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

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Updated on Aug 12, 2011

1. d.   You are looking for n, and of the 200,000 sample population bicycle to work.
2. c.   Each job will pay \$21,200 after 4 years. You can see this by making a chart:
3. a.   Ricardo spends 11% for his car, half of the 22% he saves. (You can use % for the pie chart values without doing any additional math, since the values are already out of 100.)
4. a.   Savings and housing together make up 50% of Ricardo's budget: 22% + 28%.
5. c.   Ricardo spent 6 cents more per dollar on housing than on food: 28 — 22 = 6. Six cents is 6% of each budgeted dollar. \$46,500 × 0.06 = \$2,790, which is about \$2,800.
6. a.   The unreduced ratio is 8,000:5,000,000; reduced, the ratio is 8:5,000. Now divide: 5,000 ÷ 8 = 625, for a ratio of 1:625.
7. d.   It takes 9 square feet to make a square yard. To find out how many square yards are in 182 square feet, divide: square yards. Since Donna cannot purchase part of a square yard, she has to round up. She must purchase 21 square yards to have enough to carpet the room.
8. b.   Jack is likely to make of his next 25 free-throw attempts.
9. b.   Let x equal the number of people remaining in the room. You have: Thus, x = 1 person.
10. a.   or map distance in inches/actual distance in miles.
11. c.   This is a two-step problem involving both addition and division. First, arrange the three numbers in a column, keeping the decimal points aligned. Add: 113.9 + 106.7 + 122 = 342.6. Next, divide your answer by 3: 342.6 ÷ 3 = 114.2.
12. d.   You want to know R = helicopter's speed in miles per hour. To solve this problem, recall that rate × time = distance. It is given that T = 6:17 – 6:02 = 15 minutes = 0.25 hour and D = 20 miles. Substitute: r × 0.25 = 20. Simplify: r = 20 ÷ 0.25. Thus, r = 80 miles per hour.
13. c.   Multiply the number of minutes in an hour by the given number of hours. There are 60 minutes in each hour. Therefore, there are 720 minutes in 12 hours: 12 hours × 60 minutes = 720 minutes.
14. d.   Figure the amounts by setting up the following equations: First, S = \$3 + \$23 = \$26. Now, B = (\$1 × 5) + (\$2 × 2) or \$5 + \$4 = \$9. MR = \$1 × 2 = \$2; and D = \$4 × 1 = \$4. Now, add: \$9 + \$2 + \$4 = \$15. Now subtract: \$26 – \$15 = \$11.
15. b.   You want to find S, the rate Sharon charges to mow a lawn in dollars per hour. You are given Kathy's rate, which is K = 7.50, and you are told that S = 1.5K. Substitute: S = 1.5(7.50). Thus, S = \$11.25 per hour.
16. d.   A scale is a ratio of model to real, keeping the units consistent. The tower is 986 feet tall, and the replica is 4 inches; 986 feet must be converted to inches, by multiplying by 12: 986 times 12 is 11,832 inches. Set up the ratio of replica to real and simplify:
17. a.   10:30 A.M. to 5:30 P.M. is a seven-hour period. Mike can give 13 lessons, each lasting 30 minutes, if he takes 30 minutes for lunch. \$20 } 13 = \$260.
18. c.   First, determine the distance to drive to work, using the formula D = R × T. Substitute known values and then multiply: so D = 30. The distance to work is 30 miles.
19. Now, determine the time to drive to work at a rate of 40 miles per hour, again using the formula D = R × T. Substitute known values and then divide by 40: 30 = 40 × T, so 0.75 = T. The new time is 0.75 hour, or three-quarters of an hour. The problem asks how much extra time it will take to drive. This is the difference between one-half hour and three-quarters of an hour. Subtract the fractions, after changing one-half to two-quarters: One-quarter of an hour is 15 minutes.

20. a.   Set up a ratio of length to height. The proportion is Cross multiply to get 8 × l = 10 × 5.6. Multiply 10 times 5.6 to get 8 × l = 56. Divide 56 by 8 to get 7 feet long.
21. b.   There has been an increase in price of \$3; \$3 ÷ \$50 = 0.06. This is an increase of 0.06, or 6%.
22. c.   Take the words in order and substitute the letters and numbers. Patricia has (P =), four times (4 ×) the number of marbles Sean has (S). The statement becomes P = 4 × S, which is equal to P = 4S.
23. b. Let x equal the unknown quantity of each denomination. You know that all the coins total \$8.20 and that each denomination is multiplied by the same number, x. Therefore, 0.25x + 0.10x + 0.05x + 0.01x = 8.20. This reduces to (0.25 + 0.10 + 0.05 + 0.01)x = 8.20, or 0.41x = 8.20. Thus, x = 20 coins in each denomination.
24. c.   12 × 5% + 4 × 4% = x times 16; x = 4.75%.
25. a.   You are asked to find F, Fluffy's age. Begin the solution by breaking the problem into parts: Fluffy is half the age of Muffy becomes Muffy is one-third as old as Spot becomes and Spot is half the neighbor's age becomes You know the neighbor's age is 24 or N = 24. Substitute and work backward through the problem: Thus, Fluffy is two years old.
26. a.   Mario has finished of his test, which reduces to so he has of the test to go.
27. b.   Let x equal D'Andre's rate. D'Andre's rate multiplied by his travel time equals the distance he travels; this equals Adam's rate multiplied by his travel time: 2x = D = 3(x – 5). Therefore, 2x = 3x – 15, or x = 15 miles per hour.
28. b.   There are three steps involved in solving this problem. First, convert 4.5% to a decimal: 0.045. Multiply that by \$26,000 to find out how much the salary increases. Finally, add the result (\$1,170) to the original salary of \$26,000 to find out the new salary, \$27,170.
29. b.   Let L equal the number of gallons of gas lost, which is equal to the rate of loss times the time over which it occurs, or L = RT. Substitute: gallons. Notice that the 14-gallon tank size is irrelevant information in this problem.
30. a. Let R equal Veronica's average speed. Recall that for uniform motion, distance = rate × time or D = RT. Substitute: 220 = R(5) or Thus, R = 44 miles per hour.
31. b.   860 feet × 560 feet ÷ 43,560 square feet per acre = 11.06 acres.