TIMO 2021 Grade 6 Heat Set 1

There are some chickens and rabbits in a cage. The number of chickens is 3 times and 10
more as the number of rabbits. They have 110 legs in total. How many chicken(s) is / are
there?

Every cell A will split into 2 cell B after 1 minute and every cell B will split into 2 cell A
after 2 minutes. There are few cells A now. After 10 minutes, scientists observe 1792 cells.
How many cells are there in the beginning?

A book store had a box of text books. One half and 8 fewer books were sold on the first
day. One half of the remaining part and 2 more books were sold on the second day. One
half of the remaining part and 1 fewer book were sold on the third day. Finally, 9 books
are left. How many book(s) did the box contain originally?

5 numbers, A, B, C, D and E, represent 5 different numbers from 0 to 9.
Given the following conditions:
1. E > D > C > B > A
2. The sum of A, B and C is greater than D.
3. The sum of C and D equals to E.
4. C is divisible by B.
5. The sum of A, B and D is less than E.
6. E is greater than 7.
Find the number to represent D.

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

Find (3+1/3)×5+(5+1/6)×7+(2+1/6)×13.

Find 1/(1×2)+1/(2×3)+...+1/(20×21).

Find the value of 4420 × 2368 − 4421× 2367 .

Convert the recurring decimal 0.1(36 repeating) into the simplest fraction.

Find the value of 5+8+10+13+15+...+35+38+40.

How many simplified fractions with denominator 1386 are there?

The remainder of dividing a positive integer K by 9 is 2. What is the remainder of
dividing( 4 K + 7 ) by 12?

Find the last digit of A if A=2²+4²+6²+8²+...+98²+100².

If a 9-digit number 1523459 A2 is divisible by 12, find the value of A .

The sum of 13 consecutive natural numbers is 260. Find the largest number.

There is a cuboid. When the length increases 4cm, the volume will be increased by 24
cm 3 . When the width increases 2cm, the volume will be increased by 24 cm 3 . When the
height increases 7cm, the volume will be increased by 14 cm 3 . What is the original
volume of the cuboid? (Unit in cm 3 )

Small cubes with side length 1 are combined according to the pattern shown below. Find
the total volume of the 12th generation.

The area of a rectangle is 504. The value of its length and width are both integers. What is
the minimum possible value of its perimeter?

The figure below is formed by 7 identical regular hexagons and 6 identical triangles. If
the area of triangle is 1, find the area of the figure.

P is a point in the parallelogram ABCD. Given that area of ΔAPD = 74 and the area of
ΔBCP equals to 13% of ABCD. What is the area of ABCD?