VTMO 2013 — Grade 5 — semifinal

Question 1

Which replacement for * makes $1 + 1 \cdot 1 - 2 = 100$ true?

+
−
$\times$
$0$
$1$

Question 2

Hoang multiplies an integer by $8$. Which cannot be the result?

$24$
$48$
$56$
$72$
$84$

Question 3

Hoang lives with his father, mother, sister, $a$ dog, $a$ cat, two parrots and four fish. How many legs are there?

$18$
$20$
$22$
$24$
$26$

Question 4

Distinct shapes represent distinct digits. In the illustrated addition, square+square+circle-circle=triangle-triangle-triangle. Find square.

Question illustration

Question 5

A father is $36$ and child $6$. After how many years will the father be three times the child’s age?

$30$
$15$
$12$
$18$
$9$

Question 6

Find the perimeter of the shape below, with sides marked $2 \,\mathrm{cm}$ and $4 \,\mathrm{cm}$.

Question illustration

$12 \,\mathrm{cm}$
$16 \,\mathrm{cm}$
$18 \,\mathrm{cm}$
$20 \,\mathrm{cm}$
$22 \,\mathrm{cm}$

Question 7

Find the black area: base width $5 \,\mathrm{cm}$, two vertical sides $4 \,\mathrm{cm}$, and top height $10 \,\mathrm{cm}$ as shown.

Question illustration

$20 \,\mathrm{cm}^{2}$
$25 \,\mathrm{cm}^{2}$
$35 \,\mathrm{cm}^{2}$
$40 \,\mathrm{cm}^{2}$
$50 \,\mathrm{cm}^{2}$

Question 8

Class $5 A$ has $12$ more students than $5 B$. How many must move from $5$ A to $5 B$ to leave a difference of $4$?

Question 9

A herd has $315$ heads and legs combined. How many cows are there?

$60$
$61$
$62$
$63$
$64$

Question 10

A boat takes $2$ hours downstream $A$→$B$ and $4$ upstream. How long does a drifting raft take $A$→$B$?

Question 11

Pi colors $TITAN$ EDUCATION: identical letters have the same color and different letters have different colors. How many colors are required?

$7$
$8$
$9$
$10$
$11$

Question 12

The rectangular gray-and-striped tile pattern has lost some tiles as shown. How many missing tiles are gray?

Question illustration

Question 13

An $L$-shaped tile consists of $4$ unit squares as shown. How many of the five shapes below can be formed from two such $L$ tiles?

Question illustration

Question 14

Which expression has an even result?

$1 \times 3 \times 5 \times \ldots \times 99$
$2013 \times 2014 + 2015$
$1 \times 2 \times 3 \times \ldots \times 100 + 101$
$2 \times 4 \times 6 \times \ldots \times 100 + 101$
$1 + 3 + 5 + \ldots + 99$

Question 15

How many three-digit numbers are divisible by $8$?

$26$
$111$
$112$
$124$
$125$

Question 16

A village never uses numbers containing digit $3$. Houses on the right side are numbered with increasing odd numbers, starting $1 , 5 , \ldots$ . What is the number of the $15$ th house?

$29$
$41$
$49$
$45$
$47$

Question 17

Five boxes contain $A , B , O , R , V$ as shown. Remove letters so each retains one, and all five retained letters differ. Which letter remains in box $5$?

Question illustration

Question 18

A triangle and a square of side $4 \,\mathrm{cm}$ have equal perimeters and share an edge as shown. What is the combined perimeter?

Question illustration

$12$
$24$
$26$
$28$
$32$

Question 19

There are $60$ seats around a circular table. Seat students so each has exactly one occupied neighboring seat. What is the maximum number?

$60$
$40$
$30$
$20$
$10$

Question 20

The first Saturday is the $5$ th. What weekday is the $25$ th?

Tuesday
Wednesday
Thursday
Friday
Saturday