## April 2015 Logic & Maths Problems

1. What is the least number of square pieces of paper of any size, laid one over the other, which is required to produce this pattern?

2. This diagram shows the same cube in three positions with each face labelled with a letter from a to f. What face is directly opposite “d”?

3.
Given eight squares of paper that are all the same size, it is possible to make the above pattern by laying them one on top of the other with some overlapping. The last square to go on is H. List the order in which the squares of paper were placed from bottom up.

4.
There are two glasses, one containing a litre of milk, the other a litre of water. Take one tablespoon of milk and mix it with the water. Now take one tablespoon of the water/milk mixture and mix it in with the pure milk to obtain a milk/water mixture. Is there
(A) more water in the milk/water mixture? OR
(B) more milk in the water/milk mixture? OR
(C) as much water in the milk/water mixture as milk in the water/milk mixture?

5. Suppose you buy 100 kg of potatoes that are 99% water. After leaving them outside for a day, they are now 98% water.
What is the weight of these slightly dehydrated potatoes?

6. Alice, Beth, Carla, Dianne, and Emma were in a 1 km race. When Alice had just passed the midway mark, Beth was 150 metres away from the finish, and Dianne had run 400 metres. Emma had run twice as far as Dianne. Carla was at the 700 metre mark. List the runners in order, starting with the girl closest to the finish line.

7. At the end of 2005 Fred was half as old as his grandfather. The sum of the years in which they were born is 3860. How old was Fred at the end of 2014?

8. Bob drove at a very slow average speed of 20km/h to his driving test.

After passing, his drive home averaged 60km/h.

What was his average speed for the round trip?

9. If a hen and a half lays an egg and a half in a day and a half, how many eggs do 7 hens lay in 6 days?

10.

Chas and Dave insist on sitting next to each other
Alf and Bill don’t mind where they sit, except that Bill prefers to sit to Dave’s immediate right.
Taking all these preferences into account, how many different ways can you sit Alf, Bill, Chas and Dave in four seats in a line from left to right?

SOLUTIONS