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Goldman Sachs Interview Questions

Problems
58
Topics
9
Hard
2

Below are 58 quant interview questions of the kind asked at Goldman Sachs, spanning Brain Teasers, Probability, Stochastic Processes, Calculus & Linear Algebra, Algorithms & Numerical, Finance, Options & Greeks, Portfolio & Risk, Statistics. Each comes with a full worked solution — sign in to check your answers and track your progress.

2
Trailing Zeros in 100!
Brain TeasersGoldman SachsJ.P. Morgan
52%Easy
3
Two Eggs, 100 Floors
Brain TeasersGoogleGoldman Sachs
31%Medium
6
Sum 1 to 100
Brain TeasersJane StreetGoldman Sachs
72%Easy
9
Last Digit of 2^100
Brain TeasersGoldman SachsMorgan Stanley
60%Easy
11
Burning Ropes — 45 Minutes
Brain TeasersGoldman SachsMorgan Stanley
76%Medium
13
Handshakes at a Party
Brain TeasersGoldman Sachs
67%Easy
15
Ants on a Triangle
Brain TeasersGoldman SachsOptiver
84%Medium
17
Three Switches
Brain TeasersGoldman SachsMorgan Stanley
70%Medium
22
Monty Hall
ProbabilityGoldman SachsMorgan Stanley
56%Easy
24
Birthday Problem
ProbabilityGoldman SachsCitadel
52%Medium
28
Bayes — Disease Test
ProbabilityGoldman SachsTwo Sigma
55%Medium
32
Two Children
ProbabilityGoldman SachsMorgan Stanley
66%Easy
48
Expectation of GBM
Stochastic ProcessesGoldman SachsMorgan Stanley
59%Hard
49
Variance of Brownian Motion
Stochastic ProcessesGoldman SachsMorgan Stanley
69%Easy
50
Covariance of Brownian Motion
Stochastic ProcessesGoldman SachsTwo Sigma
65%Medium
53
Quadratic Variation of BM
Stochastic ProcessesGoldman SachsTwo Sigma
66%Medium
55
Expected Running Max of BM
Stochastic ProcessesGoldman SachsDE Shaw
54%Hard
62
Definite Integral of x²
Calculus & Linear AlgebraGoldman Sachs
78%Easy
63
Limit of sin(x)/x
Calculus & Linear AlgebraGoldman SachsMorgan Stanley
91%Easy
64
Eigenvalues of a 2×2
Calculus & Linear AlgebraGoldman SachsCitadel
80%Medium
65
Gaussian Integral
Calculus & Linear AlgebraGoldman SachsTwo Sigma
43%Medium
68
Geometric Series
Calculus & Linear AlgebraGoldman Sachs
86%Easy
69
Limit of (1+1/n)^n
Calculus & Linear AlgebraGoldman SachsMorgan Stanley
55%Easy
70
Integral of x·e^(−x)
Calculus & Linear AlgebraGoldman SachsTwo Sigma
74%Medium
71
L'Hôpital — (eˣ−1)/x
Calculus & Linear AlgebraGoldman SachsMorgan Stanley
84%Easy
72
Derivative of ln(x)
Calculus & Linear AlgebraGoldman Sachs
85%Easy
74
Trace = Sum of Eigenvalues
Calculus & Linear AlgebraTwo SigmaGoldman Sachs
82%Easy
76
Integrate x·eˣ
Calculus & Linear AlgebraGoldman SachsMorgan Stanley
73%Medium
87
Monte Carlo — Estimate π
Algorithms & NumericalGoldman SachsTwo Sigma
65%Easy
88
Newton’s Method for √2
Algorithms & NumericalGoldman SachsJane Street
79%Easy
104
Put-Call Parity
FinanceGoldman SachsMorgan Stanley
66%Easy
105
Black-Scholes ATM Call
FinanceGoldman SachsMorgan Stanley
72%Medium
106
Risk-Neutral Probability
FinanceGoldman SachsJ.P. Morgan
81%Medium
107
Zero-Coupon Bond Price
FinanceGoldman SachsPIMCO
63%Easy
108
Futures Fair Value
FinanceGoldman SachsOptiver
63%Easy
109
Duration & Price Sensitivity
FinanceGoldman SachsJ.P. MorganPIMCO
72%Easy
110
Perpetuity Value
FinanceGoldman SachsJ.P. Morgan
61%Easy
111
Rule of 72
FinanceGoldman SachsMorgan Stanley
71%Easy
112
Gordon Growth Model
FinanceGoldman SachsMorgan Stanley
62%Medium
114
Coupon Equals Yield
FinanceGoldman SachsPIMCO
64%Easy
117
FX Forward by Interest Parity
FinanceGoldman SachsBarclays
65%Medium
124
Most Negative Put Delta
Options & GreeksGoldman SachsOptiver
66%Easy
128
Early Exercise of a Call
Options & GreeksGoldman SachsMorgan Stanley
71%Medium
132
Find the Put from Parity
Options & GreeksGoldman SachsMorgan Stanley
58%Easy
155
Sharpe Ratio
Portfolio & RiskGoldman SachsAQR Capital
83%Easy
156
Two-Asset Portfolio Volatility
Portfolio & RiskGoldman SachsAQR Capital
44%Medium
157
Value at Risk (Normal)
Portfolio & RiskGoldman SachsMorgan StanleyMillennium Management
54%Medium
162
VaR Time Scaling
Portfolio & RiskGoldman SachsMorgan Stanley
52%Medium
164
Portfolio Beta
Portfolio & RiskGoldman SachsAQR Capital
86%Easy
167
Minimum-Variance Hedge Ratio
Portfolio & RiskGoldman SachsPIMCO
52%Medium
173
Variance of Uniform(0,1)
StatisticsGoldman SachsCitadel
71%Easy
175
Variance of a Sum
StatisticsGoldman SachsMorgan Stanley
63%Easy
176
Central Limit Theorem
StatisticsGoldman SachsMorgan Stanley
74%Easy
178
Covariance of a Linear Transform
StatisticsGoldman SachsAQR Capital
74%Medium
179
Range of Correlation
StatisticsGoldman SachsCitadel
85%Easy
180
Variance of a Scaled Variable
StatisticsGoldman Sachs
84%Easy
183
Width of a 95% Confidence Interval
StatisticsGoldman SachsBlackRock
45%Easy
187
A One-Sample z-Statistic
StatisticsMorgan StanleyGoldman Sachs
75%Easy

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