Question bank MYTS 2017

Calculate 1+4+8+16+32+64+128.

How many more cells must be coloured so that the coloured area is 4/9 of the whole figure?

Nine consecutive natural numbers have sum 909. Find the smallest.

Dũng wants to complete the shown arrangement of identical small cubes into a large cube, using as few additional cubes as possible. How many cubes must he add?

How many natural numbers less than 529 leave remainder 2 when divided by 5?

Given 1+3+5+7+…+113=k×k, find k.

45 students stand in a line. A girl stands at each end. Between every two consecutive girls there are exactly 3 boys. How many girls are there?

Find the last three digits of 1133557799 × 9977553311.

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?

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?

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?

The letters of GEOMETRY are put into each grid. Consecutive letters of the word must occupy cells sharing a side or a vertex. Which grid is invalid?

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?

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

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.

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?

Calculate 1+3−5+7+9−11+13+15−17+…+205+207−209.

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?