Question bank VTMO 2016

Evaluate $(23+24+25+26+27+28+29)-(13+14+15+16+17+18+19)$.

Hai chooses any number greater than $25$ and less than $40$, adds $57$, subtracts $37$, then subtracts the original number. What is the final result?

A month has five Sundays, but neither its first nor last day is Sunday. What weekday is its $20$ th?

A diagonal of a $4 \times 3$ rectangle crosses six unit squares. How many unit squares does a diagonal of an $8 \times 6$ rectangle cross?

Find the missing term: $1 , 1 , 2 , 6$, ___, $120$.

The chart shows the favorite colors of $40$ pupils in class $1 Q$, with each pupil choosing one color. How many prefer red?

A stationery shop offers pencil bundles: $1$ pencil for $3000 VND , 2$ for $5000 VND$, or $5$ for $9000 VND$. With $53000 VND$, what is the greatest number of pencils Pi can buy?

Grade $3$ pupils stand equally spaced in a circle and count clockwise. Minh is number $6$, directly opposite number $14$. How many pupils are there?

Minh is $15000 VND$ short of buying a book, and Khoa is $19000 VND$ short of buying the same book. Their combined money is exactly enough. What is the book’s price?

Which cardboard net cannot be folded into a cube? The five nets $A \text{--} E$ are shown below.

Find the sum of the two numbers in the tenth pair: $\left(1 , 6\right) , \left(3 , 8\right) , \left(5 , 10\right) , \left(7 , 12\right) , \ldots$

A bag contains red, yellow and blue balls. Exactly $3$ are not red, $4$ are not yellow, and $5$ are not blue. How many balls are there?

Thanh concatenates the numbers $1$ through $25 : 1234567891011121314 \ldots 232425$. What is the central digit?

Numbers $226$ and $138$ have three digits whose product is $24$. How many three-digit numbers have digit product $24$, including $226$ and $138$?

The elder brother has $6$ more candies than the younger. Their mother gives the elder $2$ more and the younger $5$ more, bringing their combined total to $31$. How many did the younger originally have?

Different letters $C , A , R , T$ represent different digits, with $T = 0$ and A odd. Find $C$ in $\overline{CAR}+\overline{CAR}=\overline{ART}$.

Tom writes $1$ through $30$. Jerry erases all even numbers. What is the units digit of the product of the remaining numbers?

A square is divided into two rectangles as shown. Their combined perimeter is $30 \,\mathrm{cm}$. Find the square’s area.

An, Binh and Chau have candies. First An gives Binh and Chau as many candies as each currently has (for example, $10$ more if Binh has $10$, and $7$ more if Chau has $7$). Next Binh doubles Chau’s and An’s holdings in the same way. Finally Chau doubles An’s and Binh’s holdings. All three then have $16$. How many did An originally have?

Ti’s four friends Suu, Dan, Mao and Thin have a race. Afterwards they say:
• Suu: “Mao finished first.”
• Dan: “Unfortunately, $I$ did not finish first.”
• Mao: “Dan won.”
• Thin: “I did not win.”
Exactly one statement is false and three are true. Who won?