MYTS 2018 — Grade 7 — Round 1

A shop buys T-shirts for 200 thousand đồng each and marks them up by 40%. It later discounts the marked price by 25% and sells all the shirts. What is the profit per shirt in đồng?

How many equilateral triangles have all their vertices among the vertices of a given cube?

The chart shows spelling-error counts for a group of students in an English writing test. What percentage made fewer than 4 errors?

Let $A=2018^2-2017^2+2016^2-2015^2+\cdots+2^2-1^2$. Find its last two digits.

Ánh Viên’s 200 m freestyle time at SEA Games 28 is 1 minute 59 seconds. After the starting dive she swims steadily at 1.6 m/s. Ignoring the dive’s duration, how far does the starting dive carry her, in metres?

How many positive integers $n$ have remainder equal to the square of the quotient when divided by 45?

The odd numbers are arranged in rows:

$1$

$3\quad5$

$7\quad9\quad11$

$13\quad15\quad17\quad19$

$21\quad23\quad25\quad27\quad29$

$\ldots$

Find the sum of row 20.

Xuân Trường and Văn Thanh practise penalties, each taking at least one shot. Their exact success rates are 80% and 95%, respectively. With 125 shots in total, what is the greatest combined number of successful shots?

Triangle $ABC$ is right-angled at $A$, with $AB=3$ cm and $AC=4$ cm. Square $BCED$ is constructed externally as shown. Find $AD$ in cm.

An has thirteen cards numbered 1 through 13. What is the largest number of cards that can be selected so that the product of their numbers is a perfect square?

A fishing group has equally many students from each of three schools. The smallest individual catch is $1/15$ of the total and the largest is $1/9$. How many people are in the group?

Châu builds a cube of side 4 from 64 unit cubes, then removes 14 cubes as shown. Find the surface area of the resulting solid.

Four children sing and accompany one another. For each song, one accompanies and the other three sing. An sings 9 songs, Bình 5, Lan 6 and Hoa 7. How many songs does Bình accompany?

Given square $ABCD$, construct equilateral triangles $ABE$ and $BDF$ as shown. Find angle $EFD$ in degrees.

How many assignments put a tiger, leopard, lion, bear and wildcat into five cages numbered 1–5, one animal per cage, with the tiger not in cage 1 and the leopard not in cage 5?

An athlete trains for 9 consecutive days. Every four consecutive days total 87 km. Day 2 covers 22 km and the last day 19 km. What is the combined distance on days 3 and 8?

Farms $A,B,C,D$ lie in order on a straight road, with $AB=2$ km, $AC=5$ km and $AD=6$ km. Place a factory on the road so its distances to $A,B$ sum to its distances to $C,D$. How far is it from $A$, in km?

A motorcyclist is overtaken by a car. Ten minutes later the motorcycle reaches a rest stop where the car has already stopped. Their speeds are 40 and 50 km/h, respectively. How many minutes earlier did the car arrive?

Find the smallest positive multiple of 99 whose decimal representation contains no digit 9.

Real numbers $a,b,c$ satisfy $|a|\le5$, $|b+1|\le7$, $|c+2|\le9$. Find the minimum $S$ and maximum $T$ of $|a+b-c|$.