# Take The Cambridge University Interview: A 10 Question Test

THESE Questions are from the Cambridge University Engineering degree interview. Clue: None of the answers are “My daddy’s very rich”, “I can row” or “MAYBE”.

**Q1.**

I start with a pint glass full of lemonade. I drink half of it and give it to you. You then drink half of what is left and give it back to me. I then drink half of what is left, and pass it back. We keep drinking half of the remaining lemonade then passing it across until there is a negligible amount of drink left. In total, what proportion of the pint did I drink?

1/3

5/8

2/3

3/4

none of the above

**Q.2**

On a clear day, you are on an aeroplane which is at 38,000 ft above the middle of the Pacific ocean. Taking the radius of the earth as 6,400km, what is the approximate distance between you and the horizon of the earth? (1ft=0.3048m)

130km

390km

700km

1,300km

**Q.3**

A helium balloon is held by a light string in the middle of the back of a very powerful truck. The back of the truck is sufficiently large that the balloon cannot hit the sides if it sways forwards or backwards on the string. The back of the truck is completely enclosed with no windows or ventilation from the outside. The truck now accelerates rapidly forwards. What is the motion of the balloon relative to the truck when the truck is accelerating? Does the balloon sway forwards, backwards or remain at the same position?

The balloon sways forwards

The balloon sways backwards

The balloon does not move

**Q.4**

My office is 3.5m wide, by 3.5m high, by 7m long. I have 200 books and 7m of A4 size files on the shelves. The office also contains a two-draw filing cabinet, a desk, a table and a computer. My office is in Cambridge which is near to being at sea level. Estimate the total mass of all the air molecules in the office.

1kg

10kg

50kg

100kg

None of the above.

**Q.5**

I have 28 black and 8 brown socks in my sock drawer. If it is completely dark and I cannot see the colour of the socks that I am picking, how many socks do I need to take from the drawer to be sure that I have at least one pair of socks that are the same colour?

3

4

14

18

**Q.6**

Without using a calculator, calculate 4020×3980

1,600,400

15,999,600

16,000,000

16,000,400

None of the above

**Q.7**

Three male prisoners are sitting in a line one behind another. They are shown 2 red and 3 green hats, and a hat on is put on each man’s head so that each cannot see his own hat, but can see the hats on the other prisoners ahead of him. As a result, the front prisoner cannot see anything; the middle prisoner can see the front prisoner’s hat and the back prisoner can see the hats on both the front and middle prisoner. They are told that they will be set free if any of them can get his own hat colour right without communicating with any other prisoner. The front prisoner becomes aware that both the back and middle prisoners have chosen to remain silent. Assuming that all the prisoners make optimal logical decisions throughout the challenge, what is the best action that can be taken by the front prisoner?

Say that his hat is red

Say that his hat is green

Remain silent

None of the above

**Q.8**

An unbiased cubic die has numbers 1 to 6 inscribed on each side. On average, how many rolls will you need in order to get a 6?

1

3

6

8

None of the above

**Q.9**

Consider a large metal sheet, 5mm thick, with a 20cm diameter hole in the middle. You can assume that metal expands when heated. The metal sheet is placed in an oven and heated from room temperature to 100celsius. What happens to the diameter of the hole as the sheet is heated: does it decrease, increase or stay the same?

The diameter of the hole decreases

The diameter of the hole increases

The diameter of the hole stays the same

**Q.10**

What is the minimum number of guests that need to be present at a party so that there is a more than 50% chance that two of them have the same birthday? Note that they do not necessarily have to be the same age, they just must have the same birthday. We can assume that a year consists of 365 days and that the probability of birth is equal for each day.

10

23

188

366

None of the above

*

*

*****

**Answers:**

1. 2/3

2. 390km

3. The balloon sways forwards

4. 100kg

5. 3

6. 15,999,600

7. Say that his hat is green

8. 6

9. The diameter of the hole increases

10. 23

This is how you get into the Cambridge Drinking Society.

Posted: 24th, October 2013 | In: News Comment | Follow the Comments on our RSS feed: RSS 2.0 | TrackBack | Permalink