TIMO 2020 Grade 6 Heat Set 2

There are 16 pieces of white chopsticks, 27 pieces of yellow chopsticks and 46 pieces of
blue chopsticks mixed together. If you want to get 2 pairs of white chopsticks and 3 pairs
of chopsticks in another colour, at least how many pieces of chopsticks should be taken
out randomly?

There are some chickens and rabbits in a cage. The number of chickens is 4 times as the
number of rabbits. They have 240 legs in total. How many chickens are there?

It requires 16 minutes to cut a piece of wood into 9 sections. If the time required to cut
into each section is the same, how many minute(s) is / are required to cut the wood into
11 sections?

Find the average of the following 8 numbers.

Leo needs 18 days to finish a project. Bruce needs 21 days to finish the same project. If
Leo, Bruce and Mary do that project together, it takes 9 days. How many days does Mary
take to finish the project alone?

Find the value of 1+4+7+10+...+31+34.

Find the value of 1369 ×1722 − 1364 ×1717 .

Find 1/110+1/132+1/156+...+1/342+1/380.

Find the value of (2+1/400)×169+(5+1/800)×10+(4+1/200)×113.

Using S=(3S−S)÷2, find the value of 1+3+9+27+...+59049.

If a 9-digit number 202015 A2 B is divisible by 12 and A, B ≠ 0 , find the sum of all
possible values for AB .

Find the last digit of A if A=5+12+19+26+...+(5+7×99)+(5+7×100).

Find the number of all positive factors of 996.

The remainder of dividing a positive integer K by 17 is 11. What is the remainder of
dividing ( 6 K + 16 ) by 17?

The sum of 25 consecutive numbers is 900. Find the second largest number.

How many rectangle(s) is / are there in the figure below?

Small cubes with side length 1 are combined according to the pattern shown below. Find
the total volume of the 30th generation.

The figure below is a square overlapped by two right-angled triangles and one quarter
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circle. Find the area of the shaded region. (Take π= ).
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How many rectangle(s) with both 2 “*” is / are there in the figure below?

The perimeter of a circle is 18.84. If the diameter of the circle is the same as the diagonal
of a square, what is the area of the square? (Take π= 3.14 )