 # The Supposition Method

### What is the Supposition Method in Maths?

The Supposition Method, also known as the Assumption Method, is a very useful Maths Heuristic that you can apply to solve Guess and Check Maths problem sums in Primary 4, Primary 5 and Primary 6. Much faster and systematic than the Guess and Check method, this method is often used by more sophisticated Math students.

Before we learn how to use the Supposition method, let’s see how to identify questions that we can solve with this method first.

### Examples of Supposition Questions

Here are some examples of Supposition questions for Primary 3 and Primary 4 students.

There are 15 mosquitoes and pest busters somewhere in Singapore. There are 54 legs altogether. How many mosquitoes are there?

Jay is practising 20 Math questions furiously on Practicle to gain some experience points. He receives 5 marks for every correct answer and for every wrong answer, he gets 2 marks deducted. If Jay earned 35 experience points for his Math practice in the end, how many questions did he get wrong?

If you want to see how to solve Supposition questions for Primary 5 and Primary 6 using the Supposition or Assumption Method, don’t forget to check out our video on that.

As you can see from the examples of supposition questions above, such questions usually give us a total that’s made up of a few kinds of items. Here we have mosquitoes and pest busters and these 2 items make up a total of 15.

Besides that, the items will share something in common and we’ll know the number of that something for each item. The number of legs is the common item between the mosquitoes and pest busters. In addition, we also know the no. of legs for each item – 6 legs for a mosquito and 2 legs for the pest buster.

Lastly, in most cases, we will be asked to find the exact number of one of the items. In this question, we’ll need to find the no. of mosquitoes.

Now that we know how to look for a Supposition question that we can solve with the Supposition Method, we’re ready to learn how to use the Supposition method to solve it!

### How do we do the Supposition Method?

The word “supposition” means “to assume”. Therefore, we’ll start to solve the question with an assumption – “Suppose this is the extreme situation…then what do we have?” After determining the situation, we’ll work step-by-step to dig up more information. Finally, we’ll arrive at the solution to the problem. Now, let’s see how this really works with an example by using the first question.

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### Supposition Method Example Explained

Let’s look at this question on Supposition.

There are 15 mosquitoes and pest busters somewhere in Singapore. There are 54 legs altogether. How many mosquitoes are there?

How to do Supposition?

Step 1: Make an assumption

As mentioned, we’ll start by making an assumption. This is where we’ll assume an extreme case where all the items are of the same type. Here, we can either assume that all the items were mosquitoes or that all the items were pest busters.

Well, we could choose to assume that all the items were pest busters since we hate mosquitoes, or you could assume that all the items were mosquitoes if you are that rare mosquito supporter, but which one would be the better choice?

Let’s think about the number of legs each item has. We have 6 legs versus 2 legs.  Since we are going to work with that number, let’s choose the smaller number for easier calculation. This also helps to reduce the chances of us making careless mistakes.

So here we have it, our first step where we write our assumption:

Assuming that all the items were pest busters,

Now that we have made an assumption, what do we use it for?

Step 2: Multiply to find the total in assumption

The next step is to multiply it with the number of legs to find the total number of legs there will be if all the 15 items were pest busters.

No. of legs of 1 pest buster x No. of pest busters in our assumption = 2 x 15 = 30

Looks like we have 30 legs. However, when we look at the question, we are supposed to have 54 legs in total.

Oh no, looks like we have much fewer legs in our assumption. Let’s find out how many legs we are missing in our next step.

Step 3: Find the Difference (The Gap between our Assumption and the Question)

54 – 30 = 24

When we subtract the total number of legs that we are supposed to have from the total number of legs we have in our assumption, you’ll notice that we are short of 24 legs. What shall we do to get more legs then?

Remember that there were supposed to be mosquitoes and pest busters in the question? Since we have been working with only pest busters all along, it’s time to get the mosquitoes in!

Step 4: Find the Difference (The Effect of Making a Replacement)

Let’s think about 1 simple case first. When we add 1 mosquito into what we have, we’ll have to get rid of 1 pest buster, correct? This is because there will always be only 15 items at any one time. When we do that, we are actually replacing 1 pest buster with 1 mosquito.

Then what happens to the total number of legs? Let’s find the difference in the number of legs between 1 mosquito and 1 pest buster. A mosquito has 6 legs while a pest buster has 2. So 6 – 2 gives us 4. In other words, we know that every time we replace a pest buster with a mosquito, the total number of legs increases by 4.

So far so good? Now that’s super helpful!

Step 5: Divide to find the number of replacements

Remember that we need an extra of 24 legs? Since we know that replacing a pest buster with a mosquito increases the total number of legs by 4, let’s find out how many replacements do we need to make up for these 24 legs. We’ll do that by dividing the difference in the total no. of legs between our assumption and reality with the difference in the total no. of legs caused by replacing 1 pest buster with a mosquito. 24 divided by 4 gives us 6.

Now we know that we’ll need to replace the 6 pest busters we have with 6 mosquitoes in order to make up for the extra 24 legs.

That’s how we know we have 6 mosquitoes out of the 15 items.

### Conclusion

Hopefully this post has helped you understand how to apply the Supposition method to solve Guess and Check questions more efficiently.

Do you prefer the Guess and Check method or the Supposition method?

Let us know in the comments below.