VTMO 2016 — Grade 4 — final

Find a three-digit number below $200$ divisible by $11$ whose digits sum to $12$.

A $10$-question multiple-choice section awards $+ 2$ correct, $- 1$ incorrect and $0$ blank. Khang scores $12$ and leaves one blank. How many are correct?

What is the hundreds digit of $1\times2\times3\times4\times5\times6\times7\times8\times9\times10$?

Two large squares of side $7 \,\mathrm{cm}$ and four small squares of side $3 \,\mathrm{cm}$ are arranged as shown. Find the shaded square’s area.

An elder sibling has $6$ more candies than the younger. A mother adds $2$ to the elder and $5$ to the younger, making $31$ total. How many did the younger initially have?

Pencils cost $3000$ dong for $1 , 5000$ for $2$, or $9000$ for $5$. Pi has $53000$ dong. What is the maximum number he can buy?

Stack one red, two blue and two yellow boxes: equal colors are not adjacent; neither top nor bottom is yellow; the middle is not red; a yellow is immediately below red. Find the bottom-to-top order.

Distinct digits $A , B$ appear in the long multiplication $\overline{AB}\times\overline{BA}$ as shown. Each partial product has three digits; the final product has four digits and ends in $3$. Find the final product.

At $14 : 00$ Tom writes $12$. Every $5$ minutes Jerry replaces it with the product of its two digits plus $12$. For example, at $14 : 05$ it is $14$. What number appears at $15 : 30$?

A quantity of apples exactly fills $10$ small $+ 8$ large boxes or $5$ small $+ 10$ large boxes. How many small boxes alone are needed?

Pi has five test scores, the first three $85 , 92 , 87$, and each score is at most $100$. What is the lowest possible remaining score if the five-test mean is $90$?

Suu says “Mao came first”; Dan says “I did not come first”; Mao says “Dan won”; Thin says “I did not win.” Exactly one statement is false and three are true. Who won?