PRACTICE GUIDE GOLDMAN SACHS
Goldman Sachs Math: what the test is, and how to train for it
The Goldman Sachs math screen is 10 questions in 22 minutes - about 2.2 minutes each - answered by picking one of the options. There is no negative marking, so leaving an item blank gains you nothing over guessing.
Where it sits: Maths section of the same sitting. 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 Goldman Sachs.
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
This section does not arrive on its own. It closes the paper, and the sitting around it runs 52 minutes and 12 items in total, with Software Fundamentals 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 Goldman Sachs sitting on this site runs on, matching the format candidates report.
| Questions | 10 |
|---|---|
| Time | 22 minutes |
| Per question | 2.2 minutes |
| Negative marking | No |
| Answer style | Multiple choice |
| Where it sits | Maths section of the same sitting |
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 non-dividend-paying share trades at $43.73 and the 9-month funding rate is 2.76% continuously compounded. The 9-month forward on 250 shares is quoted at $44.25. What is the trade?
- Buy the forward, short the shares and lend the proceeds: $98.66 at delivery
- Nothing, the difference between $44.25 and $43.73 is just the cost of carry
- Buy the forward, short the shares and lend the proceeds: $130.00 at delivery
- Buy the forward, short the shares and lend the proceeds: $96.64 at delivery
- Sell the forward, buy the shares with borrowed cash: $98.66 at delivery
Answer Buy the forward, short the shares and lend the proceeds: $98.66 at delivery
The fair forward is the spot carried to delivery: F = $43.73 x e^(0.0276 x 0.7500) = $43.73 x 1.020916 = $44.6446. The quote is $44.25, so the forward is cheap by $0.3946 a share. Buy the forward, short the stock at $43.73 and lend the proceeds: the deposit grows to $44.6446, the forward takes $44.25 of it, and the difference is kept. On 250 shares that is $98.66 at delivery. The gap between the forward and the SPOT, $0.52, is mostly carry and is not the edge. $96.64 is that edge discounted back to today, which is what it is worth now rather than at delivery.
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
On a paper of 10 questions with no penalty for a wrong answer, the only thing an unanswered question can do is cost you. 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.
- 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 the Goldman Sachs math test multiple choice?
- Multiple choice. You pick one option per question.
- How long is the Goldman Sachs math test?
- 10 questions in 22 minutes, which is about 2.2 minutes each.
- Is there negative marking on the Goldman Sachs math test?
- No. A wrong answer costs nothing beyond the mark you would have earned, so leaving an item blank is never better than guessing at it.
- 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 Goldman Sachs Strats HackerRank Battery sitting puts the sections back to back on one clock.