MYTS 2019 - Grade 5 - Round 2

Each letter $M,Y,T,S,V,N$ represents a digit less than 6, and different letters represent different digits. The numbers $\overline{MYTSVN}$, $\overline{YTSVN}$, $\overline{TSVN}$, $\overline{SVN}$, $\overline{VN}$ are divisible by 5, 11, 9, 6, 8, respectively. What is $\overline{MYTSVN}$?

A box contains 6 blue marbles and some red, purple and yellow marbles. It is known that:

(a) $\frac45$ of the marbles are not purple;

(b) The red and yellow marbles together form $\frac7{10}$ of all the marbles;

(c) The number of blue marbles plus twice the number of red marbles equals $\frac13$ of the total.

How many yellow marbles are in the box?

A square garden has side length 4 m. Show where to place four lamps inside it so that the illuminated garden area is 12.56 m². Each lamp illuminates a circular region of radius 1 m centred at the lamp. (Use $\pi=3.14$.)

There are ten stickers: one $2\text{ cm}\times2\text{ cm}$ square, two $2\text{ cm}\times1\text{ cm}$ rectangles, and seven $1\text{ cm}\times1\text{ cm}$ squares, as shown below.

(a) Which stickers should be selected to tile a rectangle with perimeter 24 cm? Show a suitable arrangement.

(b) Is it possible to select some of the ten stickers and tile a rectangle with perimeter greater than 24 cm? Explain why.

Note: Stickers may not be cut, folded or overlapped.

After the MYTS examination, Long, Ly, Quy and Phượng discuss their predicted results. All four are excited and believe they will win medals. Long makes three statements:

- My medal and Ly’s medal will be the same colour.
- My medal and Phượng’s medal will be the same colour.
- I will win a gold medal.

Quy makes one statement to each of the other three friends. His three statements are:

- You and I will both win silver medals.
- I will win a silver medal.
- You will win a silver medal.

When the results arrive, each of the four has won either a gold or a silver medal. Long and Quy each made exactly two true statements and one false statement. How many of the four won gold medals? Explain why.