PRACTICE GUIDE D. E. SHAW
D. E. Shaw Aptitude: what the test is, and how to train for it
The D. E. Shaw aptitude screen is 14 questions in 28 minutes - about 2 minutes each - answered by picking one of the options. It marks negatively, so a wrong answer costs you a mark and a skip costs you nothing.
Where it sits: Aptitude section of the same test. The practice sitting on this page runs the same item count, the same clock and the same marking rule, with questions generated by Outcry rather than taken from D. E. Shaw.
D. E. Shaw's own interviewing guide describes its US and UK quant process as interview-only, with no online assessment at all. This guide instead models the firm's India-campus screen, which does run one - so if you're interviewing for a US or UK quant role, this practice does not reflect what you'll actually sit.
Outcry is not affiliated with D. E. Shaw and has no access to their assessment content. This guide describes an assessment format that candidates report publicly; the questions here are generated by Outcry and are not D. E. Shaw’s own.
What it screens
A quantitative investment firm based in New York, among the largest and longest-running in the industry.
- ✓Expected value computed fast and used to make a decision
- ✓Conditional probability and Bayes updates without formal notation
- ✓Ranking likelihoods rather than computing them exactly
- ✓Fermi estimation: decomposing an impossible question into three easy ones
Where it sits at D. E. Shaw
This section does not arrive on its own. It opens the paper, and the sitting around it runs 95 minutes and 28 items in total, with Technical, Coding problem 1 and Coding problem 2 on the same continuous clock. Candidates who prepare only for this round tend to be caught by the pacing of the rest.
There is no going back. You answer or skip, and the next item loads, which means the decision to leave an item is final at the moment you make it.
The format
These are the numbers the D. E. Shaw sitting on this site runs on, matching the format candidates report.
| Questions | 14 |
|---|---|
| Time | 28 minutes |
| Per question | 2 minutes |
| Negative marking | Yes - a wrong answer costs a mark |
| Answer style | Multiple choice |
| Where it sits | Aptitude section of the same test |
What it tests, with a worked example
Every example below is generated by Outcry, drawn from the same question generators the timed drills run. None of them is D. E. Shaw’s.
Conditional probability
Bayes' rule in disguise: a test result, a signal, a drawn card, and what it implies.
Example
A token starts at position 1 on the integers 0 to 4. Each step it moves left or right with probability 1/2, and positions 0 and 4 absorb. What is the expected number of steps until absorption?
- 3
- 5
- 4
- 6
Answer 3
E[steps] from i is i(N−i) - the martingale Sₙ²−n stopped at the boundary: 1·3 = 3.
Distributions you should know cold
Binomial, geometric and uniform means and variances, applied rather than quoted.
Example
1% of a population carries a trait. A screen flags 95% of carriers and wrongly flags 2% of non-carriers. Someone is flagged. What is the chance they carry it?
- 95%
- 98%
- 1%
- 32.4%
- 67.6%
Answer 32.4%
True flags are 1 × 0.95 = 0.95% of everyone, false flags 99 × 0.02 = 1.98%. The share that is real is 0.95/(0.95 + 1.98) = 32.4%.
Estimation under uncertainty
A number nobody knows exactly, reasoned to the right order of magnitude out loud.
Example
An 8 by 10 grid of squares has the two squares at opposite ends of one diagonal cut out, leaving 78. A domino covers exactly two squares that share an edge. What is the largest number of dominoes that fit without overlapping or hanging off?
Answer 38
Colour the grid like a chessboard. A domino always takes one square of each colour. Opposite corners of a diagonal share a colour, so cutting them leaves 38 of one colour and 40 of the other. The smaller pile caps the dominoes at 38, and that many really do fit, so the cap is the answer. The counting argument, not a picture, is what settles it.
Ranking outcomes
Ordering several events by likelihood, where only the exact order scores.
Example
The spread FOXTROT minus a hedge ratio times ECHO has a long-run mean of $4.16 and a standard deviation of $2.60. It is trading at -$2.63. What is the z-score, as a signed number?
Answer -2.612
A z-score measures the distance from the mean in standard deviations: (-$2.63 - $4.16) / $2.60 = -$6.79 / $2.60 = -2.612. The spread is 2.61 standard deviations below the mean, so the trade is to buy the spread: long FOXTROT and sell the hedge and wait for reversion. The z-score is the whole signal in a stat arb book, and it is only as good as the estimate of the mean and the standard deviation behind it: a pair whose relationship has genuinely broken keeps printing larger z-scores all the way down.
Waiting times and repeated trials
How long until the first success, and why the answer is rarely the average you expected.
Example
A quote engine throws an average of 1.9 errors an hour, Poisson. What is the chance of an error-free hour, as a percentage?
Answer 15
P(0) = e^−1.9 = e^−1 × e^−0.9 ≈ 0.3679 × 0.41 ≈ 0.1496, so about 15%.
Reading the question exactly
At least, exactly, and given that - the three phrases that change the answer entirely.
Example
Revenue by division, $m Division 2016 2017 2018 2019 Rates 140 420 430 325 Macro 390 325 335 300 Credit 305 160 230 480 Equities 175 195 155 225
What was Rates average annual revenue across the four years shown?
- 1315
- 285
- 328.75
- 325
Answer 328.75
140 + 420 + 430 + 325 = 1315, over four years that is 328.75. The midpoint of the highest and lowest, 285, is not the mean.
What a good score looks like
On a paper of 14 questions marked +1 and -1, the arithmetic of the threshold matters as much as the threshold: every wrong answer costs you two places against someone who skipped it. Probability rounds are usually marked as part of a wider battery, so a standalone threshold is rarely reported. Where candidates do describe one it clusters around getting two thirds of the items right, with the caveat that these sections are short enough that two mistakes move you a long way.
How to train for it
- 01Work the standard results until they are recall, not derivation: complement, conditional, binomial mean and variance, geometric expectation.
- 02Practise setting up before calculating. Most wrong answers on these are a correct calculation of the wrong quantity.
- 03Do them timed. A probability question you can solve in four minutes and the paper gives you ninety seconds for is a question you cannot solve.
TRAIN IT HERE
The drills that match each section
Likelihood Ranking
Order events from most to least likely - the exact screen-question format.
Fermi Estimation
Piano tuners in Chicago, atoms in a body - scored on order of magnitude.
Quitters Never Lose
A casino stopping-strategy game that is secretly a martingale lesson.
Tail Risk
Rare events and fat tails, and what they do to a plain expected-value estimate.
SIT THE FULL BATTERY
All the sections back to back on one clock, marked the way the real screen marks them, with a by-skill breakdown at the end. Included with any pass.
Also reported at D. E. Shaw
Common questions
- Is the D. E. Shaw aptitude test multiple choice?
- Multiple choice. You pick one option per question.
- How long is the D. E. Shaw aptitude test?
- 14 questions in 28 minutes, which is about 2 minutes each.
- Is there negative marking on the D. E. Shaw aptitude test?
- Yes. A wrong answer costs you a mark, so an item you cannot see a route through is worth skipping outright - a blind guess on this paper is negative expected value.
- How do I practise for it free?
- Every drill linked on this page is free to play, with no account, inside a daily run cap. Questions are generated fresh each run, so there is nothing to memorise between attempts. The full D. E. Shaw India Campus Online Test sitting puts the sections back to back on one clock.