International Contest-Game Math Worksheet With Answers - Grade 5 And 6, Kangaroo, 2007 Page 4
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8Solution: If the squares did not overlap, the length of the resulting rectangle would have been
18 cm. Since its length is 13 cm, therefore, the overlapping rectangle is 5 cm long. The other
dimension of this rectangle is the same as the width of the original rectangles, 9 cm. Hence, the
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area is 5×9=45 cm
.
Answer: B
13. There were 60 birds on three trees. At some moment 6 birds flew away from the first tree, 8
birds flew away from the second tree, and 4 birds flew away from the third tree. After that,
it turned out that the number of birds on each tree was the same. How many birds were there
on the second tree in the beginning?
A) 26
B) 24
C) 22
D) 21
E) 20
Solution: Solution: At the end, the total number of birds on the three trees was
60-6-8-4=42. There were the same number of birds on each tree, hence, there were 42/3=14
birds on each tree. Working backwards, we obtain
14+6=20 birds on the first tree;
14+8=22 birds on the second tree;
14+4=18 birds on the third tree.
Answer: C.
A parallelogram is divided into two parts, P1 and P2, as shown on
the picture. Which of the following statements is surely true:
A) P2 has a greater perimeter than P1
B) P2 has a smaller perimeter than P1
C) P2 has a smaller area than P1
D) P1 and P2 have the same perimeter
E) P1 and P2 have the same area
Solution: The original parallelogram has two pairs of equal opposite sides. One side of each pair
is included in the perimeters of P1 and P2. The dividing broken line is included in both
perimeters, so it adds equal length to both of them. Hence, P1 and P2 have the same perimeters.
Answer: D.
th
14. What is the 2007
letter in the sequence KANGAROOKANGAROOKANG… ?
A) K
B) A
C) N
D) R
E) O
Solution: The sequence consists of repetitions of the 8-letter word KANGAROO. Since
2007=250×8+7, to write a sequence of 2007 letters we need to repeat the word 250 times and to
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include only 7 letters of the 251-th word. So, in the 2007
position, there will be the letter O.
Answer: E.
15. The squares on the figure are formed by intersecting
the segment AB by the broken line AA
A
...A
B.
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2
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The length of AB is 24 cm. What is the length of the
broken line AA
A
...A
B?
1
2
12
A) 48 cm
B) 72 cm
C) 96 cm
D) 56 cm
E) 106 cm
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