VTMO 2021 — Grade 5 — cup

The figure combines $a = 10 \,\mathrm{cm}$ square and $a = 15 \,\mathrm{cm}$-long rectangle as shown. Find unshaded area minus shaded area.

How many birth years from $1900$ through $2021$ have age equal to their digit sum? Age $= 2021$−birth year.

Fifteen pupils all receive candy. Eight get more than $1$, five more than $2$, three more than $3$, and one gets $5$; none gets more than $5$. Find total candies.

Pencils cost $10$ thousand dong, notebooks $15$. An buys $23$ pencils and $12$ notebooks. Binh buys $35$ items and spends $30$ thousand more. Chau spends more than Binh but buys fewer notebooks. What minimum pencils does Chau buy?

Machine A produces $24$ more items per minute than $B$. $A$’s $= 25$-minute output is twice $B$’s $= 20$-minute output. Find $A$’s rate.

An takes $S$→A $_{1}$→A $_{2}$→A $_{3}$→A $_{4}$→A $_{5}$→A $_{6}$→A $_{7}$→A $_{8}$→A $_{9}$→$F$; Binh takes $S$→$B _{1}$→$B _{2}$→$F$. Equal route lengths, $SA _{1} 30 m , SB _{1} 50 m$, as shown. Find A $_{2}$ A $_{3}$+A $_{4}$ A $_{5}$+A $_{6}$ A $_{7}$.

Tank base $48 dm^{2}$, initial water depth $6 dm$. Tap A adds $32$ liters/minute and $B$ drains $18$. After $36$ minutes the water reaches $\frac{3}{4}$ of the tank height. Find tank height; $1$ liter $= 1 dm^{3}$.

A sequence of more than one consecutive odd integer has sum $165$. What is the largest possible sum of its endpoints?

In the $5 \times 5$ Ken Ken, each row and column contains $1 \text{--} 5$ once. Each bold cage must satisfy its shown operation and target:+sum,−difference, $\div$ quotient, $\times$ product (examples $7 + , 2 - , 2 \div , 4 \times$). The diagonal givens are $5 , 3 , 4 , 1 , 2$. Find $A + B$ in the pictured puzzle.

Exactly one of $A , B , C , D$ stole gold. A says“$B$ is a liar”and“$C$ or $D$ stole it”; $B$“$C$ is a liar”and“$D$ or A stole it”; $C$“$D$ is a liar”and“$A$ or $B$ stole it”; $D$“$A$ is a liar”and“$B$ or $C$ stole it”. A truthful person has two true statements; a liar at least one false statement. How many of the eight statements are true?

Taps $A , B$ together fill an empty tank in $30$ minutes. A runs $12$ minutes, then stops, and $B$ runs $42$ minutes, also filling it. How long before $B$ should A be opened so each supplies equal water when the tank is full?

$48$ red and green marbles are split among four boxes. Red: green ratios are $A = 1 : 1 , B = 2 : 1 , C = 3 : 1 , D = 6 : 1$. Green counts are four consecutive natural numbers and total $20$ fewer than reds. Find each box’s counts.