"Today I am setting you ten questions from this year’s International Singapore Maths Competition, aimed at primary Years 5 and 6. (That’s kids aged 10-11 and 11-12). The questions are all based on Singapore’s much lauded maths syllabus, which aims to teach fewer topics in greater depth. 

The children taking these tests had a total of 25 questions to answer in 90 minutes. They did not have the multiple choice responses, but had to work everything out by themselves. They were, however, allowed to use calculators.

[The percentage in square brackets is the percentage of Singaporean schoolchildren expected to get the right answer.]"

For Year 5 pupils:

#1: Mary cut off 2/5 of a piece of string. Later, she cut off another 14 m. The ratio of the length of string remaining to the total length cut off is 1 : 3. What is the length of the remaining string? 

• A. 5 m
• B. 7 m
• C. 10 m
• D. 14 m

#2: The areas of the faces of a rectangular box are 84 cm2, 70 cm2 and 30 cm2. What is the volume of the box?

• A. 300 cm3
• B. 420 cm3 
• C. 490 cm3
• D. 504 cm3

#3: There are four numbers. If we leave out any one number, the average of the remaining three numbers will be 45, 60, 65 or 70. What is the average of all four numbers? 

• A. 50
• B. 55
• C. 60
• D. 65

#4: A march goes through the streets from the School (S) to the Community Centre (CC). One of the streets is closed. If the march can only travel East or South, what is the number of different possible ways to get to the Community Centre? [10 per cent]

• A. 16
• B. 19
• C. 20
• D. 22 

#5: Sally was given a set of 5 cards numbered 1 to 5 and Peter was also given a set of 5 cards numbered 1 to 5. They were then blindfolded and told to pick a card from their respective sets. The sum of the numbers from the two cards was told only to Sally and the product of the numbers was told only to Peter. They were then told to guess the two numbers. Below is what each of them said:

Peter: I do not know the two numbers.

Sally: Now I know the two numbers.

Peter: I still don’t know the two numbers.

Sally: Let me help you. The number I was told is larger than the number you were told.

Peter: Now I know the two numbers.

What are the two numbers? 

• A. 1 and 4
• B. 1 and 5
• C. 2 and 4
• D. 2 and 5

For Year 6 pupils:

#6: There are 4 keys and 4 locks. What is the maximum number of times you need to try the locks so as to match all 4 keys to their locks? 

• A. 4
• B. 6
• C. 10
• D. 16

#7: In the diagram (not drawn to scale), the sloping line divides the area of the rectangle in the ratio 1 : 6. What is the ratio a : b?

• A. 2 : 3
• B. 1 : 2
• C. 2 : 5
• D. 1 : 3

I am definitely not smarter than a 10 year old. ;)