February 2016 Logic & Maths Problems

1. Amanda and Krystal have 14 lollies between them. If Amanda had twice as many lollies as she does now she would have one more than Krystal has now. How many lollies do they each have?

2. I have some square tiles. Half of them are black and the other ones are white. I arrange them so that the black ones form a rectangle and the white ones make a border around them one tile thick. I have no tiles left over. How many tiles do I have?

3. Freda’s hobby is collecting dolls from all over the world. She’s hoping to build her collection up to 50 dolls soon.
20% of her dolls come from India, while one seventh of them are Australian. How many dolls does she own?

4. Santa sent Prancer, Dancer, Comet, Vixen, and Rudolf, each to a different city, each with a sleigh of a different colour, to bring various gifts to good children.
Comet was sent to Melbourne, while another reindeer was sent to Sydney.
Vixen was sent to Perth.
The yellow sleigh went with Dancer, but another reindeer was sent to Adelaide.
The blue sleigh did not go with Prancer.
The red sleigh went with Rudolf, the red nose reindeer.
The green sleigh went to Brisbane, while the orange sleigh went to a different city.
The blue sleigh did not go to Melbourne.
Which city did each reindeer visit?
What was the colour of the sleigh that went with each reindeer?

5. Three eighteen-year-olds bought their first car between them. It cost \$9000.
Bill contributed 50% more than Jim.
Arthur contributed twice as much as Jim.
How much did Jim spend on the car?

6. Tom asked his Granny how old she was. Rather than giving him a straight answer, she replied:
“I have 6 children, and there are 4 years between each one and the next. I had my first child (your Uncle Peter) when I was 19. Now the youngest one (Your Auntie Jane) is 19 herself. That’s all I’m telling you!”
How old is Tom’s Granny?

7. Twelve contestants are narrowed down to three in a KNOCKOUT competition.
The winner is then decided by best performance in a ROUND ROBIN.
How many matches are played in total?

8. I am thinking of a whole number between 1 and 20, inclusive.
• If my number is even, then it is also a multiple of 3.
• If my number is not a multiple of 3, then it is greater than the length of the diagonal of a square with an area of 81.
• If my number is not greater than the length of the diagonal of a square with an area of 81, then it is square.
• If my number is not square, then it is one greater than a multiple of 5.
What is my number?

9. In simplest terms, what is five eighths of two fifths?

10. A census taker approaches a house and asks the woman who answers the door “How many children do you have, and what are their ages?”
Woman: “I have three children, the product of their ages are 36, the sum of their ages are equal to the address of the house next door.”
The census taker walks next door, comes back and says “I need more information.”
The woman replies “I have to go, my oldest child is sleeping upstairs.”
Census taker: “Thank you, I now have everything I need.”

What are the ages of each of the three children? (Assume all ages are exact whole numbers)

SOLUTIONS