BBB 2021 - Primary 6 - Preliminary Round

A 4-digit natural number is divided by 6, 11 and 12 to get the same remainder of 3. What is the minimum value of this number?

It requires 9 people to take 5 days to complete a task. How many day(s) is / are needed for 15 people to finish the same task?

Refer to the figure below, how many rectangle(s) is / are there?

The sum of 3 prime numbers is 34. Find the maximum value of the product among these 3 prime numbers.

Find the value of $\left(\frac34+\frac38+\frac3{16}+\frac3{32}+\frac3{64}\right)\div\left(\frac47+\frac4{14}+\frac4{28}+\frac4{56}+\frac4{112}\right)$.

If $4\otimes2=4\times5$, $4\otimes5=4\times5\times6\times7\times8$. Find the value of $6\otimes5$.

Editorial interpretation: $a\otimes b$ is the product of $b$ consecutive integers beginning at $a$. The examples suggest this rule but do not uniquely define an arbitrary operation. The grading answer is conditional on this intended rule.

It is known that the sum of 7 consecutive odd numbers is 1743. Find the value of the smallest number.

Find the value of $7654\times2345-7655\times2344$.

Find the value of $\frac1{14\times9}+\frac1{18\times11}+\frac1{22\times13}+\cdots+\frac1{66\times35}+\frac1{70\times37}+\frac1{74\times39}$.

Find the value of $\frac{3699\times616-1232}{770+3692\times154}$.

Today is 31st December 2021 (Friday). Which year was satisfied that 11th December was on Tuesday for the closest case?

In the first 2046 natural numbers, how many number(s) is / are divisible by 17?

Original choices: A. 120; B. 121; C. 118; D. 119.

Editorial qualification: the source does not say whether natural numbers start at 0 or 1. These conventions give different supplied choices. This item is presented for written explanation, not automatically keyed to one option. State your convention and justify your count; the reference solution explains both.

How many simplified proper fraction(s) with denominator 119 is / are there?

Editorial domain clarification: count positive proper fractions, with numerator from 1 to 118, as intended by the English statement.

Find value of $\frac{5^2+6^2+7^2+\cdots+88^2+89^2+90^2}{5+6+7+\cdots+93+94+95}$.

Now there are 300 books in the bookshelf. 30% of the books are Chinese books. 30% of the books are English books. How many English book(s) should be added to reduce the number of Chinese books to be 10% of the bookshelf?

A triangle with all integral lengths has side lengths 21 and 11. Find the greatest value of the longest side length.

There is a cuboid. When the length increases 2cm, the volume will be increased by 112 $\text{cm}^3$. When the width decreases 3cm, the volume will be decreased by 189 $\text{cm}^3$. When the height increases 2cm, the volume will be increased by 144 $\text{cm}^3$. What is the volume of the cuboid in cm³?

Between 5am and 6am, when does the number “7” on the clock locate between the hour hand and the minute hand? (choose the closest answer)

Editorial clarification from the Vietnamese source: “chính giữa” means exactly halfway in angle between the hands. The English merely says “between”; the answer uses the more specific Vietnamese condition.

Given $k\gt 0$ and $k^{2021}-\frac1{k^{2021}}=0$, find the value of $k$.

Find the value of $3^3+6^3+9^3+\cdots+33^3+36^3$.