VTMO 2014 — Grade 6 — semifinal

How many primes lie strictly between $50$ and $100$?

Fill the blank in $2014 \times 2015 = 2014 \times 2000 - 2014 + 2014 \times \ldots$

$A$ is the largest odd four-digit number with distinct digits. Find its digit sum.

Sawing $a = 72 \,\mathrm{cm}$ bar into $6 \,\mathrm{cm}$ pieces takes $165$ minutes. How long for $a = 144 \,\mathrm{cm}$ bar with the same piece length?

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.

Find the last digit of $7^{2014}$.

$a \equiv 1$ and $b \equiv 2$ modulo $8$. Find the remainder of $3 a + 6 b$ modulo $8$.

$A = 400 m$ 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?

January $1 , 2015$ is Thursday. What weekday is the last day of that month?

A number consists of $2014$ sevens. What minimum number of digits must be deleted to leave a multiple of $63$?

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

A team plays $90$ matches and won $40$ of its first $50$. How many remaining wins give exactly $70 \%$ wins?

Tap A fills a tank in $15$ minutes, $B$ in $10$. How long if both are opened?

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

Rectangle $ABCD$ has perimeter $240 \,\mathrm{cm} , AB = 40 \,\mathrm{cm}$. Find the illustrated shaded area.

The sequence begins $1 , 2 , 3$, with each later term the sum of the previous three. Find the eighth term.

$A = 2 \times 2 \times 2$ cube is colored black and white as pictured. Which illustrated net unfolds it?

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

Evaluate $1+\frac1{1+\frac1{1+1}}$.

Jerry runs two equal laps. The first speed is $200 m /$ min. What second-lap speed gives $240 m /$ min overall?