Đề thi Toán Kangaroo năm 2016 Cấp độ Benjamin, Khối 5-6

 Lietuvos Respublikos §svietimoir mokslo ministerija VU Matematikos ir informatikos fakultetas
 Keng©uros organizavimo komitetas VU Matematikos ir informatikos institutas
23. What is the greatest number of shapes shown in the
 picture 1 that can be cut out from a 5×5 square (see pic. 2)?
 A) 2 B) 4 C) 5 D) 6 E) 7
 KANGAROO 2016
 Pic. 1 Pic. 2
24. Luigi started a small restaurant. His friend Giacomo gave him some square tables and
 chairs. If he uses all the tables as single tables with 4 chairs each, he would need 6
 more chairs. If he uses all the tables as double tables with 6 chairs each, he would have
 4 chairs left over. How many tables did Luigi get from Giacomo? Time allowed: 75 minutes Benjamin
 A) 8 B) 10 C) 12 D) 14 E) 16 Calculators are not permitted 5--6 grades
25. Clara wants to construct a big triangle using identical small triangular Questions for 3 points
 tiles. She has already put some tiles together as shown in the picture. 1. 2 + 0 + 1 + 6 + 2 · 0 · 1 · 6 =
 How many tiles does she need to complete a triangle? A) 11 B) 0 C) 21 D) 9 E) 18
 A) 5 B) 9 C) 12 D) 15 E) 18
26. A big cube was built from 8 identical small 2. Mike cuts a pizza into quarters. Then he cuts every quarter into thirds. What part of
 cubes, some black ones and some white ones. the whole pizza is one piece?
 Five faces of the big cube are shown in the A) A third B) A quarter C) A seventh D) An eighth E) A twelfth
 picture. What does the sixth face of the big cube look like?
 Ann has written numbers in 5 of the 10 circles as shown at the figure. She wants to write a
 number in each of the remaining 5 circles such that the sums of3. the 3A numbers thread along of lengtheach 10 cm is folded into equal parts as shown
 A) B) C) side of the pentagonD) are equal. E) in the gure. The thread is cut at the two marked places.
 Which number will she have to write in the circle marked by X ? What are the lengths of the three parts?
27. Kirsten wrote numbers in 5 of the 10 circles as shown in the gure. 7 A) 2 cm, 3 cm, 5 cm B) 2 cm, 2 cm, 6 cm C) 1 cm, 4 cm, 5 cm
 3 D) 1 cm, 3 cm, 6 cm E) 3 cm, 3 cm, 4 cm
 She wants to write a number in each of the remaining 5 circles such X
 that the sums of the 3 numbers along each side of the pentagon are
 1 2 4. On Lisa's refrigerator 8 strong magnets hold some postcards.
 equal. Which number will she have to write in the circle marked
 What is the largest number of magnets that she could remove so
 by X? 6
 that no postcard falls to the ground?
 A) 7 B) 8 C) 11 D) 13 E) 15
 A) 7 B) 8 C) 11 D) 13 E) 15A) 2 B) 3 C) 4 D) 5 E) 6
28. The symbols , , and represent 3 dierent digits. If you add the digits of the 3-digit
 number the result is the 2-digit number . If you add the digits of the 2-digit 5. Cathy draws a square with side length 10 cm. She joins the midpoints
 number , you nd the 1-digit number . Which digit does represent ? of the sides to make a smaller square. What is the area of the smaller
 A) 4 B) 5 C) 6 D) 8 E) 9 square?
 A) 10 cm2 B) 20 cm2 C) 25 cm2 D) 40 cm2 E) 50 cm2
29. Grandpa brought 132 apples and 204 pears from his garden. He gives all these fruits to 10 cm
 children such that each child gets the same amount of apples and the same amount of 6. The trapezoid is divided into 5 equal isosceles triangles as shown
 pears. How many children at most can get the fruits? in the gure. The perimeter of each of the triangles is 40 cm and
 A) 4 B) 11 C) 12 D) 6 E) 17 the perimeter of the trapezoid is 80 cm. What is the length of the
 longer base of the trapezoid?
30. Two 3-digit numbers have all their 6 digits distinct. The rst digit of the second number
 A) 15 cm B) 20 cm C) 30 cm D) 40 cm E) 45 cm
 is twice the last digit of the rst number. What is the smallest possible sum of two such
 numbers? 7. A centipede has 25 pairs of shoes. It needs one shoe for each of its 100 feet. How many
 A) 552 B) 546 C) 301 D) 535 E) 537 more shoes does the centipede need to buy?
 A) 15 B) 20 C) 35 D) 50 E) 75

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