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how to use assumption and supposition methods to solve guess and check questions | Matrix Math Singapore


05 February 2024

BY: matrixmath

Is your child wasting too much time on guess and check questions or having problems identify such questions? Is your child having difficulties with headings of guess and check table? Look no further! Here’s a 4 simple step-by-step approach (Assumption/Supposition Method) to solve such questions!

How To Identify Guess And Check Question?

In a standard Guess and Check question there will be 3 key information:-

(1) There will be 2 types of items and each have a certain value (e.g. could be 10 cents coins and 20 cent coins; could be cows(item) or legs(values)

(2) Question will give the total number of items but will not provide how many of each type.

(3) Question will provide the total value of all these items.

If these criteria are met, the question can be solved using Supposition Method instead of Guess and Check method.

Supposition Method (aka Assumption Method) 

John invited 30 boys and girls to his birthday party. He gave 5 chocolates to each boy and 2 chocolates to each girl. If John gave away 141 chocolates, how many girls did John invite?

Step 1

Assume all are boys (assume the opposite of what the question is asking for. Eg: Qns asking for how many girls so assume opposite = boys)

Total number of chocolates = 30 X 5 = 150

Step 2

Find the difference between the actual and assumed

Extra chocolates = 150 – 141 = 9

Step 3

Find the extra number of chocolates needed for every exchange from 1 boy to 1 girl.

1 exchange = 5 – 2 = 3

Step 4

Find the number of exchanges needed. This will give us the number of girls (when we assume all are boys in step 1, step 4 will give the opposite i.e. girls)

No. of exchanges = 9 ÷ 3 = 3 (no. of girls)


If the question is asking for both girls and boys such as: “How many boys and girls did Yenni invite?”

Step 5

Find the number of boys. Since we know that girls = 3, we can use the total number minus the number of girls

No. of boys = 30 – 3 = 27

Supposition Method with Penalty

In a test, there were a total of 40 questions. For every question answered correctly, a student was awarded 4 points. For each question answered wrongly, 1 point was deducted. If Anna scored 130 points, how many questions did she answer wrongly?

Step 1

Assume all questions answered are correct (Penalty Question, always assume the positive that adds value/earned For e.g.: this question: assume those that are correct to be awarded points).

Total no. of points = 40 X 4 = 160

Step 2

Find the extra number of points that needs to be removed to obtain the actual points.

Extra points = 160 – 130 = 30

Step 3

Find the extra number of pointsdeducted for every exchange from 1 correct question to 1 wrong question.

1 exchange = 4 + 1 = 5

(It is an “addition” for due to the fact that I not only lose the 4 points from removing 1 correct question, I also had to deduct 1 point when I change it to a wrong. As such, I lose 5 points each time I change from a correctly answered question to a wrongly answered question.)

Step 4

Find the number of exchanges needed. This will give us the number of wrong questions (when we assume all questions are correct in step 1, step 4 will give the opposite i.e. wrong questions)

No. of exchanges = 30 ÷ 5 = 6 (wrong questions)


Step 5

Find the number of correct questions. Since we know that wrong questions = 6, we can subtract the number of wrong questions from the total number of questions.

No. of correct questions = 40 – 6 = 34

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At Matrix Math, we incorporate spatial reasoning elements into our classroom learning to help our students understand the concepts being taught and to give them the tenacity to try and try again if at first they don’t succeed.