Reference: If the guard hits 45% of his shots and takes 160 shots he'll make /100= = 72 shots. The center makes 44% (0.44) of his shots so he'll have to take 72/0.44 = 164 shots to make the same number of shots as the guard and thus score the same number of points. QUESTION 31 A circular logo is enlarged to fit the lid of a jar. The new diameter is 45% larger than the original. By what percentage has the area of the logo increased? A. 17.5%

16 B. 32.5% C. 22.5% D. 12.5% /Reference: The area of a circle is given by the formula where r is the radius of the circle. The radius of a circle is its diameter divided by two so So, if the diameter of the logo increases by 45%, the radius increases by 45/2 = 22.5% which, in turn, increases the total area by 22.5%. QUESTION 32 Find the average of the following numbers: 10, 36 A B C D /Reference: To find the average of these 2 numbers add them together then divide by 2: 46 / 2 = 23.0 QUESTION 33 How many 14-passenger vans will it take to drive all 46 players and coaches on the football team to the away game? A. 3 B. 2

17 C. 5 D. 4 Correct Answer: D /Reference: Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van: 46 / 14 = 3 4/14 vans. Because taking 4/14 of a van isn't possible one extra van is needed bringing the total to 4. QUESTION 34 If Connie deposits $200 into a savings account with a 9% annual interest rate and doesn't withdraw any of the money for 5 years, what will her balance be at the end of 5 years? A. $90.00 B. $ C. $ D. $ Correct Answer: D /Reference: The important thing to remember when calculating this answer is that the balance that Connie will earn interest on is increasing each year with each new annual interest payment. Here's a yearly breakdown remembering that 9% interest is (9/100) = 0.09 as a decimal: Year 1: $ x 0.09 = $ interest and $ total Year 2: $ x 0.09 = $ interest and $ total Year 3: $ x 0.09 = $ interest and $ total Year 4: $ x 0.09 = $ interest and $ total Year 5: $ x 0.09 = $ interest and $ total Which, when rounded to two decimal places, is $ NOTE Here's a shortcut formula for figuring out the accumulation due to annual interest: A=P(1+i) t where A is the amount accumulated, P is the principal, i is the interest rate, and t is the number of years. Plugging in our variables we get: A=200(1+0.09) 5

18 A=200(1.09) 5 A= A= Feel free to use this formula (or look up "compound interest formula" to get the full version). We chose to show you how to calculate the result without using the shortcut so you'll know how the process works and be better prepared for whatever interest rate questions the test may throw at you. QUESTION 35 Connie loaned Sam $1,000 at a yearly interest rate of 9%. After one year what is the interest owed on this loan? A. $108 B. $9 C. $90 D. $1,090 /Reference: The yearly interest charged on this loan is the annual interest rate (9%) multiplied by the amount borrowed ($1,000). To get the interest charged first convert the interest rate from a percentage to a decimal by dividing by 100 (9 / 100) to get 0.09 then multiply 0.09 by $1,000 to get $90. NOTE When you're dealing with percentages you'll always need to convert the percent to a decimal by dividing by 100 before doing any calculations with it. QUESTION 36 A 2 ton truck is taxed at a rate of $0.2 per pound. How much is owed in taxes? A. $1,200 B. $400 C. $800 D. $.40 /Reference: The key to this question is remembering that a ton contains 2,000 pounds. Then, it's just a matter of multipling 2,000 by the number of tons the truck weighs to get the weight in pounds: 2,000 x 2 tons = 4,000 pounds then multiplying by the tax rate per pound. So, the answer is 4,000 x $0.2 = $800.

19 QUESTION 37 In a class of 25 students, 6 are taking German and 8 are taking Spanish. Of the students studying German or Spanish, 4 are taking both courses. How many students are not enrolled in either course? A. 16 B. 15 C. 19 D. 14 Correct Answer: B /Reference: The number of students taking German or Spanish is = 14. Of that group of 14, 4 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 14-4 = 10 who are taking at least one language = 15 students who are not taking either language. QUESTION 38 If a car travels miles in 4.7 hours what is its average speed? A miles per hour B miles per hour C miles per hour D miles per hour /Reference: Average speed in miles per hour is the number of miles travelled divided by the number of hours: / 4.7 = 60.7 miles per hour. QUESTION 39 If a rectangle is twice as long as it is wide and has a perimeter of 18 inches, what is the area of the rectangle? A. 9 B. 6

20 C. 18 D. 15 /Reference: The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 18 inches so the equation becomes: 2w + 2h = 18. Putting these two equations together and solving for width (w): 2w + 2h = 18 w + h = 18 / 2 w + h = 9 w = 9 - h From the question we know that h = 2w so substituting 2w for h gives us: w = 9-2w 3w = 9 w = 9 / 3 w = 3 Since h = 2w that makes h = 6 and the area 3 x 6 = 18 QUESTION 40 What is the sum of 6.12 and 0.68? A B C D /Reference: You find the sum of two numbers by adding them = 6.80 QUESTION 41 After being dropped a ball always bounces back to 2/7 of the height of its previous bounce. After the first bounce it reaches a height of 290 inches. How high will it reach on bounce number 4?

21 A inches B inches C inches D inches /Reference: This problem is a series of multiplications by 2/7: 290 inches 2/7 2/7 2/7 = /7 7 7 = 2320/343 = 6.76 inches QUESTION 42 What's the quotient of / 0.77? A B C D Correct Answer: A /Reference: The first step to solving this problem is that the word 'quotient' means the result of division. After that, it's simply a matter of dividing by by 0.77 to get QUESTION 43 What is?

22 A. B. C. D. /Reference: When multiplying fractions simply multiply the numerators (top numbers) and the denominators (bottom numbers) to get the result QUESTION 44 Connie loaned Sam $1,500 at a yearly interest rate of 7%. After one year how much will Sam owe Connie? A. $1,605 B. $105 C. $1,507 D. $1,395 Correct Answer: A /Reference: The yearly interest charged on this loan is the annual interest rate (7%) multiplied by the amount borrowed ($1,500). To get the interest charged first convert the interest rate from a percentage to a decimal by dividing by 100 (7 / 100) to get 0.07 then multiply 0.07 by $1,500 to get $105. But, the question doesn't ask how much annual interest was charged it asks how much is owed at the end of the year. So, the answer is the loan amount of $1,500 + $105 interest charged which is $1,605. QUESTION 45 Connie scored 19% on her final exam. If each question was worth 6 points and there were 600 possible points on the exam, how many questions did Connie get right? A. 81 B. 114

23 C. 19 D. 486 /Reference: Connie scored 19% on the test meaning she earned 19% of the possible points on the test. There were 600 possible points on the test so she earned 600 x 0.19 = 114 points. Each question is worth 6 points so she got = 19 questions right. QUESTION 46 After being dropped a ball always bounces back to 2/5 of the height of its previous bounce. After the first bounce it reaches a height of 123 inches. How high will it reach on bounce number 5? A inches B inches C inches D inches Correct Answer: B /Reference: QUESTION 47 Connie scored 32% on her final exam. If each question was worth 6 points and there were 600 possible points on the exam, how many questions did Connie get right? A. 68 B. 408 C. 192 D. 32 Correct Answer: D

24 /Reference: Connie scored 32% on the test meaning she earned 32% of the possible points on the test. There were 600 possible points on the test so she earned 600 x 0.32 = 192 points. Each question is worth 6 points so she got = 32 questions right. QUESTION 48 Find the average of the following numbers: 15, 27, 25, 26, 11 A B C D Correct Answer: A /Reference: To find the average of these 5 numbers add them together then divide by 5: 104 / 5 = 20.8 QUESTION 49 Connie loaned Sam $500 at a yearly interest rate of 3%. After one year what is the interest owed on this loan? A. $36 B. $515 C. $3 D. $15 Correct Answer: D /Reference: The yearly interest charged on this loan is the annual interest rate (3%) multiplied by the amount borrowed ($500). To get the interest charged first convert the interest rate from a percentage to a decimal by dividing by 100 (3 / 100) to get 0.03 then multiply 0.03 by $500 to get $15. NOTE When you're dealing with percentages you'll always need to convert the percent to a decimal by dividing by 100 before doing any calculations with it. QUESTION 50 6 years ago Connie was 2 times as old as Sam was. If Connie is now 26 years old, how old is Sam now?

25 A. 16 B. 14 C. 11 D. 20 Correct Answer: A /Reference: Creating an equation from the variables in this problem: [Connie's Age Now] - [6 Years Ago] = [2 Times as Old] x [Sam's Age 6 Years Ago] 26-6 = 2 x Sam's Age 6 Years Ago Sam's Age 6 Years Ago = (26 6)/2 = 20/2 = 10 so Sam is now = 16 years old. QUESTION 51 What is the sum of 8.97 and 0.16? A B C D /Reference: You find the sum of two numbers by adding them = 9.13