VTMO 2015 — Grade 4 — final

Five consecutive natural numbers have mean $100$. What is the largest?

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

Use each digit $1$ through $8$ once to form two four-digit numbers. What is the largest possible sum?

Pi spends $78000$ dong. What is the fewest banknotes needed to pay exactly?

Distinct letters stand for distinct digits. Find the sum in $\overline{DECB}+\overline{DEAB}=\overline{ABCDB}$.

Define $\otimes n=n+(n-1)+\cdots+1$. Find $\otimes10-\otimes9$.

A $117$-minute movie starts at $7 : 30$ p.m. Ti must arrive $15$ minutes early for tickets, and the journey takes $20$ minutes. What is the latest departure time?

Of $13$ flowers, $5$ are roses and the rest daisies. Six flowers are white and the rest red. What is the least number of red daisies?

Minh, Hung and Thanh have $75$ marbles combined. If Hung gives Minh $5$, the two have equal amounts. If Thanh gives Minh $5$, Minh and Hung’s combined amount exceeds Thanh’s by $15$. Find each original amount.

An and Binh play bowling with natural-number scores. $a$) An’s first two scores are $108$ and $125$; rounds $3$ and $4$ average $122$. What fifth score makes the five-round mean $120$? $b$) Binh’s first three average $113$, and his fourth and fifth scores are equal. Can his five-round mean be $120$? Explain.

On odd dates Ti reads twice the date in pages; on even dates he reads half the date. How many pages does he read during March?