Division

Singapore and Asian

P3 Schools Math Olympiad
2015

Full Name:
Index Number:
Class:
School:
SASMO 2015 Primary 3 Contest

INSTRUCTIONS
1. Please DO NOT OPEN the contest booklet until the Proctor has given permission.

2. TIME: 1 hour 30 minutes.

3. Attempt all 20 questions.

Questions 1 to 10 score 2 points each, no points are deducted for unanswered question
and 1 point is deducted for wrong answer.
Questions 11 to 20 score 4 points each. No points are deducted for unanswered or
wrong answers.

4. Shade your answers neatly using a pencil in the answer sheet.

5. PROCTORING: No one may help any student in any way during the contest.

6. No electronic devices capable of storing and displaying visual information is

allowed during the course of the exam.

7. Strictly No Calculators are allowed into the exam.

8. All students must fill and shade in in their Name, Index number, Class and School in
the answer sheet and contest booklet.

9. MINIMUM TIME: Students must stay in the exam hall at least 1h 15 min.

10. Students must show detailed working and transfer answers to the answer sheet.

11. No exam papers and written notes can be taken out by any contestant.
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SASMO 2015, Primary 3 Contest

SASMO 2015 PRIMARY 3 [10 MCQ + 10 non-MCQ = 20 Q]

Starting Score = 10 marks (to avoid negative marks); Max Possible Score = 70 marks

Section A (Correct answer = 2 marks; no answer = 0; incorrect answer = minus 1 mark)

1. Find the missing term in the following sequence: 1, 2, 4, 7, _____, 16.

(a) 10
(b) 11
(c) 12
(d) 13
(e) 14

________________________________________________________________
2. 25 means 2 multiplied by itself 5 times, i.e. 25 = 2  2  2  2  2 = 32. What is
34 equal to?

(a) 7
(b) 12
(c) 27
(d) 81
(e) None of the above

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SASMO 2015, Primary 3 Contest

3. An operator  acts on two numbers to give the following outcomes:

3  2 = 51
5  3 = 82
6  1 = 75
9  4 = 135

What is 7  5 equal to?

(a) 112
(b) 121
(c) 122
(d) 212
(e) None of the above

_______________________________________________________________
4. The diagram shows a figure that contains 7 identical squares. The area of the
figure is 112 cm2. Find its perimeter.

(a) 56 cm
(b) 60 cm
(c) 64 cm
(d) 68 cm
(e) 72 cm

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SASMO 2015, Primary 3 Contest

5. Fill in the blank: __________ is 4 tens 5 ones greater than 2 tens 7 ones.

(a) 18
(b) 28
(c) 62
(d) 72
(e) None of the above

______________________________________________________________

6. Which of the following statement(s) is or are correct?

Statement A: 7 + (0  2) = 7

Statement B: 7 + (0  2) = 7

Statement C: 7 + (2  0) = 7

(a) All the three statements are correct.

(b) Only Statements A and B are correct.
(c) Only Statements A and C are correct.
(d) Only Statements B and C are correct.
(e) None of the above

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SASMO 2015, Primary 3 Contest

7. There are 4 types of cakes available in a cake shop: chocolate, cheese, blueberry
and blackforest. Naomi wants to buy 2 different types of cakes. How many
different choices does she have?

(a) 4
(b) 6
(c) 8
(d) 10
(e) 12

___________________________________________________________________

8. Find the total number of squares in a 3  3 square grid.

(a) 9
(b) 10
(c) 13
(d) 14
(e) 15

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SASMO 2015, Primary 3 Contest

9. Find the smallest whole number between 14 and 40 that is divisible by 3 and
by 4.

(a) 12
(b) 16
(c) 18
(d) 24
(e) 36

_________________________________________________________________

10. What is the length of the largest square that can be made from 50 one-
centimetre square tiles?

(a) 5 cm
(b) 6 cm
(c) 7 cm
(d) 8 cm
(e) None of the above

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SASMO 2015, Primary 3 Contest

Section B (Correct answer = 4 marks; incorrect or no answer = 0)

11. Two numbers are such that

 the first number is greater than or equal to 5, but less than or equal to 8
 the second number is greater than or equal to 2, but less than or equal to
10.
Find the least possible value of the sum of the two numbers.

_____________________________________________________________

12. If the four-digit number 12N4 is divisible by 3 and N is less than 5, find N.

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SASMO 2015, Primary 3 Contest

13. A whole number multiplied by itself will give a special type of numbers called
perfect squares. Examples of perfect squares are 9 (= 3  3) and 16 (= 4  4).
What is the smallest number that can be multiplied by 28 to give a perfect
square?

________________________________________________________________

14. Find the day of the week that is 50 days from a Monday.

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SASMO 2015, Primary 3 Contest

15. Amy wants to cut rectangular cards of length 4 cm by 3 cm from a rectangular

sheet 32 cm by 21 cm. Find the biggest number of cards that can be cut from
the sheet.

_______________________________________________________________________

16. There are 5 items (a ruler, a pen, an eraser, a sharpener and a hole puncher)
lying in a straight row on a table. The eraser is next to the hole puncher and the
sharpener. The ruler is next to the hole puncher. The sharpener is the first item
on the left. What is the order of the items on the table from left to right?

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SASMO 2015, Primary 3 Contest

17. In the following, all the different letters stand for different digits. Find the two-
digit NO.

N O N
 A N

N O

_____________________________________________________________________________

18. 50 cakes are packed in two different box sizes. The small box holds 4 cakes and
the big box holds 6 cakes. If less than 10 boxes are used and all the boxes are
fully packed, how many big boxes are used?

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SASMO 2015, Primary 3 Contest

19. Alice and Ben are sister and brother. Alice has as many sisters as she has
brothers, but Ben has twice as many sisters as he has brothers. How many boys
and girls are there in their family?

________________________________________________________________

20. The diagram shows a rectangle being divided into 3 smaller rectangles and a
square. If the perimeter of the unshaded rectangle is 16 cm and the area of the
square is 9 cm2, find the total area of the shaded rectangles.

End of Paper
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SASMO 2015, Primary 3 Contest

Solutions to SASMO 2015 Primary 3

Section A
1. Find the missing term in the following sequence: 1, 2, 4, 7, _____, 16.

(a) 10
(b) 11 [Ans: 7 + 4]
(c) 12
(d) 13
(e) 14

Solution

The pattern is as follows:

1, 2, 4, 7, _____, 16

+1 +2 +3 +4 +5

 the missing term is 7 + 4 = 11.

2. 25 means 2 multiplied by itself 5 times, i.e. 25 = 2 × 2 × 2 × 2 × 2 = 32. What is

34 equal to?

(a) 7
(b) 12
(c) 27
(d) 81 [Ans]
(e) None of the above

Solution
34 = 3 × 3 × 3 × 3 = 81

3. An operator  acts on two numbers to give the following outcomes:

3  2 = 51
5  3 = 82
6  1 = 75
9  4 = 135

What is 7  5 equal to?

(a) 112
(b) 121
(c) 122 [Ans]
(d) 212
(e) None of the above
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SASMO 2015, Primary 3 Contest

Solution

a  b = (𝑎 + 𝑏)(𝑎 − 𝑏)
 7  5 = 122

4. The diagram shows a figure that contains 7 identical squares. The area of the
figure is 112 cm2. Find its perimeter.

(a) 56 cm
(b) 60 cm
(c) 64 cm [Ans]
(d) 68 cm
(e) 72 cm

Solution
Area of 7 identical squares = 112 cm2
Area of one square = 16 cm2
Length of square = 4 cm
Since the perimeter of the figure is made up of 16 sides of a square, then its
perimeter
= 16 × length of square
= 16 × 4
= 64 cm

5. Fill in the blank: __________ is 4 tens 5 ones greater than 2 tens 7 ones.

(a) 18
(b) 28
(c) 62
(d) 72 [Ans]
(e) None of the above

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SASMO 2015, Primary 3 Contest

Solution
4 tens 5 ones greater than 2 tens 7 ones is 45 + 27 = 72.
 the missing number is 72

6. Which of the following statement(s) is or are correct?

Statement A: 7 + (0 × 2) = 7
Statement B: 7 + (0 ÷ 2) = 7
Statement C: 7 + (2 × 0) = 7
(a) All the three statements are correct. [Ans]
(b) Only Statements A and B are correct.
(c) Only Statements A and C are correct.
(d) Only Statements B and C are correct.
(e) None of the above

Solution
Statement A: 7 + (0 × 2) = 7 + 0 = 7
Statement B: 7 + (0  2) = 7 + 0 = 7
Statement C: 7 + (2 × 0) = 7 + 0 = 7
 all the three statements are correct.

7. There are 4 types of cakes available in a cake shop: chocolate, cheese, blueberry
and blackforest. Naomi wants to buy 2 different types of cakes. How many
different choices does she have?

(a) 4
(b) 6 [Ans]
(c) 8
(d) 10
(e) 12

Solution

Method 1 (Systematic Listing)

Chocolate   
Cheese   
Blueberry   
Blackforest   

 total no. of choices = 6

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SASMO 2015, Primary 3 Contest

Method 2 (Rephrase the Problem)

Choosing 2 types of cakes from 4 types is the same as the handshake problem of
4 people shaking hands once with one another.
 total no. of choices = 3 + 2 + 1
=6

8. Find the total number of squares in a 3  3 square grid.

(a) 9
(b) 10
(c) 13
(d) 14 [Ans]
(e) 15

Solution

No. of 1  1 squares = 9
No. of 2  2 squares = 4
No. of 3  3 squares = 1
 total no. of squares in a 3  3 square grid = 9 + 4 + 1 = 14

9. Find the smallest whole number between 14 and 40 that is divisible by 3 and by
4.

(a) 12
(b) 16
(c) 18
(d) 24 [Ans]
(e) 36

Solution

Method 1
Numbers between 14 and 40 that are divisible by 4 are:16, 20, 24, 28,32 and 36.
Of these 6 numbers, only 24 and 36 are divisible by 3.
 the smallest whole number between 14 and 40 that is divisible by 3 and by 4
is 24.
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SASMO 2015, Primary 3 Contest

Note: A number that is between 14 and 40 does not include 14 and 40. If we
start with numbers divisible by 3, there will be more possibilities.

Method 2
A number that is exactly divisible by both 3 and 4 must also be exactly divisible
by 12.
The only numbers between 14 and 40 that are exactly divisible by 12 are 24 and
36.
 the smallest whole number between 14 and 40 that is divisible by 3 and by 4
is 24.

10. What is the length of the largest square that can be made from 50 one-
centimetre square tiles?

(a) 5 cm
(b) 6 cm
(c) 7 cm [Ans]
(d) 8 cm
(e) None of the above

Solution

Since 7  7 = 49 and 8  8 = 64, then the length of the largest square that can
be made from 50 one-centimetre square tiles is 7 cm.

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SASMO 2015, Primary 3 Contest

Section B
11. Two numbers are such that

 the first number is greater than or equal to 5, but less than or equal to 8
 the second number is greater than or equal to 2, but less than or equal to
10.

Find the least possible value of the sum of the two numbers.

Solution

Least possible value of the sum of the two numbers

= least possible value of first number + least possible value of second number
=5+2
=7
12. If the four-digit number 12N4 is divisible by 3 and N is less than 5, find N.

Solution

Using the divisibility test for 3, 1 + 2 + N + 4 = N + 7 is also divisible by 3.

Since N is a single digit, N = 2, 5 and 8.
But N is less than 5 (given).
N=2

13. A whole number multiplied by itself will give a special type of numbers called
perfect squares. Examples of perfect squares are 9 (= 3  3) and 16 (= 4  4).
What is the smallest number that can be multiplied by 28 to give a perfect
square?

Solution

Since 28 = 2  2  7 = (2  7)  2, then the smallest number that can be

multiplied by 28 to give a perfect square is 7, so that (2  7)  (2  7) = 14  14
is a perfect square.

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SASMO 2015, Primary 3 Contest

14. Find the day of the week that is 50 days from a Monday.

Solution

By counting, 7 days from a Monday is Monday.

So 49 days (= 7  7 day) from a Monday is still Monday.
 50 days from a Monday is Tuesday.

15. Amy wants to cut rectangular cards of length 4 cm by 3 cm from a rectangular

sheet 32 cm by 21 cm. Find the biggest number of cards that can be cut from
the sheet.

Solution

32 cm  4 cm = 8 cards along the length of the rectangular sheet.

21 cm  3 cm = 7 cards along the breadth of the rectangular sheet.
 biggest number of cards that can be cut from the sheet = 8  7 = 56

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SASMO 2015, Primary 3 Contest

16. There are 5 items (a ruler, a pen, an eraser, a sharpener and a hole puncher)
lying in a straight row on a table. The eraser is next to the hole puncher and the
sharpener. The ruler is next to the hole puncher. The sharpener is the first item
on the left. What is the order of the items on the table from left to right?

Solution

The sharpener is the first item on the left.

__S__, _____, _____, _____, _____

The eraser is next to the hole puncher and the sharpener.
This means that the eraser is the second item next to the sharpener, and the
hole puncher is the third item.

__S__, __E__, __H__, _____, _____

The ruler is next to the hole puncher.

__S__, __E__, __H__, __R__, _____

Thus the last item is the pen.

 the order of the items on the table from first to last is sharpener, eraser,
hole puncher, ruler and pencil.

17. In the following, all the different letters stand for different digits. Find the two-
digit NO.
N O N
 A N

N O

Solution
In the ones column, N  N = O, so O = 0.
In the hundreds column, if N ≥ 2, the final answer for the subtraction will be a 3-
digit number, so N = 1.
NO  A = N implies that 10  A = 1, so A = 9.
Now ̅̅̅̅
 NO = 101  91 = 10.

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SASMO 2015, Primary 3 Contest

18. 50 cakes are packed in two different box sizes. The small box holds 4 cakes and
the big box holds 6 cakes. If less than 10 boxes are used and all the boxes are
fully packed, how many big boxes are used?

Solution

Since the question states that ‘less than 10 boxes are used’, it suggests that
there should be more big boxes than small boxes. So we use guess and check
starting with fewer small boxes:

No. of Small No. of Cakes No. of Big Boxes Total No. of

Boxes Left Boxes
1 50  4 = 46 46  6 has left over 
2 50  8 = 42 42  6 = 7 9
3 50  12 = 38 38  6 has left over 
4 50  16 = 34 34  6 has left over 
5 50  20 = 30 30  6 = 5 10

Note: Actually you can stop after getting a total of 9 boxes because if you use
more small boxes, the total no. of boxes will be bigger than 9.

 no. of big boxes used = 7

19. Alice and Ben are sister and brother. Alice has as many sisters as she has
brothers, but Ben has twice as many sisters as he has brothers. How many boys
and how many girls are there in their family?

Solution

Method 1 (Guess and Check)

Since Alice is a girl and she has as many sisters as she has brothers, then the
number of girls in the family is one more than the number of boys.

Ben has twice as many sisters as he has brothers.

True or false?

2 girls and 1 boy Ben has 2 sisters and 0 brother. Above statement is false.

3 girls and 2 boys Ben has 3 sisters and 1 brother. Above statement is false.

4 girls and 3 boys Ben has 4 sisters and 2 brothers. Above statement is
true.

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SASMO 2015, Primary 3 Contest

Using guess and check as shown in the above table, there are 3 boys and 4
girls in the family.
Method 2 (Model Method)

For Alice
Boys

Girls 1

For Ben
Boys 1

Girls

From the model for Ben, 1 unit for Girls = 1 + 1 = 2.

 there are 3 boys and 4 girls in the family.

20. The diagram shows a rectangle being divided into 3 smaller rectangles and a
square. If the perimeter of the unshaded rectangle is 16 cm and the area of the
square is 9 cm2, find the total area of the shaded rectangles.

Solution
Put the two shaded rectangles to form a long rectangle as shown:

1
Length of long rectangle = × perimeter of unshaded rectangle
2
1
= × 16 cm
2

= 8 cm
Breadth of long rectangle = length of square = 3 cm
 total area of shaded rectangles = 8 cm × 3 cm = 24 cm2
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