Back to the 2026–2027 Junior CandiTech guide.

Older Junior, New Grad, and full-time Akuna Quant Research assessments, kept separate from the current CandiTech format.

Coverage: Junior Quantitative Researcher · New Grad Quantitative Researcher · earlier full-time Quant Research math, video, and coding OAs · 2020–2025

How to use this question bank

The current 2026–2027 Junior CandiTech format is covered in the main guide. The prompts below come from earlier Akuna math, video, and coding assessments.

1. Use the Junior questions first. Moments and improper integrals came from a Junior Quantitative Researcher math-video assessment.
2. Use the broader Quant Research questions for topic practice. They show repeated probability, Markov-chain, calculus, and spoken-reasoning patterns.
3. Keep coding separate from CandiTech. Frequency Sort, graph order, Extraordinary Substrings, project selection, and k-star were HackerRank-style questions.
4. Practice under a five-minute timer. Short solving and explanation windows appeared repeatedly in the math rounds.

Historical Junior math and video OA questions

1. Work with moments of a random variable.
2. Decide whether an improper integral converges or diverges.
3. Solve five technical mathematics questions on video.
4. Use five minutes to understand, calculate, and explain each answer.
5. Give a final numerical or mathematical conclusion rather than only describing an approach.

Additional historical MCQs and math prompts from other Akuna Quant Research tracks

These were reported in earlier Akuna Quant Research assessments. They are included for topic practice, separate from the current Junior CandiTech set.

Probability and expected value

1. Roll a fair die until the cumulative sum is divisible by 3. Find the expected number of rolls.
2. Compare two games with different small and large payouts. Calculate both expected values and choose one.
3. Pick two random points on a rope. Find the expected distance between them.
4. Break a stick at two random points. Find the probability that the three pieces form a triangle.
5. Use fair-coin flips to generate one of {0,1,2} uniformly. Find the expected number of flips.
6. Given two variances and a correlation, find the variance of the sum of the random variables.
7. Determine the possible range of a correlation coefficient under stated conditions.
8. Analyze the distribution or CDF of a sum of iid Uniform random variables.
9. Solve a mod-3 state problem using a Markov chain.
10. Work through a Poisson-distribution word problem.

Statistics and modeling

1. Explain the bias–variance tradeoff.
2. Describe how Monte Carlo simulation could solve a probability problem.
3. State the assumptions behind a statistics word problem.
4. Explain what data is needed to model an open-ended scenario.
5. Defend a statistical method rather than only naming it.
6. Connect a quantitative project to its model choices, weaknesses, and validation.

Linear algebra

1. Find the eigenvalues and eigenvectors of a matrix.
2. For an n × n matrix with n on the diagonal and 1 everywhere else, derive its eigenvalues and eigenvectors.
3. Diagonalize a matrix.
4. Use rank to decide whether Ax=b has one solution, no solution, or many solutions.
5. Reason about column space and null space.
6. Compare statements about X+Y and X-Y when X and Y are normal random variables.
7. Decide which three-dimensional point is closest to the origin.

Calculus and numerical methods

1. Differentiate x^x.
2. Integrate 1/(x ln x).
3. Evaluate limits involving x/(e^x-1).
4. Evaluate a limit involving cos(2x)/(x(e^x-1)).
5. Use Newton’s method to solve x^n=a.
6. Discuss Newton’s method convergence.
7. Given a moment-generating function, recover a mean, variance, or second moment.
8. If X is standard normal, derive the density of X².
9. Solve a basic derivative-based optimization problem.

Counting and discrete reasoning

1. Sum the integers from 1 through 100 after removing every number containing the digit 7 or 8.
2. Count the integers in that range that contain a 7 or 8.
3. Assign 30 hires to two offices under stated restrictions.
4. Find the distribution of the median of three iid Uniform random variables.
5. Arrange digits so that every adjacent pair has a divisor-or-multiple relationship.
6. Work through short combinatorics questions under a five-minute timer.

Junior and New Grad coding OA questions

Frequency Sort

Sort values by frequency. When two values have the same frequency, use the value itself as the tie-breaker.

Delivery Management

Given an unweighted graph and a starting node, return the nodes in visit order. Order nodes by distance from the start, then use node value to break equal-distance ties.

Extraordinary Substrings

Map each character to a numerical value. Count substrings whose average satisfies the required integer condition.

Project selection

Use project cost and profit data to choose two projects that maximize total profit.

Maximum k-star

Find the maximum-sum k-star in a graph.

Coding conditions reported across Junior and New Grad assessments

1. Three questions in 60 minutes.
2. Some versions asked candidates to finish any two, with the third treated as bonus.
3. One Junior assessment did not allow external libraries.
4. Code cleanliness and readability were explicitly mentioned.
5. Tight runtime limits and hidden edge cases mattered.

Candidate timelines by role

01: Junior math-video assessment

Interview cycle: 2021–2022
Role: Junior Quantitative Researcher

1. The HackerRank stage contained three medium coding problems.
2. The candidate could complete any two; the third counted as bonus.
3. The next round contained five technical math questions on video.
4. Reported topics included moments and divergent integrals.
5. Each response allowed five minutes.
6. The candidate still advanced after believing only one answer was correct.

02: Five-question Junior video round

Hiring cycle: 2026
Role: Junior Quantitative Researcher

1. A coding OA came first.
2. The math-video invitation arrived about three days later.
3. The round contained five math or brainteaser questions.
4. Each question allowed five minutes.
5. The candidate had to explain the solution while being recorded.

03: Junior coding assessment without libraries

Interview date: August 2023
Role: Junior Quantitative Researcher
Result: No offer

1. Three coding questions in one hour.
2. The candidate did not consider the questions unusually difficult.
3. External libraries were not allowed.
4. The process ended after this assessment.

04: New Grad algorithm set

Interview cycle: 2023 New Grad
Role: Quant Research

1. Three algorithm questions in one hour.
2. The reported tasks were Frequency Sort, Delivery Management, and Extraordinary Substrings.
3. The substring problem required more than a simple brute-force solution.

05: Strict-runtime New Grad assessment

Interview cycle: 2024 New Grad
Role: New Grad Quantitative Researcher
Result: Did not advance

1. The tasks covered two-project profit, graph visit order, and maximum k-star.
2. The execution environment had a tight runtime limit.
3. The candidate completed two problems and left skeleton code for the third.

06: Six-question one-way math assessment

Interview date: October 2020
Role: Full-time Quantitative Researcher

1. Six questions with five minutes for each.
2. The final five questions were multiple-choice mathematics.
3. One preserved question gave E[e^(tX)] = e^(t²) and asked for E[X²].

07: Markov chains and calculus limits

Interview date: October 2022
Role: Full-time Quant Research

1. Five questions with five minutes for each.
2. There was no preparation period before a question began.
3. One prompt asked about the candidate’s strongest project.
4. The mathematics included a mod-3 Markov-chain problem and an exponential calculus limit.

08: Three probability and combinatorics recordings

Interview cycle: 2023
Role: Quant

1. Three multiple-choice questions.
2. Five minutes for each response.
3. The candidate explained the reasoning while being recorded.
4. Preserved prompts included the cumulative-die mod-3 problem and assigning 30 hires to two offices.

09: Seven probability questions with spoken explanations

Interview date: December 2025
Role: Quantitative Researcher

1. Three Python problems came first.
2. The next assessment contained seven probability questions.
3. Each answer allowed five minutes and required a spoken explanation.
4. Several questions involved Markov chains.

What repeated often enough to prioritize

Tier 1: Core mathematics

1. Expected value, variance, and moments.
2. Conditional probability and independence.
3. Markov-chain states and expected stopping times.
4. Common discrete and continuous distributions.

Tier 2: Supporting mathematics

1. Improper integrals and convergence.
2. Limits involving exponential functions.
3. Combinatorics under a short timer.

Tier 3: Coding patterns

1. Custom sorting and tie-breaking.
2. Graph traversal and distance order.
3. Substring counting with a character-to-number mapping.
4. Runtime analysis and clean implementation.

Final checklist

Math and video OA

☐ Solve five probability questions with a five-minute limit for each.

☐ Review moments, variance, covariance, and moment-generating functions.

☐ Practice one Markov-chain stopping-time problem.

☐ Review improper integrals and exponential limits.

☐ Explain every assumption while solving.

Coding OA

☐ Complete three coding problems in one hour.

☐ Practice custom sorting and graph tie-breaking.

☐ Test runtime, duplicates, and boundary cases.

☐ Repeat one mock without third-party libraries.

Return to the 2026–2027 Junior CandiTech guide.