PIMSO 2025 - Mathematics - Primary 5 - National Round

Find the ones digit of the product of the digits of the 2025-digit number $123412341234\ldots$.

If $P,I,M,S$ and $O$ are whole numbers, find their sum. $3.69=P+\frac{1}{I+\frac{1}{M+\frac{1}{S+\frac{3}{O}}}}$.

Write the sum as a single fraction in simplest form: $\frac2{17}\times\frac{289}{59}+\frac2{17}\times\frac{391}{59}+\frac2{17}\times\frac{629}{59}+\frac2{17}\times\frac{697}{59}$.

Find the sum of all the numbers from 100 to 199 that are not divisible by 19.

Consider this phrase: PIMSO MATH SCIENCE PHILIPPINES Every second, the first letter of each word is moved to the end of the word. This continues until the statement reads the same as the beginning. In how many minutes will the original statement appear back again?

What is the units’ digit of the sum of $123^5+124^6+125^7+126^8+127^9$?

How many counting numbers between $2^4$ and $2^8$ (exclusive) are divisible by 2or 5?

Find P + I - M - S × O, when 231 is 60% of P, I is 18% of 350, 28 is M% of 350, and 48 is S% of O% of 1500.

The natural numbers are arranged in a wave pattern as shown on the right. What is the difference between the sum of the numbers that appears on the 60th row and the sum of the numbers that appears on the 50th row?

The 8-digit number PIMPIMSO is divisible by 69. If the digits SO are removed the number becomes 629629. What is the biggest possible value of PIMSO?

The The rectangle ABCD has a length of 10 cm and a width of 8 cm. What is the area of quadrilateral STEP if the shaded square has a side of 2 cm?

Find the obtuse angle between the hour hand and the minute hand of a clock when the time is 14:30 (2:30 PM).

A town has three festivals that occur every 4, 6, and 9 years. If all festivals happen this year (2025), what is the next years will all occur together again?

Some years ago, there were 5 Sundays and 5 Mondays in the 11th month of the year. On which day of the week was the 20th in that month?

Alden, Bayani, Carlo, and Densio finished the race in a particular order. Each of them was asked and replied as follows: Alden: I was not the first. Bayani: Carlo was the first. I am not the last. Carlo: I came to the finish line before Alden and Densio did. Densio: I was the first. If only one of them lied, who was the last to finish the race?

Original choices: A. Alden; B. Bayani; C. Carlo; D. Densio.

The number of star apples inside the 6 baskets are consecutive odd numbers. If there are132 star apples in all, what is the product of the two middle numbers?

One of the interior angles of a regular polygon is 135˚. How many diagonals does this polygon have? (Hint: A diagonal is a line that joins any two opposite corners of the polygon.)

Jonathan and his three sons want to cross a river using a boat that can carry at most 80 kg. Jonathan weighs 60 kg and his sons weigh 50 kg, 40 kg and 30 kg, respectively. What is the minimum number of trips needed to get everyone to the other side of the river?

A triangle has side lengths of OM = 29 cm, SO = 69 cm, and SM = c cm, where the third side c is a whole number. How many values of c are possible?

The quadrilateral PHIL is divided into four regions as shown below. If the areas of $\triangle POH$, $\triangle POL$, and $\triangle LOI$ are $72\text{ cm}^2$, $48\text{ cm}^2$, and $56\text{ cm}^2$, respectively, find the area of $\triangle HOI$.