VTMO 2014 — Grade 5 — semifinal

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?

Five baskets contain $538$ oranges total. Adding $2 , 4 , 8 , 16 , 32$ respectively makes all basket counts equal. How many were initially in basket $1$?

Vinh has $10$ more candies than Quang. If Vinh gives Nam $2$, Nam’s count equals Vinh’s remainder. How many more than Quang did Nam initially have?

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.

Two squares have side-length ratio $\frac{2}{3}$. What is their area ratio?

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

a leaves remainder $3$ on division by $9$. What is the remainder of $5$ a?

Two consecutive even integers sum to $102$. Find their product.

The question assumes February $1 , 2014$ is Sunday. Under this assumption, what weekday is the last day?

Squares $I , II , III$ are arranged as shown. Perimeters $I = 12$ and $II = 24$. Find $III$’s perimeter.

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.

Repeat OLYMPICTOANTITAN indefinitely. What is the $2014$ th letter?

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

Class $5 B$ forms a line. Minh is $10$ th from the front and $6$ th from the back. How many pupils are in the line?

Different letters represent distinct digits. $ABC + ABC + ABC = CCC$. Find $B$.

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?

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

Fold the shown net into a die. Which face is opposite the diamond?

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

$A = 400 m$ track is quartered by $A , B , C , D$. An starts at the midpoint of $AB$ and walks counterclockwise at $1.4 \frac{m}{s}$ for $30$ minutes. Which marked point is closest?