Here are hints for the questions, followed by the actual answers at the bottom of the page.

HINTS:

Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Question 9
Question 10

ANSWERS

Question 1:

This is really a very simple pattern question. The first row starts with 1. The next row then describes the first row as "one 1". The next row describes the second row as "two 1s" and so on. So what do you reckon are the last two rows? (Do not restrict yourself to 1s and 2s)

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Question 2:

Triangles are half of rectangles. There are two triangles in the diagram, meaning that BY RIGHT they should cover the whole rectangle. However, these triangles overlap, creating the empty spaces 49, 35 and 13. so the area of the overlapping red area is...

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Question 3:

This question is solved fastest by using the Venn Diagram method. You draw three interconnecting circles. Name each circle Math, Chinese and English respectively.

Math
EnglishChinese

1 failed all three subjects, so you put 1 in the centre. 7 failed both Chinese and Maths, so you should put 7 in the space between chinese and maths right? Wrong. 7 students who failed both subjects include the student who failed all three, so you put 7 minus 1 (=6) in the space between Chinese and Maths. The same goes for all the other double failures. However, for single failures, the question states that these people only failed ONE subject, so you put them in the green part, without any minusing. Finally to find the people who pass, you just take 46 minus all the numbers in the Venn diagram.

Thus, as you can see, this question is quite simple, you just have to read it carefully.

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Question 4:

Thinking of this question in a simple way will help you get the answer. 997 children do not have to send letters in a "broken telephone" fashion. This would result in a LOT of letters sent and received by each child. So the fastest way is for all the children to send their secrets to ONE child. This child writes every secret on all the letters and sends them back to the rest. So the postman only has to deliver ...

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Question 5:

The Pentagon can be cut into three pieces and pasted back together to form a square. It involves flipping of the pieces. Here's a hint and you figure out the area of this square.

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Question 6:

From the Pythagoras Theorum for right angled triangles, we know that one side of the triangle sq. plus the other side sq. is equal to the diagonal sq. (more commonly known as "A squared + B squared = C squared") Thus we need to find ? squared + ? squared = 80. Then you can draw your square using triangles like this

(however these are not the exact measurements. You'll have to find the exact measurements out yourself)

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Question 7:

All you have to do is arrange the cubes like this and maesure from point A to point B!

(By the way, this is the answer)

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Question 8:

Those lights that are still lit have been changed an odd number of times. That means their number has an odd number of factors. The only numbers from 1 - 100 with odd number of factors are...

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Question 9:

The fastest and most accurate way to solve this is by using Pascal's triangle. We identify how many ways there are to get to a particular point in this route. For example to be able to get to the end of four squares, there are 6 possible ways. In applying the adding method, we can determine how many ways there are to get to point B. However, it is always safer to WRITE DOWN the numbers you've added as you go along.

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Question 10:

This is a very simple question which many people make mistakes. Most people think that, "If at first I draw a red sock, then the next one may be a blue one, and the next one and the next one and the next one... until the ten blue socks are taken out, I will get a red pair. So the answer is twelve." However, what they overlook is that it need not be a RED PAIR. It only has to MATCH. Thus if the first two you draw do not match, then the next sock has to match one of the two. Thus the answer is actually...

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Summary:

So these are just a FEW of the MANY examples of how logic is used in Mathematics. Questions are asked in many different ways, so one must be able to interpret in different ways as well. We must also not have the misconception that a question sounds long and hard THEREFORE the method must be long and hard.

Answers to the above questions:

Question 1: 312211 & 13112221

Question 2: 97

Question 3: 7

Questioin 4: 1992

Question 5: 1

Question 6:

Question 7: (answer already given above)

Question 8: Square numbers

Question 9: 1225

Question 10: 3