SASMO 2019 Grade 5

Exam-wide scoring note: On this platform the initial score is 0; Questions 1-15 award 2 points each and Questions 16-25 award 4 points each. Incorrect and blank answers score 0. Maximum: 70 points. The official SASMO format instead starts at 15 points: Section A correct +2, incorrect -1, blank 0; Section B correct +4, incorrect or blank 0; maximum 85 points. The platform score is the approved 70-point version.

Find the sum of all digits of the following product.

$$369\times333$$

Which of the following results in an odd number?

What is the value of $C$ so that the 4-digit number $\overline{187C}$ is divisible by 9?

Find the next number in the sequence below.

$$7,\ 11,\ 22,\ 40,\ 65,\ \underline{\qquad}$$

Interpretation for this question: Continue the simple pattern in the successive differences shown by the terms.

Andrew and Caden had some stamps in the ratio 6:8. Andrew gave a quarter of his stamps to Caden. Caden then had 280 stamps more than Andrew. How many stamps did they have altogether?

From which figure onwards will the number of black circles in the figure be more than the number of white circles in the same figure?

Interpretation for this question: Continue the same triangular arrangement, with white boundary circles and black interior circles.

Find the value of the following fraction in simplest form.

$$2-\frac{1}{0+\frac{1}{1-\frac19}}$$

Which of the following will form a knot when the two ends are pulled away from each other at the same time?

Find the sum of all whole numbers $n$ such that when 60 is divided by $n$ it gives a remainder of 4.

Edison left Town A at 2:30 pm and drove towards Town B at 60 km/h. At 3 pm, Jason also left Town A and drove in the same direction as Edison at 75 km/h. What time did Jason catch up with Edison?

Interpretation for this question: Assume both continue along the same route at the stated constant speeds until they meet.

In how many different ways can the circles be coloured using 3 colours: white, blue and green so that any 2 circles connected by a line do not share the same colour?

Interpretation for this question: Count colourings of the fixed circles as drawn; different named colours give different colourings.

The number of male viewers of a YouTube channel was twice as many as the number of its female viewers. The average watch time per video of its male viewers was 24 seconds and the average watch time per video of female viewers of this channel was 36 seconds. What was the average watch time per video of all the viewers of this YouTube channel?

Two identical squares overlap each other as shown in the figure. Given the vertical sides of the squares are parallel, and the area of the square is $676\text{ cm}^2$, what is the area of the shaded triangle?

Four friends made the following statements:

- Kieran: I'm not the shortest.
- Franklin: I'm neither the tallest nor the shortest.
- Mabel: I'm the shortest.
- Jeff: I'm the tallest.

If only one of them lied, who is the tallest?

Interpretation for this question: Assume all four friends have different heights, as intended by the source.

Find the missing figure in the diagram below.

Interpretation for this question: Use the same position-by-position combination rule in all three columns, inferred from the two completed columns.

How many triangles are there in the figure?

Interpretation for this question: The source places this figure on the preceding page beneath Question 15. It belongs to Question 16 and is shown here. Count all sizes.

Answer format: enter the whole-number answer without units. Leading zeros are optional (the original paper uses four-digit answer boxes).

In a 24-hour period on a digital clock, from 0:00 to 23:59, how many times does the digit "5" occur?

[At the time 3:55, the digit "5" occurs 2 times.]

Interpretation for this question: Count the display once per minute, including 0:00 and 23:59; count every occurrence of the digit.

Answer format: enter the whole-number answer without units. Leading zeros are optional (the original paper uses four-digit answer boxes).

The following bar chart shows the number of students from Happy Primary School who received 4 different awards in SASMO competition. All the horizontal lines are equally spaced. The difference between the number of students who received Silver Award and Perfect Score was 140. Students who didn't win any award received Certificate of Participation and they weren't indicated on the graph. The ratio between the number of students who received Gold Award to the number of students who received Certificate of Participation was 4:9. Find the number of students who received Certificate of Participation.

Answer format: enter the whole-number answer without units. Leading zeros are optional (the original paper uses four-digit answer boxes).

A pipe can fill up an empty tank in 18 hours. A full tank can be emptied by a pump in 20 hours. How long (in hours) will it take to fill up an empty tank if both the pipe and the pump are turned on at the same time?

Interpretation for this question: Use constant inlet and outlet rates, with no delay or other loss, as in the source model.

Answer format: enter the whole-number answer without units. Leading zeros are optional (the original paper uses four-digit answer boxes).

Ren selected 20 different whole numbers greater than 0 such that the product of any 9 numbers is always even. The sum of the 20 numbers is an odd number. Find the least possible sum of these numbers.

Answer format: enter the whole-number answer without units. Leading zeros are optional (the original paper uses four-digit answer boxes).