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VTMO 2016 — Grade 5 — semifinal

Question 1

$11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 = 9 P$. Find $P$.
  1. $14$
  2. $15$
  3. $16$
  4. $17$
  5. $18$

Question 2

An travels $\frac{1}{4}$ of the distance from home to the market, leaving $1.2$ km. Find the full distance.
  1. $1.5$ km
  2. $1.6$ km
  3. $2.4$ km
  4. $4.8$ km
  5. $2 \,\mathrm{km}$

Question 3

Find $30 \%$ of $40 \%$ of $50 \%$ of $200$.
  1. $12$
  2. $15$
  3. $20$
  4. $50$
  5. $60$

Question 4

A fraction reduces to $\frac{2}{3}$ and its original numerator and denominator sum to $105$. Find the original numerator.
  1. $21$
  2. $42$
  3. $63$
  4. $2$
  5. $3$

Question 5

How many squares are in the figure below?

Question illustration
  1. $4$
  2. $5$
  3. $6$
  4. $11$
  5. $12$

Question 6

Color the hexagons shown so edge-sharing cells differ. What is the minimum number of colors?

Question illustration
  1. $2$
  2. $3$
  3. $4$
  4. $6$
  5. $7$

Question 7

Use each digit $2 , 3 , 4 , 5 , 6 , 7 , 8$ once in $\overline{UVW}-(\overline{XY}+\overline{MN})$. What is the minimum?
  1. $70$
  2. $73$
  3. $82$
  4. $172$
  5. $165$

Question 8

Initially $70 \%$ of attendees are men.$108$ men leave, and women then number three times the remaining men. Find the initial total.
  1. $180$
  2. $126$
  3. $240$
  4. $236$
  5. $160$

Question 9

Two diagonals of $a = 3 \times 3$ grid pass through five small cells as shown. How many cells do they pass through in $a = 9 \times 9$ grid?

Question illustration
  1. $9$
  2. $11$
  3. $16$
  4. $17$
  5. $18$

Question 10

Place $1 , \ldots , 8$ in $a = 3 \times 3$ grid with center removed. Top row sums $9$, bottom $21$, left column $13$, right $15$. Find the corner sum $A + B + C + D$.

Question illustration
  1. $19$
  2. $25$
  3. $16$
  4. $36$
  5. $22$

Question 11

Two triangles have total area $120 \,\mathrm{cm}^{2}$. Their black overlap is $\frac{1}{3}$ of the smaller and $\frac{1}{9}$ of the larger. Find the black area. The figure is not to scale.

Question illustration

Question 12

How many three-digit numbers have digit product $36$? Examples $229 , 419$.

Question 13

Juice contains $80 \%$ water. Remove $75 \%$ of that water. What percentage of the remaining concentrate is water?

Question 14

Among $65$ pupils wearing white or blue, there are $25$ boys in white, $23$ pupils in blue, and $28$ girls. How many girls wear blue?

Question 15

Tank $A = 40 \times 30 \times 55 \,\mathrm{cm}$ is full, and tank $B = 70 \times 30 \times 45 \,\mathrm{cm}$ is empty. Transfer water until levels are equal. Find the common height.

Question illustration