Question bank VTMO 2015

Exam papers

244 questions

Question 1

The belt passes around five wheels in the directions shown. How many wheels rotate clockwise?

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Question 2

Five consecutive natural numbers sum to $100$. What is the greatest of them?

$18$
$20$
$21$
$22$
$90$

Question 3

Given $\circledast5=5+4+3+2+1$, evaluate $\circledast10$.

$30$
$40$
$45$
$50$
$55$

Question 4

An queues for cinema tickets. He is seventh from the front and eighth from the back. How many people are in the queue?

$7$
$8$
$14$
$15$
$16$

Question 5

Both scales below are balanced. Which statement is correct?

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$\bullet=2\triangle$
$\blacksquare=3\triangle$
$\blacksquare=2\triangle$
$\blacksquare=3\bullet$
Another answer.

Question 6

Form two three-digit natural numbers using each of the digits $1 , 2 , 3 , 4 , 5$ and $6$ once. What is the greatest possible sum?

$885$
$966$
$975$
$1155$
$1173$

Question 7

Place $1$ through $9$ in the nine cells below, using each once. Both the vertical and horizontal lines sum to $23$. What number occupies the central cell?

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Question 8

The figure is a net of a cube. Which numbered face is opposite face $2$?

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Question 9

A club has $21$ males and $15$ females. Each week $4$ males and $6$ females join. After how many weeks will their numbers be equal?

Question 10

Pi writes down three odd natural numbers less than $20$, multiplies them, then adds $5$. Which could be the result?

$231$
$235$
$1006$
$8100$
$13012$

Question 11

Two brothers pick plums. The elder picks $12$ more than the younger. How many should he give the younger so their totals become equal?

There are $28$ birds on two branches. Four fly from the first to the second, then seven fly from the second to the first, leaving equal numbers on the branches. How many were originally on the first branch?

Question 13

Three books—Literature, Mathematics and Science—have blue, red and yellow covers. The red book lies between the Literature and Science books. The Science book and the blue book were bought on the same day. What is each book’s cover color?

Question 14

Pi thinks of a four-digit natural number. One digit is $1$; the hundreds digit is three times the thousands digit; the units digit is four times the tens digit; and the thousands digit is $2$. What is the digit sum?

Question 15

Eight boxes each contain at least one pebble. All counts are different except for exactly two boxes with the same count. What is the smallest total number of pebbles?

Question 16

An has clocks $A , B$ and $C$. A gains $30$ seconds per hour compared with $B$, while $B$ loses $30$ seconds per hour compared with $C$. All are reset to $8$ a.m. What does A show when $C$ shows noon?

Question 17

October has five Saturdays, and its last day is Saturday. What weekday is October $20$?

Question 18

There are $13$ flowers: $5$ daisies and the rest roses. Six flowers are white and the rest yellow. What is the least possible number of yellow roses?

Question 19

How many squares in the grid contain the letter $A$?

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Question 20

Eight cards are numbered $1$ through $8$. An, Binh and Chau each draw two cards.
• Binh: one card’s number is twice the other’s.
• Chau: the two numbers sum to $9$.
• An: the two numbers sum to $7$, but their difference is not $3$.
Which two cards remain?