MYTS 2017 - Grade 5 - Round 1

Find the smallest three-digit natural number N whose digit sum is 13.

A closed box contains 6 white,8 yellow,10 blue and 12 black marbles. What is the minimum number to draw to guarantee 5 marbles of one colour?

An equilateral triangle is divided into smaller equilateral triangles as shown. What fraction of the large triangle is coloured?

Find the largest six-digit multiple of 15 whose digits are all distinct.

Place 1,2,…,9 in the nine cells, once each. Add the horizontal row and the vertical column, then add those two sums. Dung obtains the largest possible result. What is it?

Identical polygonal paper pieces shaped like lizards are fitted together as shown. Each lizard must have one colour and neighbouring lizards must have different colours. What is the least number of colours needed?

Given 1+3+5+7+…+113=k×k, find k.

Xuân Lan is 9, her brother 3, and their mother 33. In how many years will the mother be twice the sum of the children’s ages, when the family plans to travel?

The boundary consists of four semicircles with collinear centres: a large one of radius 14 cm, a medium one of radius 7 cm and two equal smaller ones. Find the coloured area in cm², using π=22/7.

Two squares have sides 16 cm and 12 cm as shown. Find the shaded area in cm².

Find the smallest three-digit natural number N divisible by 77 whose digits are all odd.

Three carpenters make 75 chairs in 5 days. At the same constant productivity per person, how many chairs do 5 carpenters make in 8 days?

Houses are numbered with consecutive odd numbers 1,3,…,29. Cutting each metal digit costs 30000 đồng. What is the total cost, in đồng?

The C-shaped solid is built from identical cubes of side 2 cm as shown. Find its total surface area in cm².

BEAUTIFUL is repeated in a row until there are exactly 500 letters. What are the last two letters, in order?

Two small squares of areas 4 cm² and 9 cm² lie inside a square of area 81 cm² as shown. Find the coloured area in cm².

How many natural numbers less than 251 are divisible by 4 but not by 5?

Join each vertex of a square to the midpoint of the opposite side as shown. The square’s area is 200 cm². Find the coloured area in cm².

ABCD is a trapezoid of area 198 cm². Quadrilaterals EKHL and GMJN have areas 32 cm² and 41 cm². Find the total coloured area in cm².

Label the eight vertices of a cube with 1,2,…,8, once each, to maximize the number of edges whose endpoint labels have odd sum. What is that maximum?