Hint
How many students study chemistry and physics, but not biology?
Answer
500 students.
Reasoning
The answer is more easily seen if three intersecting circles are drawn, and the numbers inside each section are worked out.
We know that 73 students study all three disciplines, which allows us to work out the numbers.
97 students study chemistry and physics, so 97 – 73 = 24 study just chemistry and physics.
138 students study physics and biology, so 138 – 73 = 65 study just physics and biology.
152 students study chemistry and biology, so 152 – 73 = 79 study just chemistry and biology.
280 students study chemistry, so 280 – 73 – 24 – 79 = 104 study just chemistry.
254 students study physics, so 254 – 73 – 24 – 65 = 92 study just physics.
280 students study biology, 280 – 73 – 65 – 79 = 63 study just biology.
For a total of: 104 + 92 + 63 + 24 + 65 + 79 + 73 = 500 students.
During an exciting weekend of paintball, four friends were having great fun.
The paintballs came in blue, green, yellow and red.
Coincidentally, the four friends had T-shirts in those same colours.
Billie used blue paintballs. The person in the green T-shirt used yellow paintballs. Charlie was not wearing a red T-shirt. Drew used green paintballs and wore a blue T-shirt. Alex was the only person who used paint which was the same colour as their T-shirt.
Can you tell which colour paint they each used and the colour of their respective T-shirts?
Hint
Start by using clues (1) and (4), and then look at clues (5) and (2) to find who wore the green T-shirt.
Answer Wore Paint
Alex red red
Billie yellow blue
Charlie green yellow
Drew blue green
Reasoning
By (1), Billie used Blue paintballs: Wore Paint
Alex
Billie blue
Charlie
Drew
By (4), Drew used Green paintballs and wore a Blue T-shirt: Wore Paint
Alex
Billie blue
Charlie
Drew blue green
By (5), Alex was the only person who used paint that was the same colour as their T-shirt, which means by (2) that Charlie wore the Green T-shirt and used Yellow paintballs: Wore Paint
Alex
Billie blue
Charlie green yellow
Drew blue green
This leaves Alex with the Red paintballs, and by (1), the Red T-shirt. Wore Paint
Alex red red
Billie blue
Charlie green yellow
Drew blue green
Leaving Billie wearing Yellow. Wore Paint
Alex red red
Billie yellow blue
Charlie green yellow
Drew blue green
?
Puzzle 3
Last week, I travelled from London to Stoke.
On the first day, I travelled one half of the distance.
On day two, I travelled one third of the remaining distance.
On day three, I travelled three quarters of the remaining distance.
Yesterday I travelled one half of the remaining distance.
