From 4U Maths to Quant Trading - Q&A with IMC (1 Viewer)

[IMC Trading]

Many people are concerned about the change in climate (which is being demonstrated with the 2025 unusually severe windy weather in Sydney). Is Quant Trading environmentally friendly, and are there any goals to to minimising emissions or reaching a total output of emissions to 0 (predictions by computers are sure to use up a lot of power).

When hiring employees, you hire graduates based on their skills in mathematics. How do you assess these skills (as different universities may have different exam difficulties and competitiveness)?

I am considering a degree in physics (secondary education) or perhaps mathematics secondary education/actuarial mathematics (UNSW) or even mechanical engineering. If I do study one or more of these disciplines and decide that I want to work in IMC, are the chances of being hired still likely?

Also, what specific mathematics courses are preferred from graduates?

Thank you.

At IMC, we’re proud to be involved in a wide range of initiatives that contribute to our broader social impact. You can explore some of the work we’re doing globally via our website: IMC Positive Impact

When applying for a role at IMC, candidates will go through our recruitment process, which includes assessments designed to help us understand whether your skillset aligns with the demands of the role. These tests are an important part of ensuring both a good fit and a rewarding experience for you at IMC.

While we don't prioritise one specific degree over another, we do tend to see strong performance from students with STEM-related backgrounds, as the skills developed in those fields often align well with our roles.

 

[Trebla]

It is now the final week that we will keep this thread open for questions to IMC. If you have any lingering questions in your mind that haven't been answered already, this is your last chance to ask before the thread closes!

For round 3 of our giveaway, IMC have decided to give away a t-shirt + cap + beach towel combo. The t-shirt comes in unisex sizes S/M/L. Once again, they have kindly provided us a picture of them below:

... and now here is the third problem!

QUESTION 3

Two political parties (A and B) are deciding on which issue to campaign on during the election. Each party is aiming to get the largest possible percentage increase in its own primary vote given the campaign issue of the other party.

Independent analysts have estimated how each party’s primary vote percentage would change based on the combination of issues the two parties choose to campaign on at the same time. The possible issues are Economy, Healthcare and Education.

The table below shows the estimated percentage point change in primary vote for each party represented as (A’s change in primary vote, B’s change in primary vote):



For example:

• If A campaigns on the Economy whilst B campaigns on Education, then A will lose 1% in its primary vote whilst B will gain 3% in its primary vote. This is represented as (-1%, +3%).
• If both A and B campaign on the Economy, then A will gain 3% in its primary vote and B will gain 2% in its primary vote. This is represented as (+3%, +2%).

(a) If A chooses to campaign on Healthcare first, what should B campaign on in response to this to maximise its gain in primary vote?
(b) Suppose that each party can constantly change their campaign issue in response to the other party’s choice to maximise their gain in primary vote percentage points. Find the issue that each party will eventually end their campaign on after responding to the other party’s choice. Carefully explain your answer in full (step-by-step), including why it is the only pair of issues they will end their campaign on.

A reminder of the rules and instructions:

INSTRUCTIONS AND RULES FOR EACH ROUND

• To be eligible for the giveaway, you must PM me your solution here typed up with full reasoning that is clear and easy for me to follow without ambiguity
• You can only use concepts/terminology up to and including HSC Maths Ext2 level. Concepts used beyond that level (e.g. uni level Maths) will not be accepted.
• First user to PM me the right answers to all parts (and assessed to have clear reasoning for them) will receive instructions to get the merch prize posted to them
• Only your first message to me will be accepted in each round

 

[Flatuitous]

dropped the problem right as I'm pulling an all nighter to finish chem

 

[Sylfiphy]

is there a specific date of when applications open?

 

[IMC Trading]

is there a specific date of when applications open?

Applications will open early 2026. Please feel free to follow us on our socials or provide your email address to sydcareers@imc.com, which we can add to our distribution list, if you are interested in being notified.

 

[Trebla]

We have a winner for our Round 3 merch giveaway! Well done! Thanks to those who submitted their entries.

For anyone interested, a sample answer is below:

Spoiler

(a)
Given A chooses Healthcare, B will get the highest gain in primary vote in Healthcare (+2%) out of all the other options which give -1% or +1%.

(b)
Suppose that A chooses first
If A chooses Economy, then B has the choices of (Economy, Healthcare, Education) with gain in primary vote as (+2%, +1%, +3%) respectively. B would choose Education, which has the highest gain, in response to that.

Applying this reasoning similarly across the other choices gives the following:
(A1) If A chooses Economy, then B should choose Education in response to that
(A2) If A chooses Healthcare, then B should choose Healthcare in response to that
(A3) If A chooses Education, then B should choose Education in response to that

Suppose that B chooses first:
If B chooses Economy, then A has the choices of (Economy, Healthcare, Education) with gain in primary vote as (+3%, +1%, -1%) respectively. B would choose Economy, which has the highest gain, in response to that.

Applying this reasoning similarly across the other choices gives the following:
(B1) If B chooses Economy, then A should choose Economy in response to that
(B2) If B chooses Healthcare, then A should choose Education in response to that
(B3) If B chooses Education, then A should choose Education in response to that

Response patterns
Observe that continuing/iterating this response pattern gives the following response paths:

• If the start is (A1) then the path is (A1) -> (B3) -> (A3) -> (B3)
• If the start is (A2) then the path is (A2) -> (B2) -> (A3) -> (B3) -> (A3)
• If the start is (A3) then the path is (A3) -> (B3) -> (A3)
• If the start is (B1) then the path is (B1) -> (A1) -> (B3) -> (A3) -> (B3)
• If the start is (B2) then the path is (B2) -> (A3) -> (B3) -> (A3)
• If the start is (B3) then the path is (B3) -> (A3) -> (B3)

No matter which initial choice is taken, the response path always ends up at (A3) and (B3) which means A and B will eventually end up on campaign issues (Education, Education).

We will be having our final round of merch giveaway shortly. For the final round, there will be some slight changes to the rules, so please keep an eye out for the new instructions and questions!

 

[Trebla]

Thank you to everyone who has asked questions and to IMC for taking the time out of their busy day to answer them!

Whilst this concludes the Q&A, there is still the business of the final round of the giveaway...

Here are the new instructions and rules of this final round. Please read carefully.

INSTRUCTIONS AND RULES FOR FINAL ROUND

• I will release MULTIPLE Maths questions for you to solve (in one post)
• To be eligible for the giveaway, you must PM me your solutions here typed up with full reasoning that is clear and easy for me to follow without ambiguity
• You are given 24 hours to answer these questions starting from the time of their release. Any submissions received after that deadline will not be accepted.
• You do NOT have to answer all the questions. However, whoever fully answers the most questions within the 24-hour timeframe wins. If there is a tie, then the winner is whoever answered them the fastest.
• You can only use concepts/terminology up to and including HSC Maths Ext2 level. Concepts used beyond that level (e.g. uni level Maths) will not be accepted.
• However, the marking will be very strict this time. If there is just ONE part of your solution to ANY question that contains issues such as an error, vague/flawed/incoherent reasoning, incorrect statements, lack of adequate working and explanations, usage of concepts/results beyond HSC Maths Ext2 or assumptions of results that should be derived, then your ENTIRE submission will NOT be the winning entry!
• This time you are allowed to submit multiple posts to cover multiple questions during the 24 hours, provided they are in the SAME conversation thread. Your speed of response will be based on the time of your latest post. You cannot correct anything that you have already submitted.

It is recommended that you think very strategically about what questions you choose to submit and polish the quality of your reasoning. In this final round, it is possible for someone to win by submitting less questions, but all of them have good quality working/explanations (if others who took the gamble and attempted more questions fell short in this quality).

As a guide, assume your reader is a HSC student who just finished Maths Ext2. The clarity of your explanations has to be easily followed by a student at that level.

The final round questions will be released sometime on the weekend, so keep an eye out for them!

So...what is up for grabs in the final round? Everything from the previous rounds plus a frank green water bottle!

We would like to get as many participants as possible in this final round!

 

[Trebla]

... and now here are the FIVE questions for the final round!

QUESTION 4
An analyst attempts to retrieve data showing the distribution of funding by a major company across five sectors in five different states in the past year.

The analyst compiles the following table, but finds that a number of cells are missing (shown as *):


Find the value of funding (in $m) given to Construction in QLD. Show full working.

==================================================================================================

QUESTION 5
Suppose that you receive an income of $A at the beginning of every year, which is deposited into a bank account earning a fixed interest rate of 5% p.a. compounded annually. At the end of each year after interest is paid, you then withdraw half the balance for everyday expenses.

Explain why your bank account’s balance will never exceed $42A/19. Show full working indicating why it is the tightest upper bound in continuous time.

==================================================================================================

QUESTION 6
Players A and B are playing a game where the player who beats their opponent by two points is the winner. Suppose that both players are currently on the score 3-3 and the probability that A scores one point is 60%.

Find the probability that player B wins. Show full working and reasoning.

==================================================================================================

QUESTION 7
An integer between 1 and n (inclusive) is drawn three times at random with replacement. Let X be random variable representing the lowest value of these three numbers chosen. Prove that its expected value is given by:


Show full step-by-step working in your proof.

==================================================================================================

QUESTION 8
There are 5 cars in a race. There are three distinct medals (gold, silver, bronze) that could be potentially awarded in this race. Up to 5 medals can be awarded to these cars according to the following rules:

• Each car can only receive at most one medal
• A car that finishes with no car ahead of them receives a gold medal
• A car that finishes with exactly one car ahead of them receives a silver medal
• A car that finishes with exactly two cars ahead of them receives a bronze medal

How many ways are there for the medals to be awarded based on the above rules if ties are possible? Clearly justify your answer.

A reminder of the rules and instructions:


The 24 hours starts now!

 

[Trebla]

We have a winner for the final round of the merch giveaway who was the fastest to answer all five questions correctly! Well done and thanks to those who submitted their entries.

For anyone interested, sample answers are below:

Question 4

Spoiler

Let a, b, c, d and x be defined as follows:


Taking the row totals of Education and Construction:

100 + a + 150 + b + 417 = 1540

a + b = 873 (1)

x + c + 166 + d + 275 = 1271

x + c + d = 830 (2)

Taking the column totals of NSW and SA:

465 + 194 + 117 + a + c = 1707

a + c = 931 (3)

385 + 468 + 189 + b + d = 1614

b + d = 572 (4)

Taking (1) + (2) – (3) – (4):

x = 200

Hence, funding given to Construction in QLD is $200m.

Question 5

Spoiler

During any given year in continuous time, the balance moves as follows:

• Increases when income is added at the beginning of the year
• Increases after interest is received at the end of the year
• Decreases after withdrawal at the end of the year

In the long run, the balance will be highest at the time it gains interest and lowest at the time of withdrawal. Hence, the time that the interest is received will ultimately define the upper bound.

Let B_n be the balance in the account at the end of nth year before the nth withdrawal.

At the start of the first year $A is deposited and gains 5% interest during the year.
B₁ = A(1.05)

In the following year, half the balance is withdrawn then new income added before interest is applied again:
B₂ = (B₁(0.5) + A)(1.05) = A(1.05)(0.5) + A(1.05)

B₃ = (B₂(0.5) + A)(1.05) = A(1.05)²(0.5)² + A(1.05)²(0.5) + A(1.05)

B₄ = (B₃(0.5) + A)(1.05) = A(1.05)³(0.5)³ + A(1.05)³(0.5)² + A(1.05)²(0.5) + A(1.05)

… and so on.

At the end of the nth year before withdrawal

B_n = A(1.05)ⁿ(0.5)ⁿ + A(1.05)ⁿ(0.5)^n-1 + … + A(1.05)³(0.5)² + A(1.05)²(0.5) + A(1.05)

= A(1.05)ⁿ(0.5)ⁿ + A(1.05)[1-(1.05)^n-1(0.5)^n-1]/[1-(1.05)(0.5)]

= A(1.05)ⁿ(0.5)ⁿ + 42A[1-(1.05)^n-1(0.5)^n-1]/19

= 42A/19 + A(1.05)^n-1(0.5)^n-1 [(1.05)(0.5) – 42/19]

= 42A/19 – (1281/60) A(1.05)^n-1(0.5)^n-1

As n gets large, the (1.05)^n-1(0.5)^n-1 approaches zero so the balance increases to an upper bound of 42A/19, which it cannot exceed.

Question 6

Spoiler

There are a few ways that player B can win starting from 3-3:

• Player B get two points in a row and wins
• Player B gets a point then player A gets a point giving 4-4, the game continues in this “deuce” scenario but at some point player B eventually wins two points in a row
• Player A gets a point then player B gets a point giving 4-4, the game continues in this “deuce” scenario but at some point player B eventually wins two points in a row

Let p_B be the probability that B wins and p_D is the probability that player B wins given a “deuce” scenario described above.

p_B = (0.4)(0.4) + (0.6)(0.4)p_D + (0.4)(0.6)p_D

However, observe that p_D = p_B because the probability that B eventually wins from 3-3 is the same as the probability that B eventually wins from say 4-4 or 5-5 etc since two points are always required to win. Hence,

p_B = (0.4)(0.4) + (0.6)(0.4)p_B + (0.4)(0.6)p_B

p_B = 4/13

Question 7

Spoiler

Question 8

Spoiler

Since there is always a car that will finish first, there will always be at least one gold medal. There are four possible scenarios:

• Only gold medals are awarded
• Only gold and silver medals are awarded
• Only gold and bronze medals are awarded
• All gold, silver and bronze medals are awarded

Only gold medals are awarded
This is only possible if there are three or more tied in first place, otherwise silver/bronze will have to be awarded. The number of ways of having 3, 4 or 5 tied equal first is:


Only gold and silver medals are awarded
This is only possible if there is one car that comes first to receive the gold and at least two are tied to get silver, otherwise a bronze medal is possible. The number of ways of one car getting first place and having either 2, 3 or 4 cars tied equal second is:


Only gold and bronze medals are awarded
This is only possible if there are two tied in first place and the rest get bronze. The number of ways of two cars getting equal first place and having either 1, 2 or 3 cars tied equal third is:


All gold, silver and bronze medals are awarded
This is only possible if there is one car in first place, one car in second place and the rest get bronze. The number of ways of one car getting first place, one car getting second place and having either 1, 2 or 3 cars tied equal third is:


Adding all the counts in the scenarios gives 281.

 

[Trebla]

Once again, thank you to everyone to participated in the Q&A and the giveaways. A special thanks to @IMC Trading for taking the time to respond to the questions and for agreeing to give away their merch to the Bored of Studies users!

...and that wraps everything up for this thread!