VTMO 2013 — Grade 4 — final

A father is $33$ and his three children are $3 , 5$ and $7$. In how many years will their combined age equal the father’s?

A division has quotient $10$ and remainder $4$. Find the smallest possible dividend.

Two $15 \,\mathrm{cm}$ rulers retain only their $3 \,\mathrm{cm}$ and $4 \,\mathrm{cm}$ marks. They overlap facing opposite directions as shown, with one ruler’s $3 \,\mathrm{cm}$ mark aligned with the other’s $4 \,\mathrm{cm}$ mark. Find the total length $L$.

A box contains cards numbered $1$ to $7$. The first person randomly takes $3$ cards, and the second takes $2$ of the remaining cards. The first person knows for certain that the second person’s sum is even. What is the sum of the first person’s cards?

A mother distributes $17$ candies among An, Binh and Chau. An has the most and twice as many as Chau; Binh has more than Chau. How many candies does Binh have?

Thanh cuts a $4 m$ log into $20 \,\mathrm{cm}$ pieces. Each cut takes $10$ minutes. Starting at $7$ a.m., when does he finish?

Today is Sunday. Minh starts a $127$-page book, reading $4$ pages daily except $25$ on Sundays. Without skipping days, on which weekday does he finish?

A rectangular vegetable plot lies in a fixed field. Extending one side by $3 m$ makes it square and reduces the bean plot by $30$ square meters. Find the original vegetable area.