# Online Test - Example Questions

Feedback from successful and unsuccessful candidates alike suggests that applicants find our online tests rather different from those set by other employers. Most view this as positive, but it can also come as a bit of a surprise to some. We have provided a few examples of the type of questions that appear in our test, just to give you a bit of reassurance you'll know what to expect. This format is relevant to online tests for roles at different levels (CAA, Graduate and more senior Associates), although naturally the complexity of the questions will vary so don't be too concerned if any of these sample questions look tricky!

Solutions are provided at the bottom of the page, but we recommend attempting these questions as practice before looking at them.

#### Question 1

A knockout singles tennis tournament consists of:

- 2 Amateurs
- 2 Professionals

The semi-final draw is random. A professional player has a 90% chance of beating an amateur player, whereas two amateurs and two professional drawn together are equally likely to beat one another.

What is the probability that a professional player wins the tournament?

*(5 marks)*

#### Question 2

A government is considering making pet insurance mandatory for all pet owners.

List four groups of people who would be affected by this change and state what the effect on each would be.

*(5 marks)*

#### Question 3

An insurance product pays a 60-year-old policyholder £10,000 if they survive to 65, and £100,000 if they die before then. The insurer makes a mortality assumption that:

P(survive from age n to age n+1) = 0.99 + 0.001(100-2n)

Answer the following questions:

- What is the expected cost of the product to the insurer?
- Explain why the mortality assumption would not be suitable for selling this product to young adults.

*(5 marks)*

#### Question 4

The following pseudo-code takes a positive integer *n* as its input.

Describe what the code does, including a definition of what variables *f* and *i* represent.

* n = input*

* stored_text = ""*

* f = 0*

* for i = 1 to n-1*

* if n/i - int(n/i) = 0 then*

* stored_text = stored_text & i & ","*

* f = f + 1*

* end if*

* next i*

* output = f & ":"& stored_text & "n"*

Note that:

- The function int(x) returns the integer part of x e.g int(3.14) = 3.
- The operator "&" joins together two elements into a single text string e.g "Twenty" & 20 = "Twenty20".

*(5 marks)*

#### Question 5

- Estimate how many people in the UK will start a new job in September 2023.
- Explain briefly how and why your answer would change if you were instead considering the same question for March 2009.

*(5 marks)*

#### Question 6

Dennis' PIN is 4 digits long. The first and last digits are prime, and each digit is strictly smaller than the one before it. How many possible PINs are there?

*(5 marks)*