MYTS 2018 — Grade 4 — Round 1

Each large square in the figure has area 1. Find the difference between the two shaded areas.

Lan pays with a 100-thousand-đồng note for pens costing 14 thousand đồng. The seller has notes worth 50, 20, 10, 5, 2 and 1 thousand đồng. What is the minimum number of notes Lan can receive as change?

Lan, Hương, Thúy and Quỳnh race, with no ties. Lan finishes after Hương; Thúy finishes before Quỳnh, but Thúy is not first and Lan is not last. Who finishes first and who finishes last?

An’s family has 5 people and Bảo’s has 4. In 5 years, An’s family’s total age will exceed Bảo’s by 20 years. In 10 years, by how many years will the totals differ?

Three kinds of tiles cover a rectangular wall in a pattern. Some tiles have fallen off, leaving the blank area shown. How many of the fallen tiles have flowers?

Dũng and Hải each eat half a cake. Dũng eats twice as fast as Hải but starts 1 minute later. They finish together. How many minutes would Hải take to eat a whole cake?

Five squares are joined as shown. Square 1 has side 1 cm and square 2 has side 2 cm. Find the perimeter of the combined shape in cm.

A cinema offers one free ticket for every five tickets bought. What is the minimum number of tickets to buy so that 53 people each have a ticket?

A class enters a room in single file. Nine students stand between An and Bình. When An enters, twice as many students are behind An as have entered before An. When Bình enters, twice as many students have entered before Bình as remain behind Bình. How many students are in the class?

A swimming pool measures $16\text{ m}\times24\text{ m}$. A 2 m wide path surrounds it as shown. Find the path’s area in m².

How many triangles are in the figure?

Thảo places the numbers 1 through 9 in a $3\times3$ grid so that all row and column sums are equal. The entries $a,b,c,d$ are then covered as shown. Find the difference between $a+b$ and $c+d$.

Ten cards show the digits 0 through 9. Use the cards to form a five-digit number and a four-digit number. What is the largest possible sum of the two numbers?

Tuấn has two electric digital clocks. Both stop during a power cut. When power returns, the first restarts at 00:00 and the second resumes from its stopped reading. Power fails at 2:30 a.m. and returns at 4:30 a.m. When Tuấn wakes at 7:00 a.m., how many minutes apart are the readings? There is only one power cut that night.

A box contains 10 red, 20 blue, 30 yellow and 40 white marbles. What is the minimum number Bình must draw to guarantee at least 5 marbles of each of three colours?

A rectangle is split into rectangles 1, 2, 3 and 4 as shown. Rectangle 4 has half the area of rectangle 1, and rectangle 2 has $2/3$ the area of rectangle 1. Find the ratio of rectangle 3’s area to the entire rectangle’s area.

How many three-digit numbers have hundreds and units digits differing by exactly 1?

Nam has a cube measuring $3\text{ cm}\times3\text{ cm}\times3\text{ cm}$. He draws lines dividing every face into 9 squares, including the cube’s edges. What is the total length of all the drawn lines in cm?

One of Fox, Snake, Vện the dog and Chicken stole an egg. They say:
- Fox: Snake stole it.
- Snake: Vện stole it.
- Vện: I have an alibi.
- Chicken: Snake is wrong.
Exactly one tells the truth. Who stole the egg?

An ant follows the broken line from $A$ to $B$ in the figure. Adjacent parallel lines are 1 cm apart. How long is the path in cm?