MYTS 2019 — Grade 5 — Round 1

Two odd numbers have exactly 2019 even numbers between them. Find the difference between the two odd numbers.

The figure consists of eight small squares. How many paths from $A$ to $C$, along the edges of the squares, avoid $B$ and have length six times the side length of a small square?

In the figure, $ABCD$ is a square of side length 2 cm. Find the shaded area. (Use $\pi=3.14$.) Give the answer in cm².

An repeats the letters $M,Y,T,S$ to form

$MYTSMYTSMYTSMYTS\ldots$

From left to right, An colours the letters blue, red, purple, yellow, orange, blue, red, purple, yellow, orange, and so on. What colour is the 2019th occurrence of $T$?

At 8:05 a.m. a digital clock displays 08:05, and at 8:19 p.m. it displays 20:19. It now displays 21:09. After at least how many minutes will it next display all four digits 2, 0, 1 and 9?

How many fractions in the following sequence are greater than 1?

$$\frac1{2019},\frac3{2017},\frac5{2015},\ldots,\frac{2017}3,\frac{2019}1.$$

In the figure, $ABCD$, $AHIJ$ and $AEGF$ are squares, and $H$ is the midpoint of $BE$. Their side lengths, in centimetres, are natural numbers. Find $AB$, given that the shaded area is 19 cm². Give the answer in centimetres.

Find the value of

$$A=\frac{20192019}{2019}\times\frac{2018}{20182018}\times\frac{20172017}{2017}\times\frac{2016}{20162016}\times\cdots\times\frac{2002}{20022002}\times\frac{20012001}{2001}.$$

Four animals, each either a frog or a toad, are named Mi, Y, Ti and Si. Toads always tell the truth; frogs always lie. Using their statements below, determine how many of the four are frogs:

- Mi says: “Y and I are different species.”
- Y says: “At least three of us are frogs.”
- Ti says: “Si is a frog.”
- Si says: “Ti is a frog.”

Hà has five boxes of fruit, each containing either oranges or lemons. Their fruit counts are 21, 39, 42, 49 and 66. After Hà sells one box of oranges, the remaining number of oranges is two thirds the number of lemons. How many oranges did Hà have originally?

A pen shop offers these promotions: buy 4 pens, get 1 free; buy 6 pens, get 2 free and receive 1000 đồng back. What is the least amount of money needed to obtain exactly 38 pens? Each pen costs 2000 đồng. Give the answer in đồng.

Hà has four stickers numbered 1, 2, 3 and 4 as shown. Hà places sticker 3 on sticker 4, then sticker 2 on sticker 3, and finally sticker 1 on sticker 2, aligning the squares marked $X$ and $Y$ on all four stickers exactly. How many of the digits 4 on sticker 4 are covered by stickers 1, 2 and 3?

Using the four digits 0, 1, 2 and 9, how many numbers less than 2019 and divisible by 3 can be formed, with each digit occurring at most once in any number?

Square $ABCD$ has side length 20 cm. Three ants, Andy, Bobby and David, crawl along its edges. Andy travels from $A$ to $B$ then $C$ at 4.5 cm/s. Bobby travels from $B$ to $C$ then $D$ at 2 cm/s. David travels from $D$ to $C$ then $B$ at 3 cm/s. When Bobby and David first meet, how many centimetres is Andy from them? All three start at the same time.

How many two-digit numbers $\overline{TS}$, with $T\ne S$, admit digits $M,Y,H$ that are distinct from one another and from $T,S$, such that $\overline{MYTS}-\overline{HTH}$ is a two-digit number?