VTMO 2019 — Grade 4 — final

A four-digit number has distinct digits: thousands is twice tens; hundreds is $2$ less than thousands; units is nonzero; digit sum $12$. Find it.

Initially boys: girls $= 3 : 4$. Two boys leave and two girls join; finally boys: girls $= 2 : 5$. How many pupils are there finally?

Numbers on a square’s boundary total $31$. The four side sums, including corners, are $5 , 7 , 13 , 14$. What is the sum at the four corners?

A square is split into three equal-area rectangular strips as shown. The black parts total $13$ square centimeters. Find the white area.

A cube staircase has $3$ cubes for $2$ steps and $6$ for $3$ as shown. Paint every exterior face of $a = 10$-step staircase at $10$ ml per unit face. A can holds $500$ ml. How many cans are needed?

An, Binh, Chau have $135$ cards total. An has $3$ times Binh and Binh twice Chau. How many more has An than Chau?

A hotel accepts bookings on five days, closing Monday and Tuesday. Saturday has $18$ rooms booked, strictly most; Wednesday $15$, strictly least; each room is booked exactly $4$ times that week. How many rooms are there?

$A , B , C , D$ are cousins. Three years ago A was $3$ times $B$’s age and $C$ was $3$ years older than $D$. Four years ago A was $4$ years older than $B$ and $C$ was $4$ times $D$’s age. Find their current ages.