Logical exam with answers

The following questions will test your ability to think laterally and mathematically. If you get more than 50% of these right you're certainly strong on your numerical and lateral thinking skills.

Questions start easy and get progressively harder.

1. When asked how old she was, Beth replied “In two years I will be twice as old as I was five years ago”. How old is she?
2. Which weighs more? A pound of iron or a pound of copper?
3. If you have two coins totaling 11p, and one of the coins is not a penny, what are the two coins?
4. Divide 40 by half and add ten. What is the answer?
5. To the nearest cubic centimetre, how much soil is there in a 3m x 2m x 2m hole?
6. A farmer has 15 cows, all but 8 die. How many does he have left?
7. The ages of a mother and her graduate son add up to 66. The mother’s age is the son’s age reversed. How old are they?
8. If a man and a half can eat a hot dog and a half in a minute and a half, how long would it take six men to eat six hot dogs?
9. Nim went into a supermarket to buy some fruit.
   There were three packs on special offer:
   1) Ten grapes and five strawberries: 70p (save 10p)
   2) Ten strawberries and ten apricots: £2 (save 40p)
   3) Thirty grapes: 100p (save 20p)
   What would be the full price of one grape, one strawberry and one apricot at normal price (no special offers)?
10. The amount of water flowing into a tank doubles every minute. The tank is full in an hour. When is the tank half full?
11. There is a pole in a lake. Half of the pole is embedded in the mud at the bottom of the pond, another one third is covered by water, and 7 feet is out of the water. What is the total length of the pole?
12. If the hour hand of a clock moves 1/60th of a degree every minute, how many degrees will it move in an hour?
13. I spend a third of my money on a guitar, half the rest on a microphone and a quarter of what I then have left on a kazoo. What proportion of my original money do I have left?
14. How can you take 1 from 19 and leave 20?
15. Here is a list of months and a code for each
    • January: 7110
    • February: 826
    • March: 5313
    • April: 541
    • May: 3513
    • June: 4610
    • July: 4710

    What is the code for the month of August?

16. There are 60 sweets in a jar. The first person took one sweet, and each consecutive person took more sweets than the person before, until the jar was empty.
    What is the largest number of people that could have eaten sweets from the jar?
17. At the University of Kent 36 students attended the LAW lecture, 39 attended an ART lecture and 37 attended the DRAMA lecture. How many attended the FILM lecture?
18. If you have a pizza with crust thickness ‘a’ and radius ‘z’, what’s the volume of the pizza?
19. A man went into a store to buy an item. He asked the assistant:
    "How much does it cost for one?"
    The assistant replied 2 pounds, Sir"
    "And how much for 10?"
    The assistant replied "£4"
    "How much for 100?"
    He got the reply "£6"
    What was the man buying?
20. There are 23 football teams playing in a knockout competition. What is the least number of matches they need to play to decide the winner?
21. How many degrees are there between clock hands at 3.15?
22. You have 8 bags of sugar, 7 weight the same, one weighs less. You also have a balance scale. Find the one that weighs less in less than 3 steps.
23. There are three boxes, one contains only apples, one contains only oranges, and one contains both apples and oranges. The boxes have been incorrectly labeled such that no label identifies the actual contents of the box it labels. Opening just one box, and without looking in the box, you take out one piece of fruit. By looking at the fruit, how can you immediately label all of the boxes correctly?
24. 1/2 of 2/3 of 3/4 of 4/5 of 5/6 of 6/7 of 7/8 of 8/9 of 9/10 of 1, 000 = ?
25. How many times do the hands of a clock overlap in 24 hours?