wizprof 2015 Good luck and most of all have fun.! you may use 75 minutes calculators are not allowed results and prizes will arrive at school in May

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Nathaniel Cunningham
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1 Good luck and most of all have fun.! Stichting Wiskunde Kangoeroe Stichting Wiskunde Kangoeroe calculators are not allowed you may use 75 minutes scribbling aer is allowed results and rizes will arrive at school in May wizprof havo 4 & 5 vwo 3, 4, 5 & 6 answers will be osted on the website March 8th solutions will be osted on the website Aril 9th

2 . Some sorts club owns 5 identical grass mowers. One layground can be mowed in 0 hours by of these mowers. In how many hours can the layground be mowed if all mowers are used? A. 3 B. 4 C. 5 D. 6 E. 7. Mother did the laundry and has hung T-shirts on a clothes line. Her son Tom is going to hang washed socks on the line. He uts a single sock between every air of T-shirts. When Tom is finished, there are 9 clothes on the clothes line. How many T-shirts are on the line then? A. 0 B. C. 3 D. 4 E The shaded area is bounded by a semicircle and quarter circle arcs. Which fraction of the square is shaded? 4 4. Ann, Beth en Cindy have bought a bag with 30 sweets. Ann aid 80 cents, Betty 50 cents, and Cindy 0 cents. Each girl gets 0 sweets. If the girls would have divided the sweets roortionally to what they aid, Ann would have received more sweets. How many more? 8 A. 6 B. 7 C. 8 D. 9 E On a catured shi, irate Jack found a note with directions for finding a treasure: the treasure is located at least 5 meters away from the wall, but less than 5 meters away from the statue. Which of the following figures shows the region where Jack should look for the treasure? 6. What is the last digit of the number ? A. B. 5 C. 6 D. 7 E Every uil in a class of 33 takes biology and/or comuter science. 3 of the uils take both subjects. The number of uils taking only comuter science is twice the number of uils taking only biology. How many uils take comuter science? 4 A. 5 B. 8 C. 0 D. E Which of the following numbers is neither a square nor a cube number? A. 9 B. 3 0 C. 4 D. 5 E Marcus lights a new candle every night. Out of the stums of 7 burnt candles he always makes new candle. This morning he has bought 00 new candles. How many days at most can he now light a new candle? A. B. 4 C. 5 D. 6 E. 7

3 0. We consider the number of right angles in a entagon having only angles of less than 80. What are all ossibilities for that number? A. 0, and B. 0,, and 3 C. 0,,, 3 and 4 D. and E., and 3. The icture shows a dice in in different ositions. What is the robability of rolling `YES with this dice? 3. The icture shows 8 squares of side length. You have to walk from Start to Finish. You can only walk along the sides and the diagonals of the squares. What is the minimum distance you could walk? A. 0+ B. + C. 4 D. 6 E Planet Galamar is inhabited by strange creatures. They all have at least ears. Inhabitants Imi, Dimi and Trimi meet each other in a crater. Imi says: I see 8 ears. Dimi: I see 7 ears. Trimi: That is strange. I see only 5 ears. Of course no one can see its own ears. How many ears does Trimi have? A. B. 4 C. 5 D. 6 E A glass container forms a rectangular rism. The base is a square with sides of length 0 cm. The container is artially filled with water. A heavy, solid cube with sides of length cm is ut in it. The water now reaches exactly u to the uer edge of the cube. To what height in cm did the water reach in the container before the cube was ut into it? A.,90 B.,9 C.,9 D.,93 E., Square ABCD has area 80, AE = BF = CG = DH en AE = 3EB. What is the area of the shaded art? A. 0 B. 5 C. 30 D. 35 E Senna adds rime numbers and gets 85 as a result. Nassim multilies the same rime numbers and adds u the digits of the outcome. What sum will Nassim get? A. B. 3 C. 4 D. 5 E.

4 7. Flora has 3 different dictionaries and different novels. She wants to ut these books on her bookshelf. The dictionaries should go side by side, and so should the novels. In how many different ways can Flora arrange the books? A. B. 4 C. 30 D. 60 E The number 58 has these roerties: it consists of 3 digits, and each air of adjacent digits differs by 3. How many numbers have both of these roerties? A. B. 4 C. 6 D. 8 E weights a, b, c and d are laced on secial scales, see figure. Then of the weights are interchanged. After this interchange the situation is as shown in the figure on the right. Which weights were interchanged? A. a and b B. a and c C. a and d D. b and c E. b and d 0. If you multily the ages of a father and his son today, the result is 05. How many years do they differ in age? A. 6 B. 9 C. 3 D. 34 E. 36. If n is a rime number, then exactly of the numbers n and n + is also a rime number. Which of the following n is a counter-examle to this statement? A. n = B. n = 9 C. n = D. n = 9 E. n = 37. Roland wants to write a number in each of the 7 regions of the figure. The number in a region should be the sum of the numbers in all neighbouring regions (the region with the question mark has 3 neighbouring regions). Roland already wrote a number in regions. Which number will be written in the region with the question mark? A. -6 B. -3 C. 0 D. 3 E How many different -digit numbers are the sum of 6 different owers of? ( 0 = is also a ower of ) A. 0 B. C. D. 3 E In a right-angled triangle, the angle bisector of an acute angle divides the oosite side in segments. One of those has length, the other has length. What is the length of the bisector? A. B. 3 C. D. 5 E. 6

5 5. In triangle ABC two lines arallel to side AC are drawn, one through oint X and one through oint Y. This way the shaded regions in the figure below are created. The shaded regions have equal areas. The ratio BX:XA = 4:. What is the ratio BY:YA? A. : B. : C. 3: D. 3: E. 4:3 6. Different letters reresent different digits, equal letters reresent equal digits. For examle: if A = and B = 5 then AB reresents the number 5. A is not equal to 0. In how many different ways can A, B and C be chosen such that AB < BC < CA? A. 84 B. 96 C. 5 D. 0 E Out of the numbers,, 3,, n, n one number has been removed. The mean of the remaining numbers is 4,75. Which number was removed? A. 5 B. 6 C. 7 D. 8 E Miss Ant would like to walk along every edge of a cube with edges of length. She starts in a vertex and wants to finish there too. What is the minimum length of Miss Ant s walk? A. B. 3 C. 5 D. 6 E Timon wrote down 0 different numbers on a iece of aer. He underlines each number that equals the roduct of the other 9. How many numbers can Timon underline at most? A. B. C. 3 D. 9 E Several oints on a line are coloured red. One red oint is called A, another one B. For oint A all line segments joining a red oint to the left of A and a red oint to the right of A, are counted. There are 80 such segments. The segments joining a red oint to the left of oint B and a red oint to the right of B are also counted. There turn out to be 90 of them. How many oints are coloured red? A. 0 B. C. D. 80 E. 90

KSF selected problems Junior (A) 100 (B) 1000 (C) (D) (E)

KSF selected problems Junior (A) 100 (B) 1000 (C) (D) (E) 3 point problems 1. Which of the following numbers is closest to 20.15 51.02? (A) 100 (B) 1000 (C) 10000 (D) 100000 (E) 1000000 2. Mother did the laundry and hanged t-shirts in line on a clothing line.