Practice Math Kangaroo Problems 86 to 90, Level 0708
Practice Math Kangaroo Problem 86 to 90, Level 0708
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Problem Kangur_2004_0708_26 (5 pts) http://www.mathkangaroo.org
In the figure there are 11 boxes. Number 7 was written in the first box and number 6 was written in the ninth box. What was
the number placed in the second field with the following condition: the sums of each three consecutive numbers in the boxes are
equal to 21?
A) 7
B) 10
C) 8
D) 6
E) 21
Solution: TBD
Problem Kangur_2004_0708_27 (5 pts) http://www.mathkangaroo.org
For each triple of numbers (a, b, c) another triple of numbers (b + c, c + a, a + b) was created. This was called operation. 2004 such operations were made starting with numbers (1, 3, 5), and resulting with numbers (x, y, z).
What is the difference x - y equal to?
A) -2
B) 2
C) 4008
D) 2004
E) (-2)2004
Solution: TBD
Problem Kangur_2004_0708_28 (5 pts) http://www.mathkangaroo.org
Number 2004 is divisible by 12 and the sum of its digits is equal to 6. Altogether, how many four-digit numbers have these two properties?
A) 10
B) 12
C) 13
D) 15
E) 18
Solution: TBD
Problem Kangur_2004_0708_29 (5 pts) http://www.mathkangaroo.org
Rings with dimensions shown in the figure were linked together, forming 1.7m long chain. How many rings were used to create the chain?
A) 30
B) 21
C) 42
D) 85
E) 17
Solution: TBD
Problem Kangur_2004_0708_30 (5 pts) http://www.mathkangaroo.org
On each face of a cube a certain natural number was written, and at each vertex a number equal to the product of the
numbers on the three faces adjacent to that vertex was placed. If the sum of the numbers on the vertices is 70 then what is
the sum of the numbers on all the faces of the cube?
A) 12
B) 35
C) 14
D) 10
E) Cannot be determined.
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Solution: TBD
Problem copyright www.mathkangaroo.org,
Solution copyright Darya and Dmitry Pavlov
