VTMO 2019 — Grade 5 — semifinal

Question 1

Select the figure with exactly half its area shaded.

Question illustration

Figure $A$
Figure $B$
Figure $C$
Figure $D$
Figure $E$

Question 2

Read the pictured ruler, whose long ticks are $5.1$ and $6.1$. What is $A$?

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$4.9$
$4.8$
$5.0$
$5.08$
$5.09$

Question 3

$2800 \,\mathrm{kg}$ of rice is divided equally into $800$ bags. A family uses $0.25$ kg daily. How many days does one bag last?

$12$
$9$
$13$
$14$
$15$

Question 4

A boxing match has $12$ rounds of $3$ minutes, with $1$ minute between rounds. How long does a full $12$-round match last?

$36$ phút / minutes
$37$ phút / minutes
$46$ phút / minutes
$47$ phút / minutes
$48$ phút / minutes

Question 5

Equal small squares form a large square, with $3$ left over. Which could be the total number of small squares?

$103$
$102$
$97$
$107$
$108$

Question 6

How many triangles are in the picture?

Question illustration

$8$
$10$
$12$
$14$
$16$

Question 7

A jar with half its water capacity weighs $16.5$ kg; with one-third, it weighs $11.5$ kg. Find the empty jar’s mass in kg.

$1$
$1.5$
$2$
$2.5$
$3$

Question 8

Color the octahedron’s faces so faces sharing an edge differ. What is the minimum number of colors?

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Question 9

If Binh gives An one card, An has twice Binh’s cards. If An gives Binh one, both have equal counts. How many cards does An have?

Question 10

What minimum class size guarantees four students share a birth month?

$4$
$12$
$36$
$37$
$48$

Question 11

$2 X = 34 Y$ is divisible by $6$. What is $Y$ when this number is as small as possible?

Question 12

Five natural numbers have mean $60$. Replacing the smallest by $80$ raises the mean to $65$. Find the replaced number.

$45$
$48$
$50$
$55$
$60$

Question 13

Fold the net into a cube. Which three faces meet at $P$?

Question illustration

$BEF$
$ACF$
$BCF$
$ABE$
$ABF$

Question 14

Consecutive natural numbers fill triangular rows of lengths $1 , 3 , 5 , \ldots$ as pictured. What is the first number in row $20$?

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$362$
$400$
$401$
$324$
$200$

Question 15

Choose one entry from each row and each column of the $3 \times 3$ table, and multiply the three. What is the maximum?

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$45$
$162$
$168$
$105$
$504$

$A = 12 \,\mathrm{cm}$ by $8 \,\mathrm{cm}$ rectangle is divided by segments from its vertices to an interior point, as pictured. Find the combined area of the striped triangles on the top and bottom bases.

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Question 17

Three dice each have faces $1 \text{--} 6$ as shown. Find the total dots on unseen faces.

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Question 18

$1 ABCDE \times 3 = ABCDE 1$, where letters are digits. Find $A + B + C + D + E$.

Question 19

Fill $1 \text{--} 9$ once each in $a = 3 \times 3$ table. Top row contains $1 , 8 , 6$; bottom row $9 , 4 , 2$. The right column excludes $8 , 3 , 5 , 1 , 9 , 4$; the left excludes $6 , 4 , 3 , 1 , 7 , 2$. What is in the center?

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Question 20

A worker paints four walls and the ceiling of a room in $20$ hours. Doubling its length and width while keeping height unchanged requires $50$ hours at the same rate. How long does the original ceiling take?