 ## Why the ‘Assumption Method’ over ‘Guess and Check’?

Whenever a question seems impossible to solve because of a lack of clues, the average person would fall back on the old but reliable method of guess-and-check. In this article, we will share a faster and more efficient method – The Assumption Method.

Although the Guess and Check method is tedious, this method guarantees that if you spend enough time and diligently work out each calculation carefully, you will eventually arrive at the correct answer.

The big question here is, “Does your child have enough time?” In a school examination, time is of the essence. The guess-and-check method does require a certain level of luck and some logical thinking to make the next intelligent guess. Blindly making guesses would be like throwing a bunch of darts at the dart board and hoping that one of it lands on the bull’s eye. This method is time-consuming since it requires a lot of checking and calculation and it does not help when time is not on your side.

Fret not!

There is a faster and surer way to solve questions that require the use of the guess-and-check method—the assumption method. We have an acronym that will help your child to remember the 4-step foolproof method. Let’s first take a look at the guess-and-check method before we introduce its faster and better counterpart (the assumption method).

### Example

A car park is filled with 25 cars and motorcycles in total. If there are 82 wheels altogether, how many more cars than motorcycles are there?
Remember:

2. Highlight keywords

3. Read the problem sum again

### Now, reread it again with the highlighted keywords.

A car park is filled with 25 cars and motorcycles in total. If there are 82 wheels altogether, how many more cars than motorcycles are there? Cars typically have 4 wheels, and motorcycles generally have 2 wheels.

Since we know that there are more cars than motorcycles, let’s start with having 1 more car than motorcycle.

### Guess-and-Check Method There are 82 wheels together, but we only have 76. Do we increase the number of cars, or motorcycles in our next guess? Since we need more wheels to reach 82 wheels, we should increase the item with the greater number of wheelscars. Do you see that we are getting there? Every time we + 1 car and – 1 motorcycle, the total number of wheels increases by 2.

This is because 4 car wheels – 2 motorcycle wheels = 2 wheels

We need an increment of 2. So let’s add 1 more car, and take away 1 more motorcycle. Since there are 16 cars and 9 motorcycles, there are 7 more cars than motorcycles.

16 – 9 = 7

Answer: There are 7 more cars than motorcycles.

Did that feel like it took quite a bit of work? It would have taken more work had bigger numbers been used. Thankfully, we have its better counterpart, the assumption method, or as some know it, the supposition method.

### What is the assumption method?

The assumption method, also known as the supposition method, is used to show a pretend-scenario in which we suppose that the total is made up solely of items of one type.

In the previous example, we would suppose that all the vehicles in the car park were either cars, or motorcycles.

### How does the assumption method work?

By assuming that the total is made up of only one item, and not the other, there is bound to be a shortage or excess in the total. Based on whether there is a shortage or excess, we find the difference and try to make up for it.

To help students to remember the steps in the assumption method, we came up with an acronym for the steps. T-E-D-O

Total

Excess

Difference

Opposite

### Example

A car park is filled with 25 cars and motorcycles in total. If there are 82 wheels altogether, how many more cars than motorcycles are there?

We can assume all the vehicles are cars or motorcycles.

1. Let’s assume that all the vehicles in the car park are cars.

Assuming that all the vehicles are cars, how many wheels will there be in total? 2. There are, however, only 82 wheels in total. This means there is an excess in the number of wheels. What is this excess?

Excess -> 100 – 82 = 18

3. The difference in the number of wheels between a car and a motorcycle is 2. This means that for every car I remove and replace with a motorcycle, the total number of wheels would decrease by 2.

What is the difference between the item with the higher value/quantity and the item with the lower value/quantity?

Difference -> 4 – 2 = 2

4. Since there is an excess of 18 wheels, how many motorcycles must replace cars so that the total would decrease by 18?

Opposite -> 18 ÷ 2 = 9 (No. of motorcycles, which is the opposite of what you assume) No. of cars -> 25 – 9 = 16

Difference between cars and motorcycles -> 16 – 9 = 7

Answer: There are 7 more cars than motorcycles.

Do you see how we kept our steps short and simple? There is hardly any deduction to be done before we arrive at our next step. For students who are not very strong in Mathematics, this is a good method for them to pick up as it is foolproof and time-saving.

To be sure that our answers are correct, we can always check if the total number of wheels adds up to 82.

Total no. of cars’ wheels -> 16 × 4 = 64

Total no. of motorcycles’ wheels -> 9 × 2 = 18

Total no. of wheels -> 64 + 18 = 82 (Correct!)

### Example

There are some chickens and cows on a farm. The total number of heads is 28 and the total number of legs is 86. How many chickens and cows are there?

Since each chicken and each cow has one head, it means that there are 28 animals on that farm.

Chickens have 2 legs and cows have 4 legs.

Again, you can assume all the animals are chickens or cows.

Let’s assume all the animals are cows.

Assumption Method

1. Let’s assume that all the animals on the farm are cows. 2. There are, however, only 86 legs in total. This means there is an excess in the number of legs. What is this excess
Excess-> 112 – 86 = 26
3. The difference in the number of legs between a cow and chicken is 2. This means that for every cow I remove and replace with a chicken, the total number of legs would decrease by 2.What is the difference between the item with the higher value/quantity and the item with the lower value/quantity?

Difference -> 4 – 2 = 2

4. Since there is an excess of 26 legs, how many chickens must replace cows so that the total number of legs would decrease by 26?
Opposite -> 26 ÷ 2 = 13 (No. of chickens) No. of cows -> 28 – 13 = 15 To be sure that our answers are correct, we can always check if the total number of legs adds up to 86.

Total no. of chicken legs -> 13 × 2 = 26

Total no. of cow legs -> 15 × 4 = 60

Total no. of legs -> 26 + 60 = 86 (Correct!)

### Example

Apples cost \$0.60 each and pears cost \$0.80 each. If a total of 130 apples and pears cost \$88, how many pears were there?

Since you want to find the number of pears, let’s assume the opposite, apples.

In this way, we can get the number of pears right away!

1. Total (assuming all were apples)

130 × \$0.60 = \$78

2. Excess (in this case, there isn’t an excess. In fact, it is not enough)

\$88 – \$78 = \$10

3. Difference (how many pears must replace apples so that the total would increase?)

\$0.80 – \$0.60 = \$0.20

4. Opposite of what you assumed at first (No. of pears)

\$10 ÷ \$0.20 = 50

Again, to be sure that our answers are correct, let’s check if the total costs adds up to \$88.

Number of apples -> 130 – 50 = 80

Total cost of apples -> 80 × \$0.60 = \$48

Total cost of pears -> 50 × \$0.80 = \$40

Total cost -> \$48 + \$40 = \$88 (Correct!)

In some cases, we need to add to find the difference, instead of subtract. Let’s explore the next question that is commonly tested in examinations. It may seem tricky at first, but once your child has mastered the assumption method, it would be a breeze.

Pay close attention to the next example. In some ways, it is similar to the previous two examples, but there is a step that is different.

### Example

In an examination, 4 points were awarded for each correct answer and 2 points were deducted for each wrong answer. If I got a score of 96 points for answering all 30 questions in the examination, how many questions did I answer wrongly?

1. Total (assuming all were correct)
4 × 30 = 120

2. Excess (difference between the perfect score and my actual score)
120 – 96 = 24

3. Difference (between points awarded and points deducted)
4 + 2 = 6

Since a correct answer would get 4 points and a wrong answer would result in a deduction of 2 points, getting a question wrong would mean a loss of 6 points!
Not only did you fail to secure the 4 points, you were further penalised by having 2 points deducted from your score. So, that is a loss of 6 points!

4. Opposite of what you assumed at first (No. of questions answered wrongly)
24 ÷ 6 = 4

Again, let’s check if the total points adds up to 96.

Number of correct answers -> 30 – 4 = 26
Total points awarded -> 26 × 4 = 104
Total points deducted -> 4 × 2 = 8
Total points -> 104 – 8 = 96 (Correct!)

### Why the ‘Assumption Method’ over ‘Guess and Check’?

• Less time-consuming (4-5 steps)
• 4-step method

Depending on how lucky or logical you are, the guess-and-check method could take any time from 2 minutes to 10 minutes to solve. Drawing the rows and columns to form the table and labelling the columns would already cost precious seconds, or minutes.
• More efficient (skip the tedious calculations)

With the assumption method, we always know what we are looking for. This is represented by a single number statement that gets us definitively to the next time in the solving process.
• Easy to understand

We start off with a ridiculous assumption and depending on whether we want the total to increase or decrease, we subtract or add.

We advise students to start mastering the assumption method now! This tool will be handy in your exams!  