More Mathematics Knowledge for ASVAB Power Practice Problems

Answers

1. d.   Subtract 5 from 25 to get 20. Then, multiply 20 by 5 to find the correct answer of 100.
2. d.   There are four sides measuring 4, and two sides measuring 8. Therefore, the perimeter is (4 × 4) + (2 × 8) = 32.
3. b.   The root cent means 100 (think of the word century), so the word percent literally means "per 100 parts." Thus 25% means 25 out of 100, which can also be expressed as a ratio: 25:100.
4. a.   To find the square root of a number, ask the question, "What number times itself equals 64?" The answer is 8.
5. c.   76 ÷ 19 = 4; the other division operations will not end in whole numbers.
6. c.   If the pentagons are similar, then the sides are in proportion. Because AB is similar to FG, and AB = 10 and FG = 30, the second pentagon is three times as large as the first pentagon. Therefore, HI is three times as large as CD, which gives a length of 15.
7. c.   A trapezoid by definition is a quadrilateral with exactly one pair of parallel sides.
8. b.   To find the greatest common factor of 3x², 12x, and 6x³ first start with the coefficients, or numbers in front of the variables. The largest number that divides into 3, 6, and 12 without a remainder is 3.With the variables, the smallest exponent on x is 1, so x¹, or x, is the largest variable factor.Therefore, the greatest common factor of all three terms is 3x.
9. b.   Because the integers must be even, the equation n + (n + 2) + (n + 4) = 30 is used. This gives 3n + 6 = 30; 3n = 24; n = 8. Therefore, 8 is the first number in the series. Choice a, (9, 10, 11) would work, but the numbers aren't even integers.
10. b.   To convert a decimal to a percent, multiply the decimal by 100, or move the decimal point two places to the right. Therefore, 6.0% is the correct answer.
11. b.   Simply set up the equation in the manner in which the problem is written. Since , the equation is . Cross multply: 1.30x = (0.40)(100). Simplify: .Thus, x = 30.7, which means that $0.40 is about 31% of $1.30.
12. c.   A right angle is exactly 90°.
13. d.   In order to form a triangle, the sum of the two shortest sides must be greater than the longest side. In choice d, the two shortest sides are 2 and 2; 2 + 2 = 4, which is greater than the largest side of 3.
14. b.   A cube has four sides, a top, and a bottom, which means that it has six faces.
15. c.   A prime number is a number that has xactly two factors, 1 and itself. Each of the number choices has more than two factors except 11, whose only factors are 1 and 11.
16. c.   The fraction reduced to lowest terms is .
17. b.   When you are performing addition or subtraction with roots, the terms can be combined only if the radicands (numbers under the square root symbols) are the same. In this case, the radicands are both 2. Subtract the whole numbers in front of the square roots and keep the 2. Then, 16 – 4 = 12 , so the final answer is 12 2.
18. c.   Since 45 is nine times larger than five in the denominators, convert to an equivalent fraction by multiplying 2 by 9 to get the resulting numerator: 2 × 9 = 18, so x = 18. Another way to solve this problem is to cross multiply to get 5x = 90. Divide both sides of the equation by 5 to get x = 18.
19. a.   All of the angles are acute, and all are different. Therefore, the triangle is acute scalene.
20. d.   The correct answer to this simple addition problem is 1.268.
21. c.   The greatest area from a quadrilateral will always be a square. Therefore, a side will be 24 ÷ 4 = 6 feet. The area is 6² = 36 square feet.
22. a.   The correct answer is 5.
23. c.   The bars on either side of –14 indicate the absolute value of –14. The absolute value of a number is its distance away from zero on a number line and, in this case, is 14. Therefore, 14 + –5 = 9. Since the signs are different, subtract and keep the sign of the larger number.
24. c.   Ten times 10 times 10 is 1,000. One thousand times 7.25 is 7,250.
25. c.   First ask how many inches are in one foot; the answer is 12 inches. Now multiply: 12 × 4 = 48 inches.