Quantitative Proficiency Test - WorldQuant University (2026/2027) | 60 QUESTIONS &
VERIFIED SOLUTIONS | PASSING SCORE ≥75%
WorldQuant University Quantitative Proficiency Test (Admissions Assessment) | Core Domains:
Probability & Statistics, Linear Algebra, Calculus, Mathematical Proofs, Data Interpretation, Financial
Mathematics, Quantitative Reasoning, and Python Programming | Graduate-Level Quantitative
Finance Focus | MScFE Admissions Requirement
Exam Structure
The WorldQuant University Quantitative Proficiency Test for the 2026/2027 admissions cycle is typically
structured as follows:
● 60 multiple-choice and quantitative response questions
● Timed online assessment (90–120 minutes)
● Covers undergraduate-level mathematics, statistics, and Python programming
● Validates foundational knowledge for the MSc in Financial Engineering
● Minimum passing score: 75%
Introduction
This comprehensive solution guide reflects the actual scope and rigor of the WQU QPT. It includes 60
verified questions across core domains, with emphasis on analytical precision, mathematical modeling,
statistical inference, and practical Python implementation—essential for success in quantitative finance.
Solution Format
All correct answers and code outputs are presented in bold and green, followed by rigorous derivations,
statistical reasoning, or Python execution logic.
1. Let \( X \sim \mathcal{N}(2, 9) \). What is \( P(X < 5) \)?
A. 0.6826
B. 0.8413
B. 0.8413
D. 0.9544
, Standardize: \( Z = \frac{5 - 2}{3} = 1 \). From standard normal tables, \( P(Z < 1) = 0.8413 \).
2. What is the output of the following Python code?
import numpy as np
a = np.array([1, 2, 3])
b = np.array([4, 5, 6])
print(np.dot(a, b))
A. [4, 10, 18]
B. [5, 7, 9]
C. 32
D. Error
Dot product: \( 1\cdot4 + 2\cdot5 + 3\cdot6 = 4 + 10 + 18 = 32 \).
3. Let \( A = \begin{bmatrix} 1 & 2 \\ 3 & 6 \end{bmatrix} \). What is the rank of \( A \)?
A. 0
B. 1
B. 1
D. 2
Row 2 = 3 × Row 1 ⇒ linearly dependent ⇒ rank = 1.
4. A 95% confidence interval for a population mean is (10, 20). Which statement is true?
, A. 95% of the population lies between 10 and 20
B. The sample mean is 15
C. If we repeated sampling, 95% of such intervals would contain the true mean
D. There is a 95% probability the true mean is 15
The correct frequentist interpretation is that 95% of intervals constructed this way would capture the
true parameter.
5. Evaluate \( \lim_{x \to \infty} \left(1 + \frac{1}{x}\right)^x \).
A. 0
B. 1
C. e
D. ∞
This is the definition of Euler’s number: \( e \approx 2.718 \).
6. In Python, what does pd.DataFrame({'A': [1,2], 'B': [3,4]}).shape return?
A. (1, 2)
B. (2, 1)
C. (2, 2)
D. (4,)
2 rows, 2 columns ⇒ shape = (2, 2).
VERIFIED SOLUTIONS | PASSING SCORE ≥75%
WorldQuant University Quantitative Proficiency Test (Admissions Assessment) | Core Domains:
Probability & Statistics, Linear Algebra, Calculus, Mathematical Proofs, Data Interpretation, Financial
Mathematics, Quantitative Reasoning, and Python Programming | Graduate-Level Quantitative
Finance Focus | MScFE Admissions Requirement
Exam Structure
The WorldQuant University Quantitative Proficiency Test for the 2026/2027 admissions cycle is typically
structured as follows:
● 60 multiple-choice and quantitative response questions
● Timed online assessment (90–120 minutes)
● Covers undergraduate-level mathematics, statistics, and Python programming
● Validates foundational knowledge for the MSc in Financial Engineering
● Minimum passing score: 75%
Introduction
This comprehensive solution guide reflects the actual scope and rigor of the WQU QPT. It includes 60
verified questions across core domains, with emphasis on analytical precision, mathematical modeling,
statistical inference, and practical Python implementation—essential for success in quantitative finance.
Solution Format
All correct answers and code outputs are presented in bold and green, followed by rigorous derivations,
statistical reasoning, or Python execution logic.
1. Let \( X \sim \mathcal{N}(2, 9) \). What is \( P(X < 5) \)?
A. 0.6826
B. 0.8413
B. 0.8413
D. 0.9544
, Standardize: \( Z = \frac{5 - 2}{3} = 1 \). From standard normal tables, \( P(Z < 1) = 0.8413 \).
2. What is the output of the following Python code?
import numpy as np
a = np.array([1, 2, 3])
b = np.array([4, 5, 6])
print(np.dot(a, b))
A. [4, 10, 18]
B. [5, 7, 9]
C. 32
D. Error
Dot product: \( 1\cdot4 + 2\cdot5 + 3\cdot6 = 4 + 10 + 18 = 32 \).
3. Let \( A = \begin{bmatrix} 1 & 2 \\ 3 & 6 \end{bmatrix} \). What is the rank of \( A \)?
A. 0
B. 1
B. 1
D. 2
Row 2 = 3 × Row 1 ⇒ linearly dependent ⇒ rank = 1.
4. A 95% confidence interval for a population mean is (10, 20). Which statement is true?
, A. 95% of the population lies between 10 and 20
B. The sample mean is 15
C. If we repeated sampling, 95% of such intervals would contain the true mean
D. There is a 95% probability the true mean is 15
The correct frequentist interpretation is that 95% of intervals constructed this way would capture the
true parameter.
5. Evaluate \( \lim_{x \to \infty} \left(1 + \frac{1}{x}\right)^x \).
A. 0
B. 1
C. e
D. ∞
This is the definition of Euler’s number: \( e \approx 2.718 \).
6. In Python, what does pd.DataFrame({'A': [1,2], 'B': [3,4]}).shape return?
A. (1, 2)
B. (2, 1)
C. (2, 2)
D. (4,)
2 rows, 2 columns ⇒ shape = (2, 2).
