PIMSO 2023 - Mathematics - Grade 5 - National Round

What is the greatest common factor of 36, 54, and 78?

Evaluate: $1+3+5+7+\ldots+99$

What is the remainder when $100\times200$ is divided by 7?

If $x+12=2x-3$, what is $x$?

John has $N$ candies. If he gives each of his friends 2 pieces, there will be 1 left over. If he gives each friend 3 pieces, there will also be 1 leftover. If $N$ is between 50 and 60, what is $N$?

Editorial note: Source wording is inconsistent for a fixed group of friends. This item is retained for manual review; see the bilingual solution after answering.

What is the next number in the sequence: $2,5,9,14,20,27,\_\_ $? (For specific purposes, the sequence follows a polynomial function)

Editorial note: Use the lowest-degree polynomial matching the given terms; the source does not specify its degree.

Find the number of triangles in the picture given below

What is the missing number in the pie below?



Editorial note: Use the natural pattern that opposite sectors have equal sums. This rule is an editorial interpretation.

Andres goes running for $3/4$ of an hour. When he comes home, he goes shopping with his mom for $2/3$ of an hour. How many minutes does Andres spend running and shopping?

If you have 7 triangles, 13 squares, 5 hexagons, and 8 pentagons, how many total sides do you have?

Suppose today is Thursday. What day of the week will it be 19 days from today?

Find the missing number in the series: $1,2,6,15,31,\_\_\_$

Editorial note: Continue the pattern of consecutive square-number differences. This rule is an editorial interpretation.

What is the least 5-digit number that is divisible by 3?

What is the least common multiple of 12 and 18?

What is the smallest prime number greater than 100?

What is the remainder when 2023 is divided by 101?

What is the value of $1010_2$ in base 10?

What is the value of $3^3$?

Right triangle ABC has legs $AB=5$ and $BC=6$ units. If the hypotenuse AC is used to construct square ACDE. What is the area of ACDE?

What is the area of the shaded region? Take $\pi=22/7$.



Editorial note: The source figure appears on physical page 9 beneath Q21 and is assigned here because Q20 asks for its shaded area. Interpret the two inner circles as congruent and tangent at the large centre, each tangent to the outer circle; 28 labels the outer radius.