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SEAMC 2007 Multiple Choice Section SEAMC 2007 Multiple Choice Section SEAMC 2007 Multiple Choice Section You will have exactly 1½ minutes to read each question and select the best answer. Following this slide will be a practice question to try. Here is the practice question: SEAMC 2007 Multiple Choice Section Question 0 (practice) In the diagram, the value of x is equal to: A. 34 B. 33 C. 46 D. 23 20o 60o xo 54o xo SEAMC 2007 Multiple Choice Section And the answer of course is … A. 34 B. 33 C. 46 D. 23 SEAMC 2007 Multiple Choice Section You will have exactly 1½ minutes to read each question and select the best answer. Shade the square of the letter of your preferred choice of answer. For example, the answer to the previous question was D: A B C D SEAMC 2007 Multiple Choice Section SEAMC 2007 Multiple Choice Section Question 1 The average of four numbers is 48. If 8 is subtracted from each number, the average of the four new numbers is: A. 16 B. 40 C. 46 D. 44 SEAMC 2007 Multiple Choice Section Question 2 PQRS is a rectangle enclosing 2 circles each of radius 2cm. The area of rectangle PQRS, in square centimeters, is: A. 8 P Q S R B. 16 C. 24 D. 32 SEAMC 2007 Multiple Choice Section Question 3 The number of nails weighing 5 grams each that can be made from 11.5 kilograms of wire is: A. 230 B. 2 300 C. 23 000 D. 230 000 SEAMC 2007 Multiple Choice Section Question 4 One of the elephants in the zoo is on a special diet, and eats every day a portion of carrots which is equal to what one of the rabbits eats in 1 year (365 days). Together, in one day, the elephant and rabbit eat 111 kilograms of carrots. How many kilograms of carrots does the rabbit eat in one day? A. 1 2 B. 37 122 111 C. 165 D. 19 61 SEAMC 2007 Multiple Choice Section Question 5 The digits 1, 2, 3 and 5 can be arranged to form 24 different four-digit numbers. The number of even numbers in this set is: A. 18 B. 12 C. 6 D. 2 SEAMC 2007 Multiple Choice Section Question 6 Between the last 5 questions, a diagram of a famous fractal has been momentarily displayed. The name of this fractal is: A. Pascal’s Triangle B. Koch Snowflake C. Sierpinski’s Triangle D. Mandelbrot Set SEAMC 2007 Multiple Choice Section Question 7 The value of the product where the 2n 1 th n factor is 1 , is: 2 3 5 7 9 41 (1 )( 1 )( 1 )( 1 )...( 1 ) 1 4 9 16 400 A. 441 B. 4041 C. 4410 D. 4001 n SEAMC 2007 Multiple Choice Section Question 8 If the figure shown is folded to form a cube, then three faces meet at every vertex. The numbers on the three faces meeting at any vertex can be multiplied together. What is the largest such product for the vertices of this cube? A. 120 B. 90 C. 72 D. 60 1 4 2 3 5 6 SEAMC 2007 Multiple Choice Section Question 9 How many positive integers less than 1000 have the sum of their digits equal to 6? A. 28 B. 27 C. 19 D. 18 SEAMC 2007 Multiple Choice Section Question 10 A formula in physics states 1 1 1 R R1 R2 If R1 = 3 and R2 = 6, then R is equal to A. ½ B. 2 C. 1/9 D. 9 SEAMC 2007 Multiple Choice Section Question 11 A 3x8 rectangle is cut into 2 pieces as indicated. The 2 pieces are rearranged to form a right-angled triangle. One side of the resulting triangle has length 4 A. 9 B. 7 C. 6 D. 4 3 4 5 8 SEAMC 2007 Multiple Choice Section Question 12 A cube with each edge of length 1 unit is turned into a solid star by adding a square pyramid with each edge of length 1 unit to every face. The number of edges this new solid has is: A. 28 B. 24 C. 48 D. 36 SEAMC 2007 Multiple Choice Section Question 13 The regular octagon shown has side length 4cm. What is the area, in square centimeters, of the shaded region? A. 16 B. 8(1 2) C. 24 D. 16(1 2) SEAMC 2007 Multiple Choice Section Question 14 What is the highest power of 2 which divides exactly into 1 000 000? A. 23 B. 25 C. 26 D. 28 SEAMC 2007 Multiple Choice Section Question 15 What is the radius of the largest circle that can be drawn inside a quarter circle of radius 1 unit? A. 2 1 2 B. 3 C. ½ D. 1 2 2 ? SEAMC 2007 Multiple Choice Section Question 16 If n is an integer, which of the following must be an odd integer? A. 5n B. n2 + 5 C. 2n2 + 5 D. n3 SEAMC 2007 Multiple Choice Section Question 17 In the diagram, all triangles are right isosceles triangles, and PQR is a straight line. Given that PQ is 12 units, what is the length of QR? 1 A. 3 5 3 C. 3 4 B. 4 2 D. 3 2 Q P R SEAMC 2007 Multiple Choice Section Question 18 If the following were arranged in order from biggest to smallest, the biggest being the first, which would be the third number? A. 2(2)7 B. 2(2)6 – 2 C. 2 + 2(2)6 D. 27 SEAMC 2007 Multiple Choice Section Question 19 If xy = 3, then x3y + 2 equals A. 11 B. 8 C. 29 D. 35 SEAMC 2007 Multiple Choice Section Question 20 If four different positive integers m, n, p and q satisfy the equation (7 – m)(7 – n)(7 – p)(7 – q) = 4 then the sum m+n+p+q is equal to A. 28 B. 26 C. 24 D. 21 SEAMC 2007 Multiple Choice Section Question 21 1 1 m where p and q are p q If p +q = n and both positive, then (p – q)2 equals A. n m n B. n 4mn 2 2 mn 4 n C. m 2 D. n m 2 SEAMC 2007 Multiple Choice Section Question 22 For m and n integers, how many solutions (m, n) of 2 2 the inequality 4 m n 17 are there? A. 36 B. 48 C. 15 D. 52 SEAMC 2007 Multiple Choice Section Question 23 Two parallel planes are 10cm apart. A point P lies on one of the planes. The set of points which are all equally distant from the two planes and 6cm from P is: A. a point B. a straight line C. a circle D. a hollow sphere SEAMC 2007 Multiple Choice Section Question 24 7 13 7 13 A. B. 13 3 2 C. D. 3 2 4 2 13 equals SEAMC 2007 Multiple Choice Section Question 25 A cube measuring 3 units on each edge is painted. It is then cut into 27 one-unit cubes. How many faces of the one-unit cubes are not painted? A. 108 B. 81 C. 72 D. 36 SEAMC 2007 Multiple Choice Section SEAMC 2007 Multiple Choice Section SEAMC 2007 Multiple Choice Section You will have exactly 1½ minutes to read each question and select the best answer. Shade the square of the letter of your preferred choice of answer. For example, if the answer is C: A B C D SEAMC 2007 Multiple Choice Section Question 26 If n is a positive integer and n(n+1) is divided by 3, the remainder can be A. 0 only B. 2 only C. 0 or 1 only D. 0 or 2 only SEAMC 2007 Multiple Choice Section Question 27 A cart track is made up of one large semicircle, and three small semicircles each of radius 100m. What is the total length of the track? A. 150π B. 300π C. 450π D. 600π SEAMC 2007 Multiple Choice Section Question 28 If A. 2 1 2 2x 3 5 B. 3 2 then C. 2 3 1 2x 1 1 D. 2 equals SEAMC 2007 Multiple Choice Section Question 29 If a, a+d, a+9d, (d>0), are the sides of a right-angled triangle, then the ratio a:d is A. 4:1 B. 8:1 C. 20:21 D. 20:1 SEAMC 2007 Multiple Choice Section Question 30 A calendar watch loses one second per day. At this rate, the approximate length of time, in years, for the watch to lose exactly 24 hours is 1 A. 360 C. 240 1 B. 240 D. 2400 SEAMC 2007 Multiple Choice Section Question 31 If 1 1 1 1 1 2 2 2 2 ... x then 2 3 4 5 1 1 1 1 1 2 2 2 2 ... is 2 4 6 8 x A. 2 x 1 B. 2 x 1 C. 4 x D. 1 4 the value of SEAMC 2007 Multiple Choice Section Question 32 The figure below which can be obtained by rotating the figure on the right is A. C. B. D. SEAMC 2007 Multiple Choice Section Question 33 A square of side 2x has four equilateral triangles drawn on its sides (and exterior to the square). The area of the figure formed is A. 4(1 3 ) x 2 ( 1 3 ) x B. 4 2 2 ( 4 3 ) x C. 2 ( 1 4 3 ) x D. SEAMC 2007 Multiple Choice Section Question 34 Consider the set of 4-digit positive integers where each integer is composed of four different digits. When the smallest of these is subtracted from the largest, the result is A. 8876 B. 8642 C. 8853 D. 8646 SEAMC 2007 Multiple Choice Section Question 35 PBCQ is a trapezoid in which PQ:BC = 2:3. If the area of triangle ABC is 36, then the area of the trapezoid PBCQ is Q P A. 100 A B. 90 C. 84 D. 72 B C SEAMC 2007 Multiple Choice Section Question 36 If m pens are bought at n dollars each, and n pens are bought at m dollars each, then the average cost per pen, in dollars, is A. mn C. m n 2 2mn B. mn D. 1 SEAMC 2007 Multiple Choice Section Question 37 Each side of a rhombus has length 10. The sum of the squares of the diagonals equals A. 50 B. 100 C. 200 D. 400 SEAMC 2007 Multiple Choice Section Question 38 The slope of OA is y A. 4/3 A B. 3/4 3 C. 5/3 D. 3/5 O 4 5 B x SEAMC 2007 Multiple Choice Section Question 39 If the distance between consecutive fence posts is 5 meters, the number of fence posts needed to build a fence around a triangular region with sides 20m, 20m, and 30m is A. 11 B. 13 C. 14 D. 15 SEAMC 2007 Multiple Choice Section Question 40 A bag contains 80 jelly beans – 20 are red, 20 are green, 20 are yellow and 20 are blue. The least number that a blindfolded person must eat to be certain of having eaten at least one of each colour is A. 5 B. 7 C. 23 D. 61 SEAMC 2007 Multiple Choice Section Question 41 xy xz If x, y and z are positive and a , b x y xz yz c , then x equals and yz abc A. ab ac bc 2abc C. ab ac bc 2abc B. bc ac ab abc D. ac bc ab SEAMC 2007 Multiple Choice Section Question 42 As everyone knows, a normal cat has 18 claws, 5 on each front leg and 4 on each back leg. At Harry’s Home for Distressed Cats there are 4 three-legged cats, each one with a different leg missing. How many claws do they have all together? A. 52 B. 54 C. 64 D. 68 SEAMC 2007 Multiple Choice Section Question 43 Three darts are thrown at the dartboard illustrated. The three scores are added together, a miss counts as zero. What is the smallest total score which is impossible to obtain? A. 14 B. 18 23 C. 19 12 D. 22 8 3 1 SEAMC 2007 Multiple Choice Section Question 44 The last digit in the sum A. 0 B. 1 C. 2 D. 4 317 + 713 is SEAMC 2007 Multiple Choice Section Question 45 Red rose plants are on sale for $3 each and yellow ones for $5 each. A young guy wants to buy a mixture of both types (at least one of each) and decides to buy 13 in total, buying more yellow ones than red ones. The number of dollars that the young guy spends could be A. 51 B. 57 C. 58 D. 65 SEAMC 2007 Multiple Choice Section Question 46 If 4 GH L A. (G H ) 2 4 B. 4 G2 H 2 then L equals C. 4 (G H ) 2 D. G2 H 2 4 SEAMC 2007 Multiple Choice Section Question 47 2 n 1 2 A. 2n+2 B. 22n+2 C. 42n+2 D. 42n+1 n 1 equals SEAMC 2007 Multiple Choice Section Question 48 For all positive integers x and y such that the greatest value that y can have is A. 60 B. 84 C. 156 D. 288 1 1 1 x y 12 SEAMC 2007 Multiple Choice Section Question 49 Each circle has an area of 1cm2. The area of the overlap between any pair of intersecting circles is 1/8 cm2. The total area in cm2 of the region enclosed by the 5 circles is A. 4 B. 4½ C. 43/8 D. 4¾ SEAMC 2007 Multiple Choice Section Question 50 Some M&M’s had been eaten without the shop owner’s permission by one or more of the 5 kids in the shop. When questioned, they gave the following answers: A. 1 B. 2 C. 3 D. 4 E. 5 Ace: One of us ate them Bea: Two of us ate them Cec: Three of us ate them Dee: Four of us ate them Eve: All of us ate them The owner knew from past behaviour that the guilty ones always lied while the others told the truth. The number of kids who ate the M&M’s was SEAMC 2007 Multiple Choice Section