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 perpendicular to :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 {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 :Q1 1. In a certain school, there are 8 students in Group A studying Spanish, and 15 pupils in Group B studying French. If 3 pupils in each group also study a second language other than French and Spanish, what is the ratio of pupils studying only Spanish to those studying only French? (a) 8:15 (b) 1:3 (c) 2:3 (d) 5:12 (e) 0:1 :RCD :Q1 2. A recipe calls for 1 part milk and 1 1/2 parts flour. If 1 1/2 pints of milk are used, how many pints of flour should be used? (a) 1 (b) 1 1/4 (c) 1 1/2 (d) 3 (e) 2 1/4 :RCE :Q1 3. A certain cloth shrinks 5% in laundering. The number of yards which must be bought to have 76 yards after laundering, allowing for shrinkage, is: (a) 79.8 (b) 80 (c) 81 (d) 91.2 (e) 106 :RCB :Q1 4. Of all the members of a senior class at a certain college, 20% go on for graduate work. Of these, 5% earn a higher degree. What percent of the senior class go on for graduate work but do not get a higher degree? (a) 1 (b) 19 (c) 99 (d) 80 (e) 95 :RCB :Q1 5. A unit of soldiers consisting of 60 men has enough rations to last 8 days. If 20 additional men join the unit, how many days will the rations last? (a) 24 (b) 10 2/3 (c) 6 (d) 2 2/3 (e) 7 :RCC :Q1 6. A swimming pool is filled with 475 to 600 gallons of water. Its total capacity is 1200 gallons. What is the greatest number of gallons required to fill it to 75% capacity? (a) 900 (b) 725 (c) 600 (d) 425 (e) 300 :RCD :Q1 7. A student has done 100 mathematics problems, of which he has scored 25 incorrect. How many more problems would he have to do correctly in order to have 1/8 incorrect? (a) 25 (b) 75 (c) 100 (d) 175 (e) 200 :RCC :Q1 8. Computer A does 20% as much work as computer B. If an insurance company requires 60 computers of type A to turn out a certain product, how many computers of type B can be used to do the same job? (a) 12 (b) 15 (c) 10 (d) 5 (e) 100 :RCA :Q1 L 2 L + K 9. - = -. Find -----. K 3 L (a) 5/2 (b) 2/5 (c) 5/3 (d) 3/5 (e) 1/5 :RCA :Q1 10. Find the side of a square that has the same area as a triangle whose base is 9 inches and whose altitude is 4 inches. (a) 6 in. (b) 9 in. (c) 6.5 in. _ _ (d) 3\/2 in. (e) 2\/3 in. :RCD :Q1 :SB :SP203094252094252024203040 :SP203040203094203094203094 :SH1329A B :SH0337C :SH0529D :SF 11. DA || CB, <D = 120^, <C = 60^, DA = 5, CB = 9 Find the area of ABCD. (a) 14 (b) 56 _ _ (c) 14\/3 (d) 28\/3 _ (e) 56\/3 :RCD :SD :Q1 12. A square 10 feet on a side has twice the area of a certain rectangle. If one side of the rectangle is 5 feet, find the number of feet in its other dimension. (a) 1 (b) 2 (c) 5 (d) 10 (e) 20 :RCD :Q1 y 13. Solve for y: - - k = 1 h k + 1 (a) ----- (b) k + h (c) hk + 1 h (d) hk (e) h(k + 1) :RCE :Q1 2 2 2 14. If (k + y) = 36 and k + y = 16, ky = ? (a) 1 (b) 2 (c) 10 (d) 20 (e) 5 :RCC :Q1 15. Find the next term in the sequence: 2 1/8, -4 1/4, 8 1/2, -17,.. (a) 34 (b) -34 (c) 34 3/4 (d) 17 3/4 (e) 17 3/8 :RCA :Q1 :SB :SP196111238111238048196111 :SH1528A C :SH0635B :SF 16. The hypotenuse AB of right triangle ABC is 10 inches. The other two sides are in the ratio of 3:4. Find the area of {ABC. (a) 6 sq. in. (b) 12 sq. in. (c) 24 sq. in. (d) 48 sq. in. (e) 3 sq. in. :RCC :SD :Q1 k 17. In the formula C = T x --, 2 M C and k are constant. If M is halved, T must be: (a) halved (b) doubled (c) multiplied by 4 (d) divided by 4 (e) squared :RCD :Q1 18. The formula for the area of a floor which contains n square tiles measuring s inches on a side is 2 A = ns . If A = 500 for a certain value of s, find A if s is halved and n remains constant. (a) 125 (b) 250 (c) 1000 (d) 2000 (e) 3000 :RCA :Q1 19. The circumference of a circle is measured and found to be equal to the perimeter of a rectangle l ft long and w ft wide. The radius (r) of the circle is: l + w l + w lw (a) ----- (b) ----- (c) -- 2PI PI PI __ /lw PI (d) / -- (e) ----- \/ PI l + w :RCB :Q1 20. The perimeter of a triangle is 20 inches. The sides are in the ratio of 4:5:6. The length of the longest side is: (a) 2/3 ft. (b) 3/4 ft. (c) 8 ft. (d) 6 2/3 ft. (e) 13 1/3 ft. :RCA :Q1 21. How many revolutions will a bicycle wheel 28 inches in diameter make in going a mile? (use PI = 22/7) (a) 60 (b) 180 (c) 360 (d) 720 (e) 30 :RCD :Q1 22. The formula for the volume of a 2 cylinder is: V = PIr h. If r is doubled and h is halved, V is: (a) halved (b) doubled (c) multiplied by 4 (d) divided by 4 (e) unchanged :RCB :Q1 23. The side of a square is 20 inches. The length of a rectangle having the same area as that of the square is 40 inches. Find the difference between the perimeter of the rectangle and the perimeter of the square. (a) 10 in. (b) 20 in. (c) 30 in. (d) 80 in. (e) 5 in. :RCB :Q1 24. A crystal of copper sulfate contains 36% water. How many centigrams would a crystal of copper sulfate weigh if it contains 576 centigrams of pure copper sulfate? (a) 207 (b) 368 (c) 900 (d) 200 (e) 350 :RCC :Q1 25. An acre is 160 sq. rd. A rod contains 5 1/2 yds. How many square yards are there in an acre? (a) 30 1/4 (b) 880 (c) 4840 (d) 9680 (e) 9000 :RCC :ET :ET Copyright ARROW INSTRUCTIONAL SYSTEMS July 1983
