VTMO 2014 — Grade 4 — semifinal

A square’s side equals a rectangle’s width. The rectangle has perimeter $100 \,\mathrm{cm}$ and length $40 \,\mathrm{cm}$. Find the square’s perimeter.

Find the fraction of triangles that are shaded.

A teacher says: think of a number, add $1$ and double it; give the result to your neighbor, who subtracts $1$ and doubles it. An thinks of $6$ and passes his result to Binh. What does Binh obtain?

Replace $A$ and $B$ by distinct digits so that $A+A+B+B=16$. Which of the following digits cannot be $A$?

How many two-digit numbers are divisible by $5$?

How many digits are needed to number a $36$-page book starting at $1$?

Four balls are red, yellow, blue and black. Red is heavier than yellow but lighter than blue; black is lighter than red but heavier than yellow. Put them in decreasing weight order.

A mother is $47$. In three years she will be twice her child’s age. How old is the child now?

How many identical small cubes form the figure below, including hidden cubes?

Class $4 B$ forms a line. Minh is $10$ th from the front and $6$ th from the back. How many pupils are in the line?

One machine makes $30$ products per minute and another $40$. After both work for $5$ minutes, how many more products has the second made?

A copying shop charges $350$ dong per page for the first $50$ pages and $300$ dong for each page from the $51 st$ onward. What is the cost of $125$ pages?

Nam picks three times as many oranges as pomelos. Which number could be their combined total?

A tap is opened at $10 : 10$ and fills the tank in $4$ hours $55$ minutes. When must it be closed?

Increasing a rectangle’s length by $3 m$, without changing its width, increases its area by $12$ square meters. What is its width in meters?

Both spouses have two-digit ages. Reversing the husband’s digits gives the wife’s age. Which number could be their combined age?

Find the missing number in the last triangle using the pattern in the first three.

Quang would have $8000$ dong left after buying $9$ notebooks, but would be $40000$ dong short of buying $13$. How much money did he bring?

Pi repeats TOANTITAN indefinitely: TOANTITANTOANTITAN… . What is the $2014$ th letter?

Binh writes integers from $1$ to $999$ but skips multiples of ten and multiples of one hundred. How many numbers does he write?