SIG Assessment 2027: Questions & Answers

Preparing for a SIG online assessment or quantitative evaluation for the 2027 recruiting cycle? Start by practicing the reasoning you can transfer between questions: arithmetic, conditional probability, expected value, and decisions under time pressure. Below are twelve original practice questions with complete solutions, followed by a two-week preparation plan.

Your preparation priorities: count outcomes accurately, update probabilities when information changes, calculate expected value, and solve unfamiliar problems without losing time. Work through the foundations first, then tackle the four harder questions. All exercises below are original Quant Blueprint practice material.

Start with the right role and instructions

Susquehanna hires across trading, research, and technology. Its trading careers page describes decision-making, game theory, and quantitative modelling as part of trader development. Build your preparation around those skills: model the problem, calculate the result, and explain what changes when you receive new information.

Before starting an assessment, check:

• Role: trading, research, software engineering, or another track. Coding preparation and trading arithmetic are not interchangeable.
• Rules: calculator use, scratch paper, navigation, breaks, and whether unanswered or incorrect responses are penalized.
• Timing: overall and per-section limits, deadline and timezone, and how technical problems should be reported.
• Adjustments: contact the recruiting team before the deadline if you need an accommodation or clarification.

For wider context, see the SIG career guide. If you want to find your weakest topic first, use our free quant interview diagnostic.

SIG Quantitative Evaluation vs Problem Solving Assessment

Train for both a short quantitative test and a longer problem-solving test. Commonly reported formats give you two useful practice benchmarks:

Use your invitation to choose the final rehearsal format. Test length can vary across applications. Check the stated time limit, question count, navigation, answer entry, and calculator rules before starting.

For a 17-question, 60-minute practice set, the average budget is about 3 minutes 32 seconds per question. Spend less on straightforward questions to create room for the difficult ones. If the test allows returning to questions, mark a problem and move on when you have no productive approach. If it does not, make the best decision available before advancing.

Eight original SIG-style practice questions

Write down your answer before expanding each solution. Begin untimed. Once you can explain the method reliably, repeat similar problems with a timer.

1. Arithmetic: 17 × 23

Question: Calculate 17 × 23 without a calculator.

Show answer and explanation

Answer: 391. Write the factors as 20 − 3 and 20 + 3. Their product is 20² − 3² = 400 − 9 = 391.

Why this helps: look for structure before doing long multiplication. A second check is 17 × 20 + 17 × 3 = 340 + 51. When training, record whether a mistake came from the method or arithmetic.

Try next: 48 × 52. The same identity gives 2,500 − 4 = 2,496.

2. Sequences: make your assumption explicit

Question: Find a simple rule for 2, 6, 12, 20, 30 and predict the next value.

Show answer and explanation

Answer: 42 under the rule n(n + 1). The differences are 4, 6, 8, 10, so extending that pattern adds 12. The nth term is the product of consecutive integers.

Common mistake: treating a finite sequence as having a mathematically unique continuation. Many rules fit five observations. In a reasoning question, state the simple rule you chose and check it against every term.

3. Sampling without replacement

Question: A bag contains three red and five blue balls. You draw two without replacement. What is the probability both are red?

Show answer and explanation

Answer: 3/28. The first ball is red with probability 3/8. Conditional on that result, two red balls remain among seven, so multiply 3/8 by 2/7: 6/56 = 3/28.

Common mistake: using 3/8 twice. That would model replacement and independence, neither of which holds here.

Follow-up: the probability of exactly one red is (3/8 × 5/7) + (5/8 × 3/7) = 15/28. Include both possible orders.

4. Bayes: identify the updated sample space

Question: You choose one of two coins with equal probability. One is fair; the other has heads on both sides. After one toss lands heads, what is the probability you selected the double-headed coin?

Show answer and explanation

Answer: 2/3. The fair-coin-and-heads branch has probability 1/2 × 1/2 = 1/4. The double-headed-and-heads branch has probability 1/2 × 1 = 1/2. Divide the branch of interest by all heads branches: (1/2) / (1/4 + 1/2) = 2/3.

Follow-up: after two heads from the same coin, the answer becomes (1/2) / (1/2 + 1/8) = 4/5. Repeated evidence changes the odds; it does not make certainty.

5. Expected value: include the entry cost

Question: A game costs $5. Roll a fair six-sided die. A six pays you $25; all other outcomes pay zero. What is your expected net profit?

Show answer and explanation

Answer: −$5/6, about −$0.83 per play. Expected payout is $25/6. Subtract the $5 entry cost on every play. A positive possible prize is not the same as positive expected profit.

Follow-up: a risk-neutral player breaks even at an entry price of $25/6. Expected value is a long-run average, not a guarantee of the outcome of any one game.

6. Conditional probability with dice

Question: Two fair dice are rolled. You are told at least one shows six. What is the probability their sum is eight?

Show answer and explanation

Answer: 2/11. There are 11 equally likely ordered outcomes containing at least one six: six with the first die showing six, plus six with the second, minus the double-counted (6, 6). Only (6, 2) and (2, 6) sum to eight.

Common mistake: answering 1/6. That answers a different question: if a particular die is known to be six, what must the other die show? The process that gives you information matters.

7. Fair value and a follow-up decision

Question: A ticket pays the sum of two independent fair dice in dollars. What is its expected payout? How does your valuation change if you learn the first die is six?

Show answer and explanation

Answer: $7 before the information and $9.50 afterward. Each die has mean 3.5. Initially, linearity of expectation gives 3.5 + 3.5. After observing the first die, use 6 + 3.5.

Explain the limit: expected payout alone does not determine a safe market-making quote. Your inventory, risk tolerance, trading costs, and what the other person knows may matter. An interviewer may be testing how you update your answer when assumptions change.

8. Should you guess under negative marking?

Question: In a hypothetical test, a correct answer earns one point, a wrong answer loses 0.25, and a blank earns zero. When does attempting a question have positive expected score?

Show answer and explanation

Answer: let p be your probability of being correct. Expected score is p − 0.25(1 − p) = 1.25p − 0.25. It is positive when p is greater than 0.20. At exactly 0.20 it is zero.

This is an example scoring system, not a claim about SIG's rules. Also consider opportunity cost: a positive-score guess can still waste time you could spend on an easier question. Read the actual rules before choosing a skipping or guessing strategy.

Four harder problems for the longer assessment

These original examples extend the foundations into counting, continuous probability, random walks, and optimization. Write the model before the calculation.

9. Paths through a grid

Question: Starting at the bottom-left corner of a grid, reach a point four steps right and three steps up. You may only move right or up. How many paths are possible?

Show answer and explanation

Answer: 35. Each path is a sequence of seven moves containing exactly three upward moves. Choose their positions: C(7, 3) = 7 × 6 × 5 / (3 × 2 × 1) = 35.

Follow-up: how many of these paths pass through the point two steps right and one step up? There are C(3, 1) = 3 ways to reach that point and C(4, 2) = 6 ways to finish. Multiply to get 18. If the point is forbidden, subtract: 35 − 18 = 17.

10. The larger of two random numbers

Question: X and Y are independent, each uniformly distributed between zero and one. What is the expected value of max(X, Y)?

Show answer and explanation

Answer: 2/3. For a value t between zero and one, the maximum is at most t only when both draws are at most t. Its cumulative distribution is t², so its density is 2t. Integrate t × 2t from zero to one to obtain 2/3.

Check: the maximum should average more than 1/2 and less than one. For n independent uniform draws, the same argument gives an expected maximum of n/(n + 1).

11. A random walk with stopping boundaries

Question: You start with two counters. Each fair coin toss adds one on heads or removes one on tails. Stop when you reach zero or five. What is the probability you reach five first?

Show answer and explanation

Answer: 2/5. Let p(i) be the probability of reaching five from i. The boundary values are p(0) = 0 and p(5) = 1. For an interior position, p(i) = [p(i − 1) + p(i + 1)] / 2. The solution is linear: p(i) = i/5.

Follow-up: the expected number of tosses from i is i(5 − i), obtained from e(i) = 1 + [e(i − 1) + e(i + 1)]/2 with zero boundary values. From two, the answer is 6 tosses. A biased coin changes the recurrence solution.

12. Optimize a simple quantity

Question: A rectangle has perimeter 20. What side lengths maximize its area?

Show answer and explanation

Answer: 5 and 5, giving area 25. If one side is x, the other is 10 − x. Area is x(10 − x) = 25 − (x − 5)². The squared term is smallest at x = 5. Calculus gives the same answer: differentiate to get 10 − 2x, then set it to zero.

What to explain: the valid domain is zero to ten, the endpoints have zero area, and the quadratic is concave. Do not present a stationary point without checking that it is the required maximum.

For another set of complete explanations, try our six solved SIG question-bank examples, including chord lengths, the broken-stick problem and order statistics.

What to prepare after the online assessment

Keep explaining your decisions aloud. Move from a written answer to a short account of your assumptions, method, result, and check. Then ask a partner to change a number or condition and update your answer in real time.

For a motivation conversation, prepare one example of making a decision with incomplete information, one of changing your mind after new evidence, and one of improving a team result. Describe what you actually did. Read Susquehanna's trading careers material and connect the work to your own interests rather than memorizing an employer slogan.

For market-making practice, start with question seven: state the expected payout, explain what information would change it, and discuss why your buy and sell prices might differ. This links probability to a decision instead of treating it as an isolated calculation.

A two-week SIG preparation plan

Use this as a starting schedule and move time toward the topics your error log identifies. If your deadline is closer, prioritize the diagnostic, core probability, and the practice review rather than trying to cover everything.

A useful error log distinguishes concept, setup, arithmetic, and time management. If you repeatedly model dependent draws as independent, faster arithmetic will not fix the problem. If your model is sound but you copy numbers incorrectly, work on execution before adding harder questions.

Common questions

What is the SIG assessment passing score?

Set a 90% accuracy target on mixed practice before pushing for speed. SIG does not publish a universal passing score in its recruiting guidance. The 90% target is our training benchmark. Start untimed, fix your recurring mistakes, then reduce the time budget while keeping accuracy high. A rushed 70% is a signal to improve your method, not to rush harder.

Track arithmetic and probability separately. If arithmetic is accurate but slow, drill shortcuts and fraction conversions. If probability is inconsistent, work on sample spaces and conditional reasoning before doing another timed mock.

Is the SIG assessment the same for trading, research, and software roles?

Prepare for the role you applied to. For trading, start with mental math, probability, expected value, and decisions under pressure. For research, add statistics, coding, and explaining your modelling choices. For software roles, put algorithms, data structures, and implementation first.

Use the sections and tools listed in your assessment invitation to set the final practice mix. The exercises in this guide build the trading and quantitative reasoning foundation.

What should I study after this guide?

First, redo every question you missed without looking at the solution. Then solve its follow-up. You have learned the method when you can handle the variation, not just repeat the answer.

Next, take the eight-question diagnostic and use your weakest topics to build a four-week study plan. If you have another firm in your pipeline, add the Optiver practice guide. Keep a written error log throughout: the repeated mistake is the next thing to fix.

Prepare with a plan and feedback

Knowing an answer is only the beginning. You need to choose the right approach quickly, explain it clearly, and adapt when the interviewer changes the question.

Quant Blueprint's interview preparation program brings together technical lessons, a question bank, mock interviews, and individual feedback. Work through the concepts, practice explaining your reasoning, and use the feedback to focus your next session.

Book a free session to learn how the program works. See the preparation process, understand the support available, and decide whether it fits your target roles and interview timeline. You can also read student experiences.

Further reading: Susquehanna trading careers and Susquehanna careers. Original practice exercises and study guidance by Quant Blueprint; updated September 28, 2026.