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TIMO 2021 Grade 6 Preliminary Set 4

Question 1

Given A and D are two non-zero digits. The reversed two-digit number DA equals 2 times (AD−2). AD is a square number. Find the two-digit number AD.

Question illustration
  1. 49
  2. 16
  3. 25
  4. 64

Question 2

There are chickens and rabbits in a cage and the number of chickens is twice the number
of rabbits. They have 352 legs in total. How many rabbits are there?

Question illustration
  1. 26
  2. 44
  3. 34
  4. 88

Question 3

The age of Andy is three times that of John now. 12 years later, the age of Andy is two
times that of John. How old is Andy now?

Question illustration
  1. 18
  2. 21
  3. 36
  4. 48

Question 4

A motorbike is running from the police station at the speed of 30km/h. After 20 minutes,
a car is running from the same station towards the motorbike with the speed of 50km/h.
How many minutes does it take the car to catch up with the motorbike?

Question illustration
  1. 45
  2. 40
  3. 35
  4. 30

Question 5

There are 6 pieces of white chopsticks, 8 pieces of yellow chopsticks and 11 pieces of
brown chopsticks mixed together. If you want to get 3 pairs of chopstick with the same
colour in the dark, at least how many pieces of chopsticks should be taken out?

Question illustration
  1. 18
  2. 16
  3. 6
  4. 12

Question 6

Find the value of 222222222÷9.

Question illustration
  1. 26 691 385
  2. 24 691 358
  3. 24 691 355
  4. 28 691 358

Question 7

Find 1/(1×2×3)+1/(2×3×4)+...+1/(7×8×9)+1/(8×9×10).

Question illustration
  1. 9/20
  2. 22/45
  3. 11/45
  4. 9/10

Question 8

Find 1×2+2×3+3×4+...+20×21.

Question illustration
  1. 2680
  2. 2880
  3. 2780
  4. 3080

Question 9

Find 144−143+142−141+140−...+4−3+2−1.

Question illustration
  1. 74
  2. 73
  3. 71
  4. 72

Question 11

If 9-digit number 2 A018901B is divisible by 11, find the value of B − A .

Question illustration
  1. 0
  2. 1
  3. 2
  4. 3

Question 12

How many simplified fractions with denominator 80 are there?

Question illustration
  1. 32
  2. 33
  3. 34
  4. 35

Question 13

How many 3-digit numbers that can be divisible by 7 or 11?

Question illustration
  1. 196
  2. 209
  3. 198
  4. 207

Question 14

A 3-digit number has a remainder 2 when divided by 3, 5 or 7. What is such largest 3-
digit number?

Question illustration
  1. 942
  2. 974
  3. 999
  4. 947

Question 15

The sum of 9 consecutive natural numbers is 126. Find the second largest number.

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

Question 16

How many rectangles are there in the figure below?

Question illustration
  1. 90
  2. 82
  3. 110
  4. 120

Question 17

A cuboid has the volume 30 and integral side lengths. Find its minimum surface area.

Question illustration
  1. 62
  2. 122
  3. 31
  4. 61

Question 18

Small cubes with side length 1 are stacked according to the pattern shown below. If there
are 11 layers, find its surface area.

Question illustration
  1. 1366
  2. 925
  3. 945
  4. 944

Question 19

A square is formed by 722 rectangles that are 1cm × 2cm. Find the decrease in the total
perimeter in cm after the combination.

Question illustration
  1. 4175
  2. 4070
  3. 4180
  4. 4174

Question 20

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

Question illustration
  1. 425.16
  2. 425.12
  3. 452
  4. 452.16