Looking for a Unsorted Math Worksheet Templates? Download it for free!

International Contest-Game Math Worksheet With Answers - Grade 5 And 6, Kangaroo, 2007 Page 6

Solution: Agnes is 10, so Lisa is 40. Agnes will be twice as old in 10 years. Then, Lisa will be

40+10=50 years old.

Answer: B

20. Three diagonals are constructed on three adjacent faces of a cube, as shown on the figure.

Which of the following nets is that of the given cube?

E) None of the above

Solution: From the picture of the cube, it is clear that the three diagonals form a triangle, that is,

every two of them share a vertex. So, the nets in B and C should be excluded. Imagine the nets

in A and D folded into a cube. The rightmost upper vertex must meet the leftmost upper vertex.

In D, this will be the common vertex of the two diagonals along the 4-squared piece of the net.

In A, these diagonals will not share a vertex.

Answer: D.

21. Four paper ribbons of uniform width of 10 cm have been

arranged to form figure A (see the diagram). Each of the

ribbons is 25 cm longer than the previous one. The same

ribbons have been rearranged to form figure B. What is the

difference between the perimeters of figure A and figure B?

A) 0 cm

B) 20 cm

C) 40 cm

D) 50 cm

E) 25 cm

Solution: The perimeter of the original figure A is equal to the

perimeter of the rectangle outscribed around it (as seen on the first

figure on the left). To see this, just imagine where on the outer

perimeter the segments from the inside of the rectangle will be

projected if we decide to “unfold” the figure.

For the figure B, a similar reasoning will show that the perimeter

of the original (grey) figure (except the two segments in dashed

lines) will be projected on the outer perimeter, thus, it will be equal to the perimeter of the

figure A, plus the two extra segments, the ones in dashed lines. Their length is 25 cm each.

Therefore, the difference between the perimeters of A and B is 50 cm.

Answer: D

22. Anna wrote a 2-digit number. Ben created a 4-digit number by coping Anna's number twice.

Then Anna divided Ben's number by her number. What was the result she got?

A) 100

B) 101

C) 1000

D) 1001

E) 10

International Contest-Game Math Worksheet With Answers - Grade 5 And 6, Kangaroo, 2007 Page 6