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# Arithmetic Reasoning Overview for ASVAB Power Practice Problems (page 2)

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1. a.   This is a two-step multiplication problem. First, multiply to find out how many weeks there are in six months:6 × 4.3 = 25.8. Then, multiply to find out how much is saved: \$40 × 25.8 = \$1,032.
2. d.   In this problem, you must multiply a fraction by a whole number. First, rewrite the whole number as a fraction: . Next, multiply: . Finally, convert to a mixed number: .
3. a.   Add each of the known sectors, and subtract the sum from 100% to get 12%.
4. d.   Since the rent sector is labeled 38%, find 38% of \$2,450: 0.38 × 2,450 = \$931.
5. d.   First, determine which recycler pays the most for each material. Recycler X pays the most for aluminum, cardboard, and plastic; recycler Y pays the most for glass. Next, multiply the amount in pounds of each material by the price per pound you determined in the first step. Then add these totals together to get your answer: 2,200 × .07 + 1,400 × .04 + 3,100 × .08 + 900 × .03 = 485.
6. c.   Let x equal the number of oranges left in the basket. Three more than seven times as many oranges as five is 7(5) + 3 = 38. Removing five leaves x = 38 – 5 = 33 oranges.
7. c.   Convert both the cost and the length to fractions: or , which is \$5.50.
8. b.   If the lamp is 0.25 off of its original price, then the sale price will be 0.75 (1.0 – 0.25 = 0.75). Convert 0.75 into a fraction and reduce; .
9. c.   This is a division of fractions problem. First, change the whole number to a fraction: . Then, invert the second fraction and multiply: .
10. d.   To find 150% of \$45, change the percent to a decimal and multiply: 1.50 × 45 = 67.50. Since this is the markup of the price, add \$67.50 to \$45 to find the new price of \$112.50.
11. b.   This is a two-step problem involving multiplication and addition. First, determine how many cards were sold on Saturday: 0.05 × 200 = 10. That leaves 190 cards. Then, find out how many cards were sold on Sunday:0.10 × 190 = 19. Next, add the cards that were sold: 10 + 19 = 29. Finally, subtract from the original number: 200 – 29 = 171.
12. b.   This is a simple addition problem. Be sure to align the decimal points: 12.98 + 5.68 + 20.64 + 6.76 = 46.06.
13. c.   Multiply the number of hours in a day by the given number of days. There are 24 hours in each day. There are 120 hours in 5 days; 5 days × 24 hours = 120 hours.
14. c.   This is a multiplication problem. To multiply a number by 1,000 quickly, move the decimal point three digits to the right— one digit for each zero. In this situation, because there are only two decimal places, add a zero.
15. c.   Hilga and Jerome's initial distance apart equals the sum of the distance each travels in 2.5 hours. Hilga travels a distance of (2.5)(2.5) = 6.25 miles, while Jerome travels (4)(2.5) = 10 miles. This means that they were 6.25 + 10 = 16.25 miles apart.
16. d.   Three inches every 2 hours = 1.5 inches per hour × 5 hours = 7.5 inches.
17. b.   For the lowest score Avi needs to get an A, assume his final average is 88. Average = (90 + 80 + 85 + a) ÷ 4 = 88. To find a, multiply 88 by 4. Then subtract Avi's first three scores: 88 × 4 = 352; 352 – (90 + 80 + 85) = 352 – 255 = 97.
18. c.   The problem is to find J, Joan's present age, in years. Begin by breaking the problem up into smaller parts: Joan will be twice Tom's age in three years becomes J + 3 = 2T; Tom will be 40 becomes T = 40. Substitute: J +3 = 2(40). Simplify: J = 80 – 3, or J = 77 years old.
19. a.   The area of each poster is 864 square inches ( 24 inches × 36 inches ). Kari may use four posters, for a total of 3,456 square inches (864 × 4). Each picture has an area of 24 square inches (4 × 6); the total area of the posters should be divided by the area of each picture, or 3,456 ÷ 24 = 144.
20. c.   This is a simple addition problem. Add 1.6 and 1.5, keeping the decimal points aligned: 1.6 + 1.5 = 3.1.
21. a.   The surface area of the trunk can be found by finding the sum of the areas of each of the six faces of the trunk. Since the answer is in square feet, change 18 inches to 1.5 feet: 2(4 × 2) + 2(4 × 1.5) + 2(2 × 1.5) = 2(8) + 2(6) + 2(3) = 16 + 12 + 6 = 34. Subtract the area of the brass ornament: 34 – 1 = 33 square feet.
22. b.   Divide the total number of seconds by the number of seconds in a minute. There are 60 seconds in a minute; 2,520 seconds is 42 minutes; 2,520 seconds ÷ 60 seconds = 42 minutes.
23. d.   Let x equal the number of hours it takes Belinda to complete the job. In one hour, the neighbor can do of the job, while Belinda can do . Working together, they take 22 hours to complete 100% of the job or: (where 1 represents 100% of the job). Simplify: or , which reduces to .Cross multiply: 16x = (22)(38), or x = 52.25 hours.
24. a.   The empty crate weighs 8.16 kg, or 8,160 g. If Jon can lift 11,000 g and one orange weighs 220 g, then the number of oranges that he can pack into the crate is equal to . Jon cannot pack a fraction of an orange. He can pack 12 whole oranges into the crate.
25. a.   Let D equal the time Dee arrived before class. Choosing to represent time before class as a negative number, you have: Jeff arrived 10 minutes early means J = –10, Dee came in four minutes after Mae means D = M + 4, Mae, who was half as early as Jeff means M = J. Substitute: M = –5, so D = –5 + 4 = –1. Thus, D = 1 minute before class.
26. d.   First, determine the percent of time that the station is NOT playing classical music. Subtract from 100%: 100 – 20 = 80. Eighty percent of the time the station does NOT play classical music. Then change thepercent to a decimal and multiply: 0.8 × 24 = 19.2.
27. b.   Divide the numerator by the denominator to find the whole number of the mixed number. The remainder, if any, becomes the numerator of the fraction: 55 ÷ 6 = 9, remainder 1. The denominator stays the same. Therefore, the mixed number is .
28. a.   In order to find the amount of fencing, the perimeter needs to be determined: 120 + 120 + 250 + 250 = 740 feet.
29. a.   This is a division problem. Because there are two decimal points in 1.25, move the decimal point two places in both numbers: .
30. d.   This is a two-step problem. Divide 12.9 by 2 to get 6.45, and then add both numbers: 12.90 + 6.45 = 19.35.

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