Kangaroo Canada 2012 G6 Question 15/28/29

We investigated some questions from the past years’ Kangaroo contest (2012 – 2013). Three questions were left for a further discussion.

Kangaroo Canada 2012 G6 Question 15:

kangaroocanada2012q15

Answer:
We make the every 4 respective cells repeated since the sum of any four consecutive numbers is 12. In each 4 cells unit [1,2,3,4], we know
unit[1] = 1 –> unit[2] = ?  –> unit[3] = 2 –> unit[4] = 4
unit[smilingFace] is in unit[2] = 12 – unit[1] – unit[3] – unit[4] = 12 -1-2-4 = 5
The answer is D.

Kangaroo Canada 2012 G6 Question 28:

kangaroocanada2012q28

Answer:
Ann to Bill >> I do not know your number. It does mean Ann does not hold 1;
Bill to Ann >> I do not know your number. It does mean Bill does not hold 1;
The next option will be started from 2. Ann knows her own number a, Bill’s number is either b=a-1 or b=a+1. Ann to Bill>>I know your number is a factor of 20, number will be one of 2,4,5,10,20. We know both a-1 and a+1 are factors of 20 must be 2 and 4, therefore, a=3.  The answer is C.

Kangaroo Canada 2012 G6 Question 29:

kangaroocanada2012q29

Answer:
The hint is that the folding process is actually dividing the square to 8 parts side by the diagonal, the each side will be divided to 4 units. Based on “The area of the original square is 64 “, we know the side = 8 cm, each unit is 2 cm. Then we can find that the shadow is 2×4 rectangle. The answer is C.

 

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