PRACTICE GUIDE GOLDMAN SACHS
Goldman Sachs Math Practice Test
Outcry’s Goldman Sachs math practice section has 10 questions in 22 minutes. These numbers describe the linked mock; the source check below distinguishes published details from practice settings.
Outcry follows those two clocks. Two coding questions, ten maths questions, JavaScript execution, navigation and scoring are practice settings. Other Engineering applicants have a different diagnostics challenge.
Outcry is not affiliated with Goldman Sachs 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 Goldman Sachs’s own.
What it screens
A global investment bank; this guide covers the Quantitative Strategist (Strats) track specifically, not the firm's other divisions.
- ✓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 Goldman Sachs
Goldman Sachs’ HackerRank guide assigns Software Fundamentals (30 minutes) and a multiple-choice maths challenge (22 minutes) to Quantitative Strategist applicants.
Practice stage: Initial technical assessment · Strats track. Outcry follows those two clocks. Two coding questions, ten maths questions, JavaScript execution, navigation and scoring are practice settings. Other Engineering applicants have a different diagnostics challenge.
The format
These are the settings used by Outcry’s Goldman Sachs practice sitting. They are not automatically the employer’s published format; see the linked assessment’s source check.
| Questions | 10 |
|---|---|
| Time | 22 minutes |
| Per question | 2.2 minutes |
| Negative marking | No |
| Answer style | Multiple choice |
| Where it sits | Initial technical assessment · Strats track |
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 Goldman Sachs’s.
Expected value and odds
Pricing a bet, converting between odds and probabilities, and deciding whether to take it.
Example
You win 20 with probability 65% and lose 20 otherwise. Expected value per bet?
- 6
- 13
- 20
- 0
Answer 6
65% × 20 − 35% × 20 = 6. The edge is the probability gap times the stake.
Counting and combinatorics
Arrangements, selections and the complement trick that turns a hard count into an easy one.
Example
A 4-sided die is rolled until it shows a 4. The first 4 on roll n pays $4^n. The game is stopped after 9 rolls and pays nothing if no 4 has come up. What is the expected payout?
Answer 9841
The first 4 lands on roll n with probability (3/4)^(n-1) x 1/4, and that roll pays $1 x 4^n. Multiplying gives $1 x 3^(n-1), so the terms grow rather than shrink and the sum over the 9 rolls is $9841. Same shape as St Petersburg: the payout outruns the probability, so only the cap keeps the expectation finite.
Estimation under uncertainty
A number nobody knows exactly, reasoned to the right order of magnitude out loud.
Example
A balance reports which of two groups is heavier, or that they match. Exactly one bar in a batch is heavier than the rest. With 4 weighings and worst-case luck, what is the largest batch you can guarantee to pin down?
Answer 81
Counting outcomes: 4 weighings produce 3^4 = 81 distinguishable results, and each result can name at most one bar. The bound is met by thirds - weigh 27 against 27 and whichever way it falls you are left with 27 candidates and 3 weighings.
Ranking outcomes
Ordering several events by likelihood, where only the exact order scores.
Example
A. exactly one tail in four coin flips B. a die roll of 5 or more C. a heart or a spade from a full deck
Rank most likely to least likely:
- B > A > C
- A > B > C
- A > C > B
- C > B > A
Answer C > B > A
A: 25.0% · B: 33.3% · C: 50.0%
Waiting times and repeated trials
How long until the first success, and why the answer is rarely the average you expected.
Example
An index rises 2.3% on 5 days and falls 2.3% on 5 other days. What is the net change over the 10 days, as a percentage?
Answer -0.26
Each up-down pair multiplies to 1 − 2.3%² = 1 − 0.05%. With 5 pairs the drag is about −5 × 0.05% = -0.26%.
Symmetry arguments
Questions that collapse to one line once you notice the two cases are mirror images.
Example
A fair coin is flipped 4 times. What is the chance every flip is heads, as a percentage?
Answer 6.25
(1/2)^4 = 1/16 = 0.063, or 6.25%.
What a good score looks like
Use this mock’s score and worked review to identify skills to practise. No Outcry score guarantees a pass or a hiring outcome; a current employer threshold for this practice paper has not been verified.
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.
- 03Sanity-check the magnitude before committing. A probability above one or an expectation outside the range of outcomes is a caught error, and these papers plant both as options.
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 Goldman Sachs
Common questions
- Is this Goldman Sachs’s official math test?
- No. Outcry generates its own questions. Goldman Sachs’ HackerRank guide assigns Software Fundamentals (30 minutes) and a multiple-choice maths challenge (22 minutes) to Quantitative Strategist applicants. Outcry follows those two clocks. Two coding questions, ten maths questions, JavaScript execution, navigation and scoring are practice settings. Other Engineering applicants have a different diagnostics challenge.
- How long is this math practice section?
- 10 questions in 22 minutes in the Outcry mock. These are practice settings unless the source check explicitly confirms them.
- How is the practice marked?
- Correct answers earn 1 mark unless the question states another weight. Wrong answers lose 0; unanswered items lose 0, including timeouts. These rules apply to this mock.
- Where can I check the employer’s process?
- See the public source check on the linked assessment. Your role-specific invitation governs the actual format, permitted tools and scoring.