Given that four circles are 1 metre in diameter, what is the area of the shaded portion? (picture)
- Join the centres of the four circles to form a square.
- Area of square = 1m x 1m
- Answer = 1m2
Arrange the numbers 1 to 7 in the circles of the magic-number ring, so that the total of three circles along each line is 10. (picture)
At the last economic downturn, a bank cut its labour force by 16 per cent, then increased it by 25 per cent. What was the overall percentage change in the size of the workforce?
- 5% overall increase
- Assume that the bank had a staff force of 100 people.
- Cutting its labour force by 16% would leave a work force of (100-15), ie. 84 people.
- By increasing this work force by 25%, this resulted in an additional of 1/4 of 84, ie. 21 people.
- So the bank had now a total of (84+21), ie. 105 jobs.
- This represents 5/10, or 5 per cent, of the total number of staff the bank started with. So there was a five percent overall increase following both exercises.
What is the value of E?
Candidate % votes received
This time round, Candidate C, a veteran politician, received 20% MORE THAN THE 21,600 votes he polled at the last election five years ago. Candidates A and B were newcomers to the election.
What was the total number of votes cast?
- At the last election, C secured 21,600 votes. This time round, C received 25,920 (equivalent to 15%) votes. Therefore, the votes cast were as follows:
- giving a total of 172,800
There are 50 coins in five bags.
The first and second bags contain between them 27 coins.
The second and third bags contain 21 coins.
The third and fourth bags contain 17 coins.
The fourth and fifth bags contain 16 coins.
How many coins are there in each bag?
- 1st bag + 2nd bag +3rd bag + 4th bag = (17 + 27) coins
- = 44 coins
- 5th bag = (50-44) coins = 6 coins
- 4th bag = (16-6) coins = 10 coins
Insert each number from 1 to 0 only once into the boxes to make a correct mathematical sentence. (Picture)
The first two scales are in perfect balance. How many clubs are needed to balance the third scale? (picture)
- 6 clubs
- From the first two scales, we can deduce that 1 club is equivalent to 2 spades
A motorist travels 160km in the same time as another motorist, travelling at 40 km/h faster, covers 240km.
How long does the journey take?
- Let the speed of one motorist be s km/h, adn the other motorist be (s+40)km/h.
- 160/s = 240/ (s+40)
- Time taken for the journey = 160km/80km/h
Square PQRS is formed by joining the centeres P, Q, R, and S of the circles. Each circle is identical to the other three.
Which is longer?
A) The perimeter of PQRS
B) The circumference of circle with center P
- Each side of the square PQRS has the length of two radii. If the radius of any circle is r, the perimeter of square PQRS will be 8r, and the circumference of any circle will be 2pi(r).
- Perimeter : Circumference
- 8r 2pi(r)
- 4 pi
- Since 4 is greater than pi, the perimeter is greater than the circumference.