PIMSO 2022 - Mathematics - Grade 4 - National Round

How many 3-digit number/s can you form such that the tens digit is divisible by the ones digit, the tens digit is higher than the hundreds digit by 2, and the sum of the hundreds and the ones digits is 10?

A rectangle has an area of 1,406 sq. meters. If its dimensions are consecutive integers, what is the perimeter of the said figure?

What fundamental operations, in chronological order, will make the equation correct when entered into a calculator?

$121\;\square\;75\;\square\;72\;\square\;9=54$

Editorial interpretation: use a calculator that follows ordinary operation precedence. Enter the three operation signs from left to right.

Suppose you have a collection of pebbles that you want to store in small boxes. If you put 9 in each box, 1 is left behind. If you put 8 each, 3 are left behind. If you put 11 instead, 3 are also left behind. Given that the total number of marbles you have is close to but does not exceed 100, how many do you have?

Bus stops A and B are located across each other wherein 14 and 4 different bus lines stop over each bus stop respectively. In regular intervals, every 14th bus that stops over at A is a Cornelia bus while every 4th bus that stops over at B is a Magnolia bus. If for every hour 10 buses stop over at each point with the first buses arriving at 8:00 am, after how many hours and minutes will a Cornelia bus and a Magnolia bus stop over their respective points at the same time?

The recorded temperature in binary number during a hot Sunday afternoon is $00100100_2$°C. What is the temperature in decimal?

My mother is three times older than my sister. My father is 30 years older than me. I was 5 years old when my sister was born. If the present age of my sister is 15 years, then the difference between my mother’s and father’s age is ____.

Editorial interpretation: “three times older” is read as “three times as old”, as intended by the key.

At the end of a meeting, seven students shake hands with each other once. How many handshakes will be there altogether?

In a certain code system, ‘OHLRNGDZSQNTMC’ is written as ‘PIMSOHEATROUND’. How can ‘OHLRNEHMZKQNTMC’ be translated in that code?

Cecilia, Dina, Elena, and Fiona are cousins with different ages who live in the same house. When a new neighbor asked them who is the oldest, they answered: Cecilia: I am the eldest. Dina: I am not the youngest. Elena: I am neither the eldest nor the youngest. Fiona: I am the youngest. Given that one of them is not telling the truth, who is the oldest of the four cousins?

It is Leta’s birthday today. She is 5 years older than Leo. If you multiply their ages the product is 546. Find the sum of their ages after 3 years from today.

What is the next number in the series? 16 21 12 18 10 17 8 ___

Pattern note: use the consecutive increases within the adjacent pairs of terms.

Simplify: 27,111 + 25,212 + 23,313 + 21,414 + 19,515 + 17,616 + 15,717 + 13,318 + 11,419 + 9,520 + 7,621 + 5,722 + 3,823 + 1,924

Simplify (1,111 × 53) × (111 × 59) ÷ 3,127.

Simplify: 321 + 322 + 323 + 324 + 325 + 326 + 327 + 328 + 329 + 330 + 331 + 332 + 333 + 334

Simplify: $\frac{8}{14}+\frac{8}{42}+\frac{8}{84}+\frac{8}{140}+\frac{8}{210}+\frac{8}{294}+\frac{8}{392}$.

Simplify: $\frac{25}{4}+\frac{25}{12}+\frac{25}{24}+\frac{25}{40}$.

If F is a counting number between 0 and 10, R is a whole number and $R>F$, find F if: $11+(R\times22)=(F\times6)+(F\times27)$ and $R-F=1$.

What do you call a solid figure formed by joining together polygons at their edges.

Johnson made a regular kite for their class activity. Two adjacent vertices of the kite have distances of 20 cm. and 21 cm. from the intersection of the diagonals. What is the area of the kite?