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SASMO 2020 Grade 5

Question 1

Scoring for this platform: initial 0; Q1–15: 2 points each; Q16–25: 4 each; wrong or blank: 0; maximum 70. Official SASMO instead starts at 15; Section A correct +2, wrong −1, blank 0; Section B correct +4, wrong/blank 0; maximum 85.

Find the value of the following.

$$8899+(6677-2233)-4455$$
  1. 8888
  2. 8877
  3. 8899
  4. 8887
  5. None of the above

Question 2

Jane thought of a number. Josh calculated one-third of Jane's number. Frank calculated two-fifths of Josh's number. If Frank got 18, what was Jane's number?
  1. 2.4
  2. 270
  3. 45
  4. 135
  5. None of the above

Question 3

In a sports league, teams can either get 7 points or 3 points in each match. What is the largest score that cannot be attained?
  1. 8
  2. 11
  3. 19
  4. 22
  5. None of the above

Question 4

The percentages of boys in two classes are 30% and 60%. The numbers of students in the two classes are 30 and 45 respectively. What is the percentage of boys in the two classes combined?
  1. 90%
  2. 48%
  3. 30%
  4. 10%
  5. None of the above

Question 5

How many pairs of non-zero whole numbers $a$ and $b$ are there such that $a+b=10$? Take note that $(a,b)$ and $(b,a)$ are the same pair.
  1. 4
  2. 5
  3. 6
  4. 10
  5. None of the above

Question 6

Ted, Bob, Andi and Beti were playing “Guess The Number”. Ted thought of a three-digit number and the others tried to guess it.

- Bob: “I guess your number is 784.”
- Andi: “I think it is 394.”
- Beti: “I think it must be 795.”

Ted replied, “Each of the numbers you said shares two digits in common with mine.” What is the sum of the digits of Ted's number?

Interpretation: “Two digits in common” means exactly two shared digit values, regardless of position.
  1. 395
  2. 794
  3. 20
  4. 22
  5. None of the above

Question 7

What is the missing number in the sequence below?

$$23,19,25,26,27,33,29,\underline{\qquad},31$$

Interpretation: Use the intended pattern of two arithmetic sequences in alternate positions.
  1. 40
  2. 30
  3. 32
  4. 36
  5. None of the above

Question 8

How many two-digit numbers are divisible by 4 but not by 8?
  1. 25
  2. 22
  3. 12
  4. 11
  5. None of the above

Question 9

There are roses and lilies at a flower shop. Two roses cost 7 dollars while three lilies cost 5 dollars. Billy bought some roses and lilies and paid 86 dollars. Which of the following can be the number of lilies he bought?
  1. 15
  2. 21
  3. 24
  4. 36
  5. None of the above

Question 10

What is the missing number in the pattern below?

Interpretation: Infer the source’s intended simple arithmetic rule using the polygon side counts; use the same rule for all rows.

Question illustration
  1. 11
  2. 33
  3. 38
  4. 55
  5. None of the above

Question 11

The dimensions of two metal cuboids are $3\times5\times7$ and $6\times8\times10$. One of the cuboids is shown on the right. Harry melts both cubes and forms the largest possible cuboid with base of size $9\times13$. What is the height of the new cuboid?

Interpretation: “Both cubes” in the original means the two cuboids. Assume no metal is lost and all dimensions use the same length unit.

Question illustration
  1. 4.5
  2. 5
  3. 6
  4. 11
  5. None of the above

Question 12

There are three boxes: one contains only apples, one contains only oranges, and one contains both apples and oranges. All boxes are labelled as follows.

- Box 1: “This box contains both apples and oranges.”
- Box 2: “Box 1 does not contain different fruits.”
- Box 3: “This box contains only one type of fruit.”

If only one box is labelled correctly, which box contains both apples and oranges?
  1. Box 1
  2. Box 2
  3. Box 3
  4. Impossible to determine
  5. Box 1 and 2

Question 13

In rectangle $ABCD$, point $E$ is on side $AB$ and point $F$ is on side $AD$ such that $BE=\frac13 AE$ and $DF=\frac25 AD$. What is the ratio of the areas of $ABCD$ and $FEBCD$?

Question illustration
  1. 40 : 31
  2. 15 : 13
  3. 48 : 35
  4. 15 : 14
  5. None of the above

Question 14

At which of the following times is the hour hand closest to the minute hand of a clock?

Interpretation: Use a standard clock with both hands moving continuously at constant rates. Compare the exact times listed.
  1. 6:30
  2. 6:31
  3. 6:32
  4. 6:33
  5. 6:34

Question 15

Which of the following options is a missing piece of the cube shown?

Question illustration

Question illustration
  1. Piece A in the figure
  2. Piece B in the figure
  3. Piece C in the figure
  4. Piece D in the figure
  5. Piece E in the figure

Question 16

How many triangles are there in the figure below?

Answer format: enter a whole number without units. Leading zeros are optional.

Question illustration

Question 17

Find the last digit of the following product.

$$\underbrace{2\times2\times\cdots\times2}_{20\text{ times}}\times\underbrace{3\times3\times\cdots\times3}_{20\text{ times}}$$

Answer format: enter a whole number without units. Leading zeros are optional.

Question 18

The ratio of the volume of water in Tank A to that in Tank C is $4:7$. The ratio of the volume of water in Tank B to the total volume in the 3 tanks is $6:50$. If there are 5 more litres of water in Tank A than Tank B, how much water (in litres) is there in Tank C?

Answer format: enter a whole number without units. Leading zeros are optional.

Question 19

How many four-digit numbers between 7500 and 9600 can be formed using only the digits 3, 7, 5, 6, 8, 9 without repeating any digit?

Answer format: enter a whole number without units. Leading zeros are optional.

Question 20

At a book fair, there were 120 more adults than girls. The number of girls was 75% of the number of boys and 12% of the total number of people. How many adults were there at the book fair?

Interpretation: Adults, girls and boys are the three non-overlapping groups making up everyone at the fair.

Answer format: enter a whole number without units. Leading zeros are optional.