International Contest-Game Math Worksheet With Answers - Grade 5 And 6, Kangaroo, 2007 Page 5
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8Solution: The broken line consists of three sides from each of the squares, so its length will be
¾ of the total sum of their perimeters. On the other hand, the segment AB consists of one side
of each square, so the length of AB is ¼ of the total sum of their perimeters. Hence, the length
of the broken line is 3(AB)=72cm.
Answer: B
Part C: Each correct answer is worth 5 points.
16. Harry Potter let an owl out at 7:30 a.m. to deliver an important message to his friend Ron.
The owl delivered the envelope at 9:10 a.m. An owl flies 4 km in 10 minutes. What was the
distance between Harry and Ron?
A) 14 km
B) 20 km
C) 40 km
D) 56 km
E) 64 km
Solution: From 7:30 am to 9:10 am, it took one hour and 40 minutes (that is, 100 minutes) to
get the message. The owl flies 4km in 10 minutes, so it would have flown (100/10)×4=40 km in
total.
Answer: C
17. Bill thought of an integer number. Nick multiplied this number either by 5 or by 6. John
added either 5 or 6 to Nick’s result. Last, Andrew subtracted either 5 or 6 from John’s
result. The final result obtained was 73. What was Bill’s number?
A) 10
B) 11
C) 12
D) 14
E) 15
Solution:
John
Nick
Change from the
Result before the
last two
last two
operations
operations
Added 5
Subtracted 5
0
73-0=73
Subtracted 6
-1
73+1=74
Added 6
Subtracted 5
+1
73-1=72
Subtracted 6
0
73-0=73
So, the possible results after Nick’s multiplication are either 73, or 74, or 72. However, this
result must be a multiple of either 5 or 6. The only possible result, thus, is 72. After reversing
Nick’s operation, we get 72/6=12. The original number of Bill was 12.
Answer: C
18. A cube with a side 1 m long has been cut into cubes of a side 1 dm each. All small cubes
have been put one on top of the other, to form a vertical structure. What is the height of this
structure?
A) 100 m
B) 1 km
C) 10 km
D) 1000 km
E) 10 m
Solution: There are 10 dm in each meter. Therefore, the original cube is cut into
10×10×10=1000 cubes of a side 1 dm. When arranging them in a linear vertical structure, the
height will be 1000dm=100m.
Answer: A
19. Agnes is 10 years old. Her mother Lisa is 4 times as old. How old will Lisa be when Agnes
is twice as old as she is now?
A) 40 years old
B) 50 years old
C) 60 years old
D) 70 years old
E) 80 years old
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