SECTION II TIME - 30 minutes 25 QUESTIONS :RA In this section solve each problem, using any available space on paper for scratchwork. Then decide which is the best of the choices given and select the answer. :RA The following information is for your reference in solving some of the problems. 2 Circle of radius r: Area = PIr ; Circumference = 2PIr The number of degrees of arc in a circle is 360^. The measure in degrees of a straight angle is 180^. Definitions of symbols: = is equal to || is parallel to > is greater than ^ is equal to degree < is equal to angle :RA :SB :SP257079203024179079257079 :SP203079203024203024203024 :SH1126A D B :SH0330C :SF Triangle: The sum of the measures in degrees of the angles of a triangle is 180. If <CDA is a right angle, then (1) area of TRIANGLE ABC AB x CD = ------- 2 2 2 2 (2) AC = AD + DC :RA :SD Note: Figures which accompany problems in this test are intended to provide information useful in solving problems. They are drawn as accurately as possible EXCEPT when it is stated in a specific problem that its figure is not drawn to scale. All figures lie in a plane unless otherwise indicated. All numbers used are real numbers. :RA :Q5 7 7 1. If y + - = 1, then y - - = 8 8 (a) -1 (b) 3/4 (c) -3/4 (d) 0 (e) 1 :RCC :Q14 2. If k, m, and n are positive integers, arrange the following fractions in ascending order of magnitude: k k + n k A: - B: ----- C: ----- m m m + n (a) C,A,B (b) B,A,C (c) A,B,C (d) C,B,A (e) A,C,B :RCA :Q14 3. If s is a negative integer, arrange the following in ascending order: 1 1 A: s B: - C: -s D: - - s s (a) A,B,C,D (b) D,C,B,A (c) B,A,D,C (d) A,B,D,C (e) C,D,B,A :RCD :Q5 4. For what temperature reading does F = C in the formula 9 F = -C + 32? 5 (a) 0^ (b) 160^/9 (c) -160^/9 (d) 128^/5 (e) -40^ :RCE :Q5 1 1 5. If y = 2k and - - - = 2, k = ? k y (a) 1 (b) 2 (c) 1/2 (d) 4 (e) 1/4 :RCE :Q11 6. A plane passes over point A at 3:26 P.M., and over point B at 3:50 P.M. If B is 170 miles from A, then what is the speed of the plane in miles per hour: (a) 425 (b) 675 (c) 300 (d) 510 (e) It cannot be determined from the information given. :RCA :Q7 7. The length of a rectangular field bears a 5:3 ratio to its width. If 480 feet of fencing are needed to enclose the field, its width is: (a) 180' (b) 150' (c) 90' (d) 144' (e) 288' :RCC :Q10 :SB :SG238104188265039135 :SP189120259040259040259040 :SP210048245128245128245128 :SH1339x :SH0535y :SF 8. From the graphs, find the values of x and y which satisfy the equations of both graphs. (a) 3,-2 (b) -2,3 (c) 2,-3 (d) -3,2 (e) -2,-3 :RCB :SD :Q5 9. Which of the following correctly expresses the statement, when n is divided by k - 2, the quotient is T and the remainder is r? n n (a) --- = T + r (b) --- = T(k - 2) + r k-2 k-2 n t (c) ----- = ----- + r k - 2 k - 2 n r (d) ----- = T + ----- k - 2 k - 2 (e) It cannot be determined from the information given. :RCD :Q10 :SB :SG210120195258039151 :SH0733M :SH1838N :SP215046218046218048215048 :SP250142253142253144250144 :SF 10. Find the distance between points M and N. __ (a) 17 (b) \/61 _ ___ (c) 6\/5 (d) \/157 (e) 13 :RCE :SD :Q6 11. An American bound for France weighed 180 pounds when the boat left New York. On arrival, he weighed 79.5 kilograms. Find to the nearest tenth, the percent change in weight. (1 kg. = 2.2 lb.) (a) 2.8% gain (b) 2.9% loss (c) 2.9% gain (d) 2.8% loss (e) It cannot be determined from the information given. :RCD :Q4 12. A 4-foot shelf can just be filled by books of 1 inch uniform thickness. The same shelf can be filled also by the same number of books some of which are 5/8 inch thick, and the rest, 1 1/8 inches thick. How many thinner books are needed? (a) 24 (b) 18 (c) 36 (d) 12 (e) It cannot be determined from the information given. :RCD :Q13 13. A board-foot of lumber is defined as the equivalent of a piece 12" x 12" x 1". If a man buys a board 5'4" long, 9" wide, and 3/4" thick, for how many board feet of lumber should he pay? (a) 3 (b) 5 1/3 (c) 36 (d) 2 13/16 (e) It cannot be determined from the information given. :RCA :Q12 14. In a certain chemical reaction, 98 grams of sulfuric acid produced 64 grams of sulfur dioxide. The number of grams of sulfur dioxide that would be produced by 245 grams of sulfuric acid is: (a) 160 (b) 25.6 (c) 211 (d) 150 (e) 256 :RCA :Q8 15. Find the thickness of a pipe whose inner circumference is 9PI, and whose outer circumference is 25PI. (a) 16PI (b) 16 (c) 8 (d) 8PI (e) 4 :RCC :Q8 :SB :SH0428B C :SH1228A E D :SP196031252031252087196087 :SP196087196031197031210087 :SP252087252031252031252031 :SF 16. ABCD is a square, and AE = 1/4 AD. The ratio of the area of TRIANGLE ABE to that of the square is: (a) 1:8 (b) 1:6 (c) 1:4 (d) 1:2 (e) It cannot be determined from the information given. :RCA :SD :Q7 17. If each side of a square is doubled, the ratio of the new area to the original area is: (a) 2:1 (b) 4:1 (c) 1:2 (d) 1:4 _ (e) \/2:1 :RCB :Q8 18. The area (A) of an equilateral triangle of side s is given by the 2 s _ formula A = -\/3. 4 Find A when s = 6. _ _ _ (a) 9\/3 (b) 2\/3 (c) 27 (d) 32\/3 (e) It cannot be determined from the information given. :RCA :Q8 19. A square has an area of n square units. Express its perimeter in terms of n. 2 n _ 2 (a) - (b) \/n (c) 4n (d) 4n 4 _ (e) 4 \/n :RCE :Q13 20. A company makes 30% on the selling price of an article. If the article costs $3.50, the selling price is: (a) $4.55 (b) $3.80 (c) $5.25 (d) $5.00 (e) It cannot be determined from the information given. :RCD :Q6 21. A team won g games and lost m games. What percent of its games did it win? (a) g/m (b) 100g/(g + m) (c) g/(g + m) (d) g/100(g + m) (e) It cannot be determined from the information given. :RCB :Q8 22. In TRIANGLE ABC, <A = 3y ^, <B = 1/2<C = 1/3 <B. Find <A. (a) 36^ (b) 54^ (c) 108^ (d) 18^ (e) 0^ :RCC :Q6 23. A team has won 62 1/2% of the 40 games it has played. How many games must it now win in succession to raise its overall average to 75%? (a) 30 (b) 20 (c) 24 (d) 5 (e) 15 :RCB :Q13 24. A certain job can be done by Abby in 9 hours when she works alone. When she and Beth work together, they do the job in 1/3 the time. How many hours would it take Beth alone to do the job? (a) 6 (b) 4 1/2 (c) 3 (d) 18 (e) 3 1/2 :RCB :Q6 25. Beef shrinks 40% in weight when roasted in a certain way. To have 5 1/4 pounds of roast beef on the table, how many pounds should be purchased? (a) 8 3/4 (b) 7 3/8 (c) 7 7/16 (d) 8 (e) 4 :RCA :ET :ET Copyright ARROW INSTRUCTIONAL SYSTEMS July 1983
