**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.

- 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?
- Which weighs more? A pound of iron or a pound of copper?
- If you have two coins totaling 11p, and one of the coins is not a penny, what are the two coins?
- Divide 40 by half and add ten. What is the answer?
- To the nearest cubic centimetre, how much soil is there in a 3m x 2m x 2m hole?
- A farmer has 15 cows, all but 8 die. How many does he have left?
- 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?
- 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?
- 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)? - The amount of water flowing into a tank doubles every minute. The tank is full in an hour. When is the tank half full?
- 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?
- If the hour hand of a clock moves 1/60th of a degree every minute, how many degrees will it move in an hour?
- 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?
- How can you take 1 from 19 and leave 20?
- 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?

- 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? - 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?
- If you have a pizza with crust thickness ‘a’ and radius ‘z’, what’s the volume of the pizza?
- 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? - 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?
- How many degrees are there between clock hands at 3.15?
- 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.
- 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?
- 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 = ?
- How many times do the hands of a clock overlap in 24 hours?

### Answers

**12**- They both weigh exactly a pound!
**10p and 1p**– the other coin can be a penny!**90.**Dividing by half is the same as multiplying by 2.**None**– it’s a hole!**Eight**- 42 and 24 years old. (One reader has pointed out that it could also be 51 and 15, although another did point out that 15 years old would be a little young to be a graduate!)
**A minute and a half**- Thirty grapes at normal price cost £1.20, thus grapes cost 4p each. Ten grapes and 5 strawberries cost 80p at normal price, the grapes must cost 40p therefore the strawberries cost 8p each. Ten strawberries and ten apricots cost £2.40 at normal price, the strawberries cost 80p, therefore the apricots cost 16p each. So one apricot + one strawberruy and one grape cost
**28p in total**. **At 59 minutes**- Half of the pole is in the mud

One third is covered by water

Therefore fraction of pole in the mud and water = 1/2 + 1/3 = 3/6 + 2/6 = 5/6

Therefore fraction of pole out of the water = 1 – 5/6 = 1/6

So one sixth of the pole is 7 feet.

So total length of pole =**42 feet.** **One degree**- After spending one third of my money on the guitar I have two thirds left. I spend half of this on a microphone, so this is again one third. I then have one third of my original money remaining. I spend one quarter of this on the kazoo. One quarter of one third is one twelfth. I thus have three quarters of one third of my money remaining. Three quarters of one third is
**one quarter of my money remaining**. (1/3 = 4/12. 4/12 – 1/12 = 3/12. 3/12 = 1/4) - If the numbers are in Roman numerals, Take I from XIX (19 in Roman numerals), you are left with
**XX**– 20 in Roman numerals. **681.**The first digit is the number of letters, the second, the position of the month in the calendar, and the final digit is the position of the first letter of the word in the alphabet.- The first person takes 1 sweet, the second two, the third three etc. 1+ 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45, so the first nine people take 45 sweets between them. The 10th person takes 15 sweets. He or she can’t possibly take fewer than 9, nor leave fewer than 11, else the jar will not be empty but there won’t be enough for the next person to follow the rule stated in the question (that each person take more than the one before. So the answer is
**10 people**. Thanks to Sam Parker for a detailed explanation of this answer **40 students.**Letter A = 1, B= 2, C = 3 and so forth, so FILM = 6 + 9 + 12 + 13 = 40- pi*z*z*a (!)
**House numbers**- In a knockout competition, every team except the winner is defeated once and once only, so the number of matches is one less than the number of teams in this case 23-1 =
**22.** - The answer is not zero degrees as you might at first think. The minute hand will be at 15 minutes (90 degrees clockwise from vertical) but the hour hand will have progressed to one quarter of the distance between 3 pm and 4 pm.

Each hour represents 30 degrees (360 / 12), so one quarter of an hour equals 7.5 degrees, so the minute hand will be at 97.5 degrees: a**7.5 degree difference**between the hands. - Put 2 bags to the side. Weight 3 of the remaining bags against the other 3 remaining. If they weigh the same then weigh the 2 bags that you put aside to find out which of them is heavier. If, however, one of the sets of 3 bags was heavier, put one of the bags from the heavier set aside. Weigh the remaining two bags from the set to find out which one is heavier. If they are equal then you know that it is the 1 bag that you put aside.
- Open the box that is labeled “Apples and Oranges”.

You know that since none of the labels are correct, the box must either contain only apples, or only oranges.

Suppose that you remove an apple from that box. Therefore, that box must be the “Apples Only” box.

One of the two remaining boxes must be the “Oranges Only” box. However, one is labeled “Apples Only”, and the other is labeled “Oranges Only”. Therefore, the one labeled “Apples Only” is the box that contains only oranges, and the box labeled “Oranges Only” is the box that contains both kinds of fruit. **100**- 22: the minute hand will go round the dial 24 times, but the hour hand will also complete two circuits. 24 minus 2 equals
**22**.

## Score

**17 or more:**excellent – you are both numerate and lateral!**10 – 16:**good**Below 10:**a little more practice on these types of test is required!

Continue at: https://www.kent.ac.uk/careers/tests/maths-logic-test.htm

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