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What Is the SIG Problem Solving Assessment?
The Susquehanna International Group (SIG) Problem Solving Assessment is one of the three common assessments used by SIG to screen candidates, alongside the SIG Quantitative Evaluation and the SIG Capital Markets Test.
It is a mathematical knowledge test used as the initial screening stage for SIG candidates applying for the roles of quantitative traders and researchers. The test is provided by the testing company Mettl and contains 9-15 questions that should be solved in 60 minutes.
Test topics cover 4 main topics:
- Combinatorics – permutations, variations, etc.
- Probability – Bayes’ theorem, binomial/geometric distribution, Markov chains, etc.
- Single Variable Calculus – solve word problems using calculus.
- Logic – solving problems using pure logic.
Let’s break down the 3 test sections, including a sample question of each.
Pro Tip
The Test Interface of the SIG Problem Solving Assessment requires you to type your answers in a very specific and accurate formatting. Work slowly and carefully, as the slightest calculation error means a wrong answer.
Test Structure and Question Format
The SIG Problem Solving Assessment will contain between 9-15 questions at various levels of difficulty. However, almost all questions (except for pure logic) are at an academic level and require knowledge of math and statistics. The questions cover 4 main areas, detailed below.
You may find the answers and explanations to all sample questions provided here in the Free Practice section. For even more practice and preparation recommendations, check out the Preparation section.
Type #1 – Probability
This type of questions constitutes the majority of the test, and cover basic principles in probability.
Sample Question – Probability
Consider a fair 20-sided die. Roll the die 8 times. Let D be the number of rolls that are divisible by 6. Calculate E(D).
Type#2 – Combinatorics
Combinatorics questions in the test cover topics like permutations and variations. This topic is also a major part of the test content, but it will normally be less common than probability.
Sample Question
There are 6 plates on the dinner table. Two plates are round, and the rest are square. In how many ways can you place 2 omelets and 1 salad so that at least one food item is on a round plate?
Assumptions:
- Only one item can be placed on each plate.
- The omelets are indistinguishable.
Pro Tip
Go over major formulas in probability and combinatorics, such as binomial coefficients, Markov chain, expected values of common probabilities (binomia, Bernoulli, geometric), etc. However, you will likely not come across normal distribution in the assessment.
Type #3 – Single-Variable Calculus
This type of question usually appears only once or twice in the assessment. However, considering the low overall number of questions, it is essential to be familiar with it.
Sample Question
A tractor is making its way daily from the farm to the work site and back. The tractor travels part of the way on the road, at 30 meters per minute, and part of it through the field, at 18 meters per minute. Let X be the distance from the farm at which the tractor goes off the road.
What should X be so that the ride takes the least time?
Pro Tip
Take a minute or two in the beginning of the test to go over all questions, before diving into solving them. See more details in the Tips section.
Type #4 – Logic
This type of question is also rather uncommon in the assessment, and it is the only type of question that will not require any previous mathematical knowledge. In this type of question, you will be required to use logical reasoning and trial-and-error to solve problems.
Sample Question
Anna, Bella, and Carol have the following conversation:
- Anna: “Bella, your age is 1.7 times my age.”
- Carol: “Anna, you are more than 8 years younger than me.”
- Anna: “Carol, your age is the average of my age and Bella’s.”
- Bella: “Carol, you’re the youngest of us.”
Assumptions:
- When one of the women speaks to someone younger, she lies. When she speaks to someone older, she speaks the truth.
- No two women are the same age.
- All ages are integers.
How old is Anna?
SIG Problem Solving Assessment Preparation
I strongly recommend JobTestPrep’s SIG Problem Solving Assessment Preparation.
- The ONLY prep accurately simulating the assessment.
- An authentic mock test + Additional practice by topic.
- A money-back guarantee policy
What Do You Get?
- A full-length test simulation (15 questions, 60 minutes)
- 4 additional practice tests by topic (35 questions total)
- Detailed answers and explanations to all questions
- A money-back guarantee
Full Disclosure: I am affiliated with JobTestPrep. Clicking the links helps me provide you with high-quality, ad-free content.
What Does the SIG Problem Solving Assessment Test Measure?
The SIG Problem Solving Assessment is designed to measure how you approach and solve quantitative problems. However, the types of problems in the assessment absoultly necessitate proper knowledge in mathematics and probability to solve.
The SIG Test Invitation
The invitation to take the SIG Problem Solving Assessment will come in two parts:
- The SIG Invitation
- The Mettl (test provider) invitation.
The SIG Invitation
Once you have passed the initial resume stage, you will get a test invitation from SIG, with some basic information about the test.
Here are the major things to consider:
- The assessment is held by a third-party testing company named Mettl.
- The invitation from SIG will not include a test link. That will be sent separately. See next section.
- You may use a pen, paper, and calculator, but no additional source.
- Do NOT try to cheat! If you navigate out of the testing window or open a new tab, your assessment will be instantly stopped and graded as is.
- You have 7 days to complete the assessment.
- Before taking the test, you will be requested to fill an online form – it’s easy to miss, so don’t!
The Mettl Invitation
The second email you will receive is from Mettl, the test provider. That is a very simple notification, containing a link to the assessment and a prerequisite system compatibility check.
Pro Tip
The SIG Assessment test interface may be a bit confusing. In lieu of the short time frame for the overall test, I recommend reading the Test Interface section as well.
Test Interface
Here is an illustration of how the SIG Problem Solving Assessment screen generally looks like:
Several things to note:
- Once you have started, you cannot pause the assessment in any way.
- You may move freely between questions.
- You may mark a question for later review.
A Word About Data Entry
The SIG Problem Solving Assessment will accept answers only in the form of integers (i.e. whole or real numbers). Inputting your answer in a decimal form will be considered an error. This means two things:
- If your answer is not a real number (e.g., √2), you are wrong.
- Through the test, do not round the fractions and try to refrain from converting them to decimals. Working with the fractions button in your calculator may come in handy. See the Tips section.
Free Practice
This free practice contains 5 sample questions and answers, adapted from the actual SIG Problem Solving Assessment.
These are intended to give you a feeling for the test’s world of content and level of difficulty. The recommended solving time is 30 minutes. Have a calculator, scratch paper and pen at hand.
Good luck!
Question 1
John is drawing red and black cards out of an infinite deck. The probability of drawing a red card is 4/5. Calculate the expected number of draws to draw three black cards consecutively.
Answer and Explanation
The correct answer is 125.
The question revolves around geometric distribution – how many Bernoulli trials are required to get a “success” outcome. The “success” in this case is three consecutive draws of black cards.
The expected value of a geometric distribution is easily calculated as:
E(x) = 1/p, where p is the probability of “success”.
In the given question:
p = The probability of drawing 3 consecutive black cards = (1/5)3 = 1/125
Plugging into the expected value formula above:
E(x) = 1/(1/125) = 125.
Therefore, the expected number of draws to draw 3 black cards consecutively is 125.
Question 2
A tractor is making its way daily from the farm to the work site and back. The tractor travels part of the way on the road, at 30 meters per minute, and part of it through the field, at 18 meters per minute. Let X be the distance from the farm at which the tractor goes off the road.
What should X be so that the ride takes the least time?
Answer and Explanation
The correct answer is X = 60 m.
The way the tractor travels is marked purple in the sketch below:
For convenience, we will denote D = 96 – X.
The total time travelled is the sum of the times on the road and through the field:
To find the value of D to allow the shortest ride time, we will differentiate T(D), and equate to zero:
After simplifying, the equation above becomes:
576D2 = 746,496
So, D = 36, and therefore X = 60 m.
Question 3
There are 6 plates on the dinner table. Two plates are round, and the rest are square. In how many ways can you place 2 omelets and 1 salad so that at least one food item is on a round plate?
Assumptions:
- Only one item can be placed on each plate.
- The omelets are indistinguishable.
Answer and Explanation
The correct answer is 54.
Note: In the following explanation we use the notation nCk for “n choose k”.
The number of options so that at least one food item is on a round plate equals:
[Total number of arrangement options] – [Number of options to arrange all food items on square plates only]
Total Number of Options
The total number of options is acquired by multiplying the number of options arranging the omelets by the number of options arranging the salad.
- Omelets – 2 omelets in 6 plates (6C2)
- Salad – 1 salad in 4 remaining plates (4C1)
So, the total number of options to arrange the food items across all plates is:
(6C2) x (4C1) = 60
Note: It is incorrect to calculate as (3C6), since while the omelets are indistinguishable, they are naturally distinguishable from the salad.
Number of Options to Arrange All Food Items on Square Plates Only
The number of options to arrange the 3 food items on square plates only is calculated similarly:
- Omelets – 2 omelets in 4 plates (4C2)
- Salad – 1 salad in 2 remaining plates (2C2)
So, the total number of options to arrange the food items across square plates only is:
(4C2) x (2C2) = 6
Number of Options So That at Least One Food Item Is on a Round Plate
As previously mentioned:
(6C2) x (4C1) – (4C2) x (2C2) = 60 – 6 = 54
Question 4
Anna, Bella, and Carol have the following conversation:
- Anna: “Bella, your age is 1.7 times my age.”
- Carol: “Anna, you are more than 8 years younger than me.”
- Anna: “Carol, your age is the average of my age and Bella’s.”
- Bella: “Carol, you’re the youngest of us.”
Assumptions:
- When one of the women speaks to someone younger, she lies. When she speaks to someone older, she speaks the truth.
- No two women are the same age.
- All ages are integers.
How old is Anna?
Answer and Explanation
Anna is 20 years old.
Let’s analyze each statement, starting with those that can yield the most accurate information.
Statement 4 – Bella: “Carol, you’re the youngest of us.”
If this statement is TRUE, Bella is older than Carol, and therefore lies – a contradiction. Therefore, this statement is necessarily FALSE.
This means that Bella is older than Carol, but Carol is not the youngest. Based on this statement alone, we can deduce the order of the speakers’ ages:
Bella is the oldest, Carol is second oldest, and Anna is the youngest.
Statement 3 – Anna: “Carol, your age is the average of my age and Bella’s.”
This statement supports our conclusion from statement 4. Now we can also formulate the first equation:
(i) C = [B + A]/2
Statement 1 – Anna: “Bella, your age is 1.7 times my age.”
Since we know that Anna is the youngest, this statement is necessarily TRUE. We can formulate the second equation:
(ii) B = 1.7A
Statement 2 – Carol: “Anna, you are more than 7 years younger than me.”
Since Carol is older than Anna, this statement is necessarily FALSE. This means that Carol is no more than 7 years older than Anna:
(iii) C – A ≤ 7
Combining equations (i) and (ii):
C = 1.35A
Since A, B, and C are all integers, A has to be divisible by 20: {20, 40, 60…}
Let’s plug in the first two options and see if it satisfies the conditions:
- Anna – 20 ; Carol – 27 ; Bella – 34
- Anna – 40 ; Carol – 54 ; Bella – 168
It’s easy to see that assuming Anna is 40 does not satisfy statement 2, since under these terms, Carol is 14 years older than Anna.
Therefore, the only possible option is that Anna is 20 years old.
Question 5
Consider a fair 20-sided die. Roll the die 8 times. Let D be the number of rolls that are divisible by 6. Calculate E(D).
Answer and Explanation
The correct answer is 6/5.
The distribution of the die rolls can be described as a discrete random variable uniformly distributed across the integers 1-20. Each roll has an equal probability of 1/20 = 0.05.
The number of possible rolls divisible by 6 is 3 (6, 12, 18), so the total probability of a such a roll is 3 x 0.05 = 0.15.
Therefore, we can consider the variable D as a binomial random variable with success probability p = 0.15 and a number of trials n = 8.
E(D) = n x p(D) = 8 x 0.15 = 6/5.
Pro Tip
The answer 1.2 will not be acceptable in the actual assessment – read in the Test Interface section.
SIG Problem Solving Assessment Preparation
I strongly recommend JobTestPrep’s SIG Problem Solving Assessment Preparation.
- The ONLY prep accurately simulating the assessment.
- An authentic mock test + Additional practice by topic.
- A money-back guarantee policy
What Do You Get?
- A full-length test simulation (15 questions, 60 minutes)
- 4 additional practice tests by topic (35 questions total)
- Detailed answers and explanations to all questions
- A money-back guarantee
Full Disclosure: I am affiliated with JobTestPrep. Clicking the links helps me provide you with high-quality, ad-free content.
Tips
Considering all the unique features of the SIG Problem Solving Assessment, here are 3 tips for acing it:
Tip #1 – Start by Briefly Going Over the Questions
Unlike many other pre-employment tests, the Test Interface of the SIG Problem Solving Assessment allows you to go back and forth between test questions. Given the complexity of the questions and the rather generous time limit, it is recommended to start by briefly going over all test questions before rushing in to solve them.
Here are several recommendations to consider:
- Start with the questions you feel more confident about.
- “Cluster” questions of the same type (e.g., combinatorics) and solve them consecutively for a better use of your time.
- Probability and combinatorics questions tend to require a higher level of mathematical knowledge and understanding, but are less time consuming. Calculus and logic questions are the opposite – more straightforward but require longer calculations.
Tip #2 – Use Your Calculator’s Fraction Button
The SIG Problem Solving Assessment allows you to use a calculator. In addition, it requires all answers to be entered in the form of integers or fractions:
- 2.25 → 9/5
- 8 → either 8 or 8/1 (depending on the input format)
Most scientific calculators include a fraction button that allows you to quickly convert decimals to fractions. With the unique input structure of the SIG test, it is especially helpful.
Tip #3 – Memorize Your Formulas
Make sure you are well-rehearsed on all the important basic formulas used in probability and combinatorics, as well as commonly used derivatives. You are not allowed to use any resources other than a pen, paper, and a calculator, so you will need to memorize them.
Preparation
There is currently only one viable, comprehensive prep option available today – JobTestPrep’s SIG Problem Solving Assessment Prep Course.
Below I give all the reasons why, All screenshots are taken from the preparation pack.
Full Disclosure: I am affiliated with JobTestPrep. Clicking the links helps me provide you with high-quality, ad-free content.
Reason #1 – Tailored for the Actual Assessment
JobTestPrep’s SIG prep course contains a full-length mock test of the SIG Problem Solving Assessment that emulates the actual test’s level of difficulty, content matter, and time constraints. It will provide you with the most authentic and accurate prep experience for the assessment.
Reason #2 – Additional Practice by Topic
Alongside the full-length mock test, the JobTestPrep’s SIG Prep Course includes a variety of practice questions divided by topics. These will allow you to strengthen your skills and work on your weaker areas, The practice drills can all be completed within the 7-day timeframe you have to take the SIG assessment.
Reason #3 – Highly Detailed Explanations and Tips
Each question in the prep course is accompanied by highly detailed explanations and solving tips, so you make the best out of the studying process.
Get serious about your career as a quantitative trader/researcher! Start preparing for your SIG Problem Solving Assessment!
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