ANSWER KEY AND EXPLANATIONS

1	The correct answer is (B). .
2.	The correct answer is (C).
3.	The correct answer is (E).
4.	The correct answer is (A).
5.	The correct answer is (B). x + 0.40x =
6.	The correct answer is (B). 212 × 212 = 44,944.
7.	The correct answer is (D). 25 = 32; n – 3 = 5; n = 8.
8.	The correct answer is (D). There is one digit in the square root for every pair of digits in the whole number.
9.	The correct answer is (B).
10.	The correct answer is (E). 5[4 – (–1) + 13] – 6 = 5 [5 + 13] – 6 = 5 × 18 – 6 = 90 – 6 = 84.
11.	The correct answer is (D). If x is less than 10 and y is less than 5, x + y is less than 15.
12.	The correct answer is (C). The area is multiplied by 22, or 4; the perimeter is doubled or multiplied by 2.
13.	The correct answer is (E). Let x = one of the numbers and y = the other number;
14.	The correct answer is (B).
15.	The correct answer is (B). (–3) + (+5) = +2 (+2) – (–4) = +6
16.	The correct answer is (E). An even number of negative signs when multiplying gives a positive product: (–6) (+5) (–4) = + 120.
17.	The correct answer is (D).
18.	The correct answer is (A). r + s = 25; 4(r + s) = 100.
19.	The correct answer is (B). 8x = 3x + 15; 5x = 15; x = 3.
20.	The correct answer is (E).
21.	The correct answer is (D).
22.	The correct answer is (C). 12 × 12 = 144; 13 × 13 = 169; thus, the square root of 150 is between 12 and 13.
23.	The correct answer is (B).
24.	The correct answer is (D).
25.	The correct answer is (D). Multiply by abc;
26.	The correct answer is (B). a2 – b2 = (a + b)(a – b) = 9 × 3 = 27
27.	The correct answer is (D).Adding
28.	The correct answer is (D). Multiply the first equation by 3 and the second equation by 7. 21x – 6y = 6; 21x + 28y = 210; subtracting, 34y = 204;
29.	The correct answer is (C).
30.	The correct answer is (A).
31.	The correct answer is (A).
32.	The correct answer is (D).
33.	The correct answer is (D). Add 2, multiply by 2; add 2, multiply by 2; etc.
34.	The correct answer is (E). C E H J M O R T D FG I KL N PQ S (Skip 1, skip 2; repeat.).
35.	The correct answer is (B). There is a difference of 20 between the last term and the first term. There are 5 terms following the initial term. the common difference (3, 7, 11, 15, 19, 23).
36.	The correct answer is (B). At 3:30 P.M., the minute hand is at the 6 and the hour hand is midway between the 3 and the 4. between numbers. = 75°
37.	The correct answer is (B). If angle BCD = 110º, angle BCA = 70º, and angle BAC = 70º. Angle ABC = 180º – 140º or 40º.
38.	The correct answer is (A). x + 5x = 90º; 6x = 90º; x = 15º.
39.	The correct answer is (E). 2x + 3x + 4x = 9x; 9x = 180º; x = 20º; the angles are 40º, 60º, and 80º—all acute angles.
40.	The correct answer is (B). The sum of the two base angles is 2x. Therefore, the number of degrees in the vertex angle = 180 – 2x.
41.	The correct answer is (B).
42.	The correct answer is (C).
43.	The correct answer is (E). Let 4x = length and 3x = width. 4x + 3x + 4x + 3x = 140; 14x = 140; x = 10. Length = 40 feet; width = 30 feet. If two sides of a right triangle are 40 and 30 feet, the hypotenuse or diagonal = 50 feet.
44.	The correct answer is (B). An inscribed angle is equal in degrees to one half its intercepted arc. Angle ABC, an inscribed angle, is equal to one half of 80º. Angle ABC = 40º.
45.	The correct answer is (C). Area = r2. If diameter = 6 inches, radius = 3 inches; area = × 32; area = 9.
46.	The correct answer is (C). 24 inches
47.	The correct answer is (E). Area = r2; r2 = 16; r = 4; diameter = 8; 4 × 8 = 32.
48.	The correct answer is (D). The length, width, and height of a cube are all equal. The volume of a cube is equal to the cube of an edge. Each edge = 3 feet. Volume = 3' × 3' × 3' = 27 cubic feet.
49.	The correct answer is (A). r2 × height = volume; × 82 × 10 = volume; inches divided by 231 cubic inches = 8.7 gallons.
50.	The correct answer is (E). 30 + 28 + 20 + 17 = 95; 100 – 95 = 5. The miscellaneous classification comprised 5% of the immigrants for that year. 360º × 0.05 = 18º.
51.	The correct answer is (C). A circle is 360º; 60º is of 360º.
52.	The correct answer is (B). There are 6 + 8 + 4 + 12 = 30 marbles. 12 + 30 = 0.40
53.	The correct answer is (B). = 20%.
54.	The correct answer is (D). 33 × 3 = 27 × 3 = 81
55.	The correct answer is (B). 0.04y = 1; y = 1 ÷ 0.04 = 25.
56.	The correct answer is (B). The number of accidents is irrelevant to the question, so A has no place in the equation. B(total deaths) ÷ 10 years = average deaths per year.
57.	The correct answer is (C). To place the decimal point in the product, add together the number of digits to the right of the decimal points in all of the multipliers. In this case, the answer requires 6 decimal places.
58.	The correct answer is (A). To find how many tons fall in a given number of minutes, multiply the number of tons that fall in one minute by the number of minutes. There are 60 seconds in 1 minute, and T tons fall in 1 second. In M minutes, the amount of snow that falls is 60MT.
59.	The correct answer is (A). Subtract A2 from both sides of the equation: B2 = X2, therefore B = X or –X.
60.	The correct answer is (A). 6 + x + y = 20 x + y = 14 = k; now substitute 20 – 14 = 6
61.	The correct answer is (D). The first step in finding a square root is grouping the digits into pairs, starting at the decimal point. If necessary, place a 0 to the left of the first digit to create a pair. Each pair represents one digit in the square root. The square root of 960 is a two-digit number in the 30s because the square root of 09 is 3.
62.	The correct answer is (D). 8 + 5(x – y) = 8 + 5x – 5y Since x = y, 5x = 5y and 5x – 5y = 0 Substituting: 8 + 0 = 8
63.	The correct answer is (C).
64.	The correct answer is (D). Each sport jacket can be worn with 5 pairs of slacks. 3 × 5 = 15.
65.	The correct answer is (B). C = 2r 60 = 2r (Divide both sides by 2ð). r = 60 ÷ 2
66.	The correct answer is (B). Pick a pair of ages and try for yourself. A is 2; B is 4; the ratio of their ages is 2 to 4 or 1 to 2. In two years, A is 4 and B is 6. The ratio of their ages is 4 to 6 or 2 to 3.
67.	The correct answer is (D).
68.	The correct answer is (B). The formula for the area of a triangle is the base times the height.
69.	The correct answer is (A). “Percent” means out of 100. If K percent are emotionally unstable, then K out of 100 are emotionally unstable. The remainder, 100 – K, is not unstable.
70.	The correct answer is (C). The formula to find the circumference of a circle is 2r. The formula to find the area of a circle is r2. The only number that has the same value when multiplied by 2 or squared is 2.
71.	The correct answer is (D). CD is a hypotenuse, so use the Pythagorean theorem:
72.	The correct answer is (B). of 60 min. = 40 min. 5:00 + 40 min. = 5:40.
73.	The correct answer is (D). Assign arbitrary values to solve this problem: A square 10 ft. × 10 ft. = 100 sq. ft. A rectangle 9 ft. × 11 ft. = 99 sq. ft.
74.	The correct answer is (C). Diagram this problem:
75.	The correct answer is (C). The formula for the area of a circle is r2. In this problem, r2 = 64, so r = 8. The circle is tangent with the square on all four sides; the radius is exactly the length of a side of the square. Each side, then, is 16 units long. The formula for the perimeter of a square is P = 4s, so 4 × 16 = 64.