Learn this concept that can help score AL1 in Math PSLE (Listing Method)

Not all tough problem sums involve fractions. Here is an example of a challenging problem that does not use fractions:

Muthu has fewer than 30 comic books. If he gives all his comic books equally to 7 friends, there will be 3 comic books left. If he gives all his comic books equally to 9 friends, he will be short of 1 comic book. How many comic books does Muthu have?

It looks difficult, right? Don’t worry. I will show you how to solve this type of question using the Listing Method.

What Are Listing Method Problems?

Listing method questions usually involve:

• Dividing an unknown total among different numbers of people
• Comparing remainders, shortages, or excess
• No direct information about the total number of items

For example:

1. If he gives all his books equally to 7 friends → 3 left
2. If he gives all his books equally to 9 friends → short of 1

Notice anything missing?

We never get the actual number of comic books.

This is why listing all possible numbers becomes the easiest way to solve the problem.

How to Spot a Listing Method Question

Look out for these features:

✔ Two “if” situations
✔ Remainders when sharing equally
✔ Words like “left”, “short of”, “excess”, “still have”
✔ You know the number of people (7 friends, 9 friends, etc.)
✔ You don’t know the number of items

These are signs that you should use the Listing Method. We will go through an example problem sum and how to solve it.

Example Problem

Muthu has fewer than 30 comic books. If he gives all his comic books equally to 7 friends, there will be 3 comic books left. If he gives them equally to 9 friends, he will be short of 1 comic book. How many comic books does Muthu have?

Let’s apply the listing method.

Step-by-Step Solution

Step 1: List the multiples

Since Muthu has fewer than 30 comic books:

Multiples of 7:
7, 14, 21, 28

Multiples of 9:
9, 18, 27

Step 2: Apply the remainders

Situation 1: 7 friends → 3 left
This means the total number of comics is multiples of 7 plus 3

Multiples of 7 (+3):
10, 17, 24, 31

Situation 2: 9 friends → short of 1
This means the total number of comics is multiples of 9 minus 1

Multiples of 9 (–1):
8, 17, 26

Step 3: Find the same number

First list: 10, 17, 24

Second list: 8, 17, 26

The number that appears in both is: 17

That means, the answer is Muthu has 17 comic books!