Weekly quiz          

2003/04

Qualifying round 2

Problems

Problem 1

Tennis balls

Lene and Hans each have some tennis balls.

If Lene gives Hans 8 of her balls they would have an equal number.

If Hans gives Lene 8 of his balls, Lene would have 3 times as many balls as Hans.

How many balls does Lene have?

 

Write your answer in the box:

Problem 2

The bike ride

All girls started at the same time.

Anne biked the CDAC route at a rate of 30 km per hour.
Bente biked the route around the isosceles triangle at a rate of 20 km per hour.
Cecilie biked the CEFBC route at a rate of 24 km per hour.

In what order did they finish, and what was the finishing time (in minutes) for the one who was first back at C?

Write A for Anne, B for Bente and C for Cecilie in the right boxes:

Problem 3

Triangles

In a bag there are bundles with three sticks in each. The length of each stick is a whole number when measured in centimeters. The total length of the three sticks in each bundle is 12 cm. All possible combinations of lengths that add up to 12 are present in the bag. All the bundles are different.  You pull an arbitrary bundle from the bag.

What is the possibility to pull out a bundle with sticks that can be formed as a triangle?

Cross out your answer:

Problem 4

 What is the side length?

Problem 5

Lunchtime

Half of the students who eat lunch in the cafeteria didn't buy anything at the cafeteria. Out of the remaining half who bought something,  bought fruit. Half of the students who bought fruit bought apples and one-fourth bought pears. The remaining 15 students bought bananas.

How many students had lunch in the cafeteria?

Write your answer in the box:

Problem 6

Tangents

8 different tangents are drawn om a circle. These tangents will divide the plane into some closed areas and some open areas.

Problem 7

Body guards

Wonderful Violet and Fancy Fia, the world famous models, together had more than 10 but fewer than 30 bodyguards. One day, one of the bodyguards, Knuckles, decided to leave Wonderful Violet and join Fancy Fia. Now both the females had the same number of bodyguards.

Eventually, Brage rejoined Wonderful Violet. Also, Mandig decided to leave Fancy Fia and join Wonderful Violet. Now, both the females had a prime number of bodyguards.

How many bodyguards did each have now?

Write your answers in the boxes

Wonderful Violet has  body guards.

Fancy Fia has  body guards.

Problem 8

What time is it?

At a certain time I looked at a 24-hour digital clock and noticed some things about the time:

1) The number in the hours section plus the number in the minutes section makes 60.
2) One of the digits in the minutes section is the square root of the other digit in the minutes section.
3) The sum of the digits in the minutes section is the number in the hours section reversed.

What was the time?

Write your answer in the boxes:

Hours :

Minutes :