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TIMO 2021 Grade 6 Preliminary Set 3

Question 1

According to the pattern shown below, what is the number in the question mark?

Question illustration
  1. 36
  2. 56
  3. 43
  4. 16

Question 2

There are chickens and rabbits in a cage. The number of rabbits is two times of the number of
chickens. They have 210 legs in total. How many rabbits are there?

Question illustration
  1. 42
  2. 45
  3. 43
  4. 30

Question 3

The age of Alice is seven times that of Peter now. 6 years later, the age of Alice is three
times that of Peter. How old is Alice now?

Question illustration
  1. 15
  2. 21
  3. 13
  4. 16

Question 4

Alice needs 20 days to finish a project. Peter needs 30 days to finish the same project. If
Alice, Peter and Mary do the project together, it takes 10 days. How many days does it
take Mary to finish the project alone?

Question illustration
  1. 50
  2. 55
  3. 60
  4. 65

Question 5

There are 5 pieces of red socks, 9 pieces of white socks and 13 pieces of blue socks in a
box. Any two pieces with the same colour can make a pair of socks. If you want to draw
2 pairs of socks, at least how many pieces of socks should be drawn randomly?

Question illustration
  1. 4
  2. 5
  3. 6
  4. 7

Question 6

Find the value of 64²−9×144.

Question illustration
  1. 2800
  2. 2750
  3. 2600
  4. 2550

Question 7

Find the value of 1/3+1/15+1/35+...+1/399+1/483.

Question illustration
  1. 1/23
  2. 22/23
  3. 11/23
  4. 8/11

Question 8

Find the value of 1/3+1/9+...+1/729+1/2187.

Question illustration
  1. 728/729
  2. 364/729
  3. 2186/2187
  4. 1093/2187

Question 9

Find the value of 1²+2²+3²+...+9²+10².

Question illustration
  1. 395
  2. 375
  3. 355
  4. 385

Question 10

Convert 0.565656... into a fraction.

Question illustration
  1. 56/99
  2. 56/999
  3. 56/100
  4. 56/1000

Question 11

If 11-digit number 20190513ABB is divisible by 33 and A ≠ B , find the greatest value of
the sum A + B .

Question illustration
  1. 4
  2. 10
  3. 7
  4. 13

Question 12

How many simplified fractions with denominator 120 are there?

Question illustration
  1. 26
  2. 27
  3. 32
  4. 30

Question 13

Define a⊕b=(a×b)/(a+1)+b. Find 4⊕(2⊕6).

Question illustration
  1. 16
  2. 17
  3. 18
  4. 19

Question 14

A 3-digit number has a remainder 4 when divided by 7, has a remainder 6 when divided
by 9 and has a remainder 8 when divided by 11. Find its value.

Question illustration
  1. 680
  2. 690
  3. 700
  4. 710

Question 15

The sum of 20 consecutive numbers is 450. Find the second largest number.

Question illustration
  1. 32
  2. 33
  3. 30
  4. 31

Question 16

How many rectangles are there in the figure below?

Question illustration
  1. 66
  2. 65
  3. 64
  4. 63

Question 17

6 equal squares are combined to get a rectangle. If the area of each small square is 16cm2,
at most how many cm does the total perimeter decrease after the combination?

Question illustration
  1. 56
  2. 40
  3. 46
  4. 50

Question 18

Small cubes with side length 1 are combined according to the pattern shown below. Find
the total volume of the 10th layer.

Question illustration
  1. 19
  2. 29
  3. 17
  4. 17

Question 19

A square is formed by 150 rectangles that are 2cm × 3cm each. Find the perimeter of the
new square in cm.

Question illustration
  1. 100
  2. 120
  3. 150
  4. 160

Question 20

The area of a circle is 12.56cm2. If the radius of the circle is the same as the diagonal of a
square, what is the area of the square in cm2? (Take π= 3.14 ).

Question illustration
  1. 1
  2. 4
  3. 6
  4. 2