, Question 1
A logistics firm uses a linear programming model to minimize shipping costs.
The optimal solution has a shadow price of $0 for a warehouse capacity
constraint. A new regulation increases that warehouse's capacity by 10%. What
is the most likely effect on total cost?
A. Total cost decreases by the shadow price times the capacity increase.
B. Total cost remains unchanged because the constraint is non-binding.
C. Total cost increases because the feasible region expands.
D. Total cost decreases, but the exact amount cannot be determined from
the shadow price alone.
Correct Answer: B - Total cost remains unchanged because the
constraint is non-binding.
RATIONALE
A shadow price of $0 indicates the capacity constraint is non-binding
(slack exists). Increasing capacity further does not relax a binding
constraint, so the optimal solution and cost remain unchanged.
Options A and D incorrectly assume the constraint affects the
optimum; C is directionally wrong.
Question 2
In a randomized controlled trial with non-compliance, an analyst uses
instrumental variables (IV) to estimate the local average treatment effect
(LATE). Which assumption is most critical for the IV estimator to be
consistent?
A. The instrument is uncorrelated with the error term and affects the
outcome only through the treatment.
B. The treatment effect is homogeneous across all units.
C. The instrument is binary and randomly assigned.
D. There is no effect modification by observed covariates.
Correct Answer: A - The instrument is uncorrelated with the
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,error term and affects the outcome only through the treatment.
RATIONALE
IV consistency requires the exclusion restriction (instrument affects
outcome only via treatment) and instrument exogeneity (uncorrelated
with error). Homogeneity (B) is not required for LATE; binary
instrument (C) is common but not necessary; D is unrelated to IV
consistency.
Question 3
A queueing system has Poisson arrivals at rate and exponential service times
at rate , with a single server. If = 0.8, which statement about the system's
stability and performance is most accurate?
A. The system is stable, and average queue length is given by ²/(1-).
B. The system is unstable because < is insufficient for stability.
C. The system is stable, and average waiting time in queue is /(-).
D. The system is stable, but average queue length grows without bound as
approaches 1.
Correct Answer: D - The system is stable, but average queue
length grows without bound as approaches 1.
RATIONALE
For M/M/1, stability requires = / < 1. Here =0.8, so stable. Average
queue length Lq = ²/(1-) for M/M/1, which grows without bound as
->1. Option A gives the correct formula but the statement 'average
queue length is given by' is true; however D is more accurate because
it highlights the asymptotic behavior. Actually A is also correct
formula, but D is the most accurate about stability and behavior. The
question asks 'most accurate'-D emphasizes the critical behavior near
=1, which is a key insight. A is a correct formula but not the most
accurate statement about performance. B is false; C gives Wq = /(-)
which is incorrect (Wq = /((1-)) or /((-))).
Page 3
, Question 4
In a decision tree analysis for a capacity expansion problem, the expected
monetary value (EMV) of a decision node is $2M, while the expected utility
(EU) using a concave utility function is 0.7. If the risk tolerance is $5M, what
does the difference between EMV and EU imply about the decision-maker's
risk attitude?
A. The decision-maker is risk-seeking because EU < EMV.
B. The decision-maker is risk-averse because the utility function is
concave.
C. The decision-maker is risk-neutral because EMV and EU are on
different scales.
D. The decision-maker is risk-averse because EU is less than the utility of
EMV.
Correct Answer: B - The decision-maker is risk-averse because
the utility function is concave.
RATIONALE
A concave utility function implies risk aversion. EU and EMV are on
different scales, so comparing their numerical values directly is
invalid. The concavity itself indicates risk aversion. Option D is also
true but B is the direct implication of concavity.
Question 5
A data pipeline ingests streaming sensor data and must guarantee exactly-once
processing semantics. Which combination of techniques is most appropriate?
A. At-least-once delivery with idempotent writes and deduplication.
B. At-most-once delivery with no retries.
C. Transactional writes with two-phase commit across all sinks.
D. Batch processing with periodic snapshots.
Correct Answer: A - At-least-once delivery with idempotent
writes and deduplication.
Page 4
A logistics firm uses a linear programming model to minimize shipping costs.
The optimal solution has a shadow price of $0 for a warehouse capacity
constraint. A new regulation increases that warehouse's capacity by 10%. What
is the most likely effect on total cost?
A. Total cost decreases by the shadow price times the capacity increase.
B. Total cost remains unchanged because the constraint is non-binding.
C. Total cost increases because the feasible region expands.
D. Total cost decreases, but the exact amount cannot be determined from
the shadow price alone.
Correct Answer: B - Total cost remains unchanged because the
constraint is non-binding.
RATIONALE
A shadow price of $0 indicates the capacity constraint is non-binding
(slack exists). Increasing capacity further does not relax a binding
constraint, so the optimal solution and cost remain unchanged.
Options A and D incorrectly assume the constraint affects the
optimum; C is directionally wrong.
Question 2
In a randomized controlled trial with non-compliance, an analyst uses
instrumental variables (IV) to estimate the local average treatment effect
(LATE). Which assumption is most critical for the IV estimator to be
consistent?
A. The instrument is uncorrelated with the error term and affects the
outcome only through the treatment.
B. The treatment effect is homogeneous across all units.
C. The instrument is binary and randomly assigned.
D. There is no effect modification by observed covariates.
Correct Answer: A - The instrument is uncorrelated with the
Page 2
,error term and affects the outcome only through the treatment.
RATIONALE
IV consistency requires the exclusion restriction (instrument affects
outcome only via treatment) and instrument exogeneity (uncorrelated
with error). Homogeneity (B) is not required for LATE; binary
instrument (C) is common but not necessary; D is unrelated to IV
consistency.
Question 3
A queueing system has Poisson arrivals at rate and exponential service times
at rate , with a single server. If = 0.8, which statement about the system's
stability and performance is most accurate?
A. The system is stable, and average queue length is given by ²/(1-).
B. The system is unstable because < is insufficient for stability.
C. The system is stable, and average waiting time in queue is /(-).
D. The system is stable, but average queue length grows without bound as
approaches 1.
Correct Answer: D - The system is stable, but average queue
length grows without bound as approaches 1.
RATIONALE
For M/M/1, stability requires = / < 1. Here =0.8, so stable. Average
queue length Lq = ²/(1-) for M/M/1, which grows without bound as
->1. Option A gives the correct formula but the statement 'average
queue length is given by' is true; however D is more accurate because
it highlights the asymptotic behavior. Actually A is also correct
formula, but D is the most accurate about stability and behavior. The
question asks 'most accurate'-D emphasizes the critical behavior near
=1, which is a key insight. A is a correct formula but not the most
accurate statement about performance. B is false; C gives Wq = /(-)
which is incorrect (Wq = /((1-)) or /((-))).
Page 3
, Question 4
In a decision tree analysis for a capacity expansion problem, the expected
monetary value (EMV) of a decision node is $2M, while the expected utility
(EU) using a concave utility function is 0.7. If the risk tolerance is $5M, what
does the difference between EMV and EU imply about the decision-maker's
risk attitude?
A. The decision-maker is risk-seeking because EU < EMV.
B. The decision-maker is risk-averse because the utility function is
concave.
C. The decision-maker is risk-neutral because EMV and EU are on
different scales.
D. The decision-maker is risk-averse because EU is less than the utility of
EMV.
Correct Answer: B - The decision-maker is risk-averse because
the utility function is concave.
RATIONALE
A concave utility function implies risk aversion. EU and EMV are on
different scales, so comparing their numerical values directly is
invalid. The concavity itself indicates risk aversion. Option D is also
true but B is the direct implication of concavity.
Question 5
A data pipeline ingests streaming sensor data and must guarantee exactly-once
processing semantics. Which combination of techniques is most appropriate?
A. At-least-once delivery with idempotent writes and deduplication.
B. At-most-once delivery with no retries.
C. Transactional writes with two-phase commit across all sinks.
D. Batch processing with periodic snapshots.
Correct Answer: A - At-least-once delivery with idempotent
writes and deduplication.
Page 4
