TIMO 2019 Grade 6 Heat Set 3

There are some chickens and rabbits in a cage. The number of chickens is four times as
the number of rabbits. They have 144 legs in total. How many chicken(s) is / are there?

It requires 24 minutes to cut a piece of wood into 5 sections. If the time required to cut
into each section is the same, how many minute(s) is / are required to cut 3 pieces of
wood each into 29 sections? (Cannot cut 2 pieces of woods at the same time)

Find the average of the following 8 numbers.

Andy’s mother’s age this year, minus 29, then multiplied by 8, increased by 4 and divided by 7, gives 12. How old is she?

There are 4 pieces of white chopsticks, 5 pieces of yellow chopsticks and 6 pieces of blue
chopsticks mixed together. If you want to get 2 pairs of chopsticks with the same colour
in the dark, at least how many pieces of chopsticks should be taken?

Find the value of 1+5+25+...+3125+15625+78125.

Find 1/(1×2)+1/(2×3)+...+1/(1013×1014).

Find the value of 1234×4567−1233×4568.

Find the value of 1−4+7−10+13−16+19−...−1198+1201−1204+1207−1210+1213.

Find the value of (10+1/4)×17+(20+1/2)×19+(30+3/4)×15.

The 10-digit number A20181014 B is divisible by 36. A and B are non-zero digits. Find
the value of A + B .

Find the last digit of A if A=1²+2²+3²+...+19²+20²+21².

The sum of 3 prime numbers is 18. Find the maximum value of the product among these
3 prime numbers.

When a 3-digit number is divided by 4, 6 or 8, the remainder is 1. What is the largest
possible value of that 3-digit number?

Find the number of all positive factors of 1014.

It is known as the lengths of shorter sides for a right-angled triangle are 7cm and 24cm
respectively. Find the length of the longest length.

P is a point in rectangle ABCD. Given that area of APD = 92cm2 , area of BCP equals to
27% of rectangle ABCD. What is the area of rectangle ABCD (in cm2)?

Little cubes with side length 1cm are combined according to the pattern shown below. If
there are 14 layers, find the surface area.

The area of a rectangle is 576. The value of its length and width are both integers. What is
the minimum possible value of its perimeter?

If the side length of a square is 14π and the perimeter of a square is equal to the
circumference of a circle, find the radius of the circle.