How do I approach Statistics & Math interview questions?

Statistics & Math questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master statistics & math interviews.

What difficulty level is this interview question?

This is a medium difficulty Statistics & Math question, commonly asked during Take-home Project rounds at Other.

What role is this question designed for?

This question is commonly asked for Data Scientist candidates at Other during technical interviews.

Compute counts and pacing for verbal section

Quick Overview

This question evaluates discrete allocation and time-constrained optimization skills, focusing on integer allocation, expected-value decision making, and efficiency trade-offs in designing a timed verbal section, within the Statistics & Math domain (probability and optimization).

Verbal Section Allocation and Time Optimization

You are designing a 15-minute verbal section (900 seconds total) with 19 questions across four subtypes. The intended distribution is 30% GMAT-style grammar, 30% TOEFL-style vocabulary-inference, 30% tense/voice, and 10% other.

Assume a fixed 60-second instruction overhead, leaving 840 seconds for attempting questions. You may skip questions.

Part 1: Integer Allocation Closest to Target Mix

Targets (as counts): 30% of 19 ≈ 5.7 for each of grammar, vocabulary, tense; 10% of 19 ≈ 1.9 for other.
Feasible set: nonnegative integers that sum to 19, with each subtype within ±2 of its target (i.e., grammar/vocab/tense ∈ [4, 7], other ∈ [0, 3]).
Objective: minimize total squared percentage error from the 30/30/30/10 targets. Break any ties by preferring higher grammar counts.
Report the chosen counts and the residual error for each subtype.

Part 2: Attempt Plan to Maximize Expected Correct

Performance profile (per attempted question):
- Grammar: 35 sec/question, 85% accuracy
- Vocabulary: 55 sec/question, 75% accuracy
- Tense/voice: 45 sec/question, 80% accuracy
- Other: 60 sec/question, 70% accuracy
Use your Part 1 counts as the maximum available per subtype.
With a 15-minute limit (900 sec) and 60 sec overhead, choose how many to attempt in each subtype to maximize expected correct answers.
Show your formulation (e.g., bounded knapsack or greedy by expected-correct-per-second), your final attempt plan, expected correct, and any leftover time.

Quick Overview

Verbal Section Allocation and Time Optimization

Assume a fixed 60-second instruction overhead, leaving 840 seconds for attempting questions. You may skip questions.

Part 1: Integer Allocation Closest to Target Mix

Targets (as counts): 30% of 19 ≈ 5.7 for each of grammar, vocabulary, tense; 10% of 19 ≈ 1.9 for other.

Feasible set: nonnegative integers that sum to 19, with each subtype within ±2 of its target (i.e., grammar/vocab/tense ∈ [4, 7], other ∈ [0, 3]).

Objective: minimize total squared percentage error from the 30/30/30/10 targets. Break any ties by preferring higher grammar counts.

Report the chosen counts and the residual error for each subtype.

Part 2: Attempt Plan to Maximize Expected Correct

Performance profile (per attempted question):

Grammar: 35 sec/question, 85% accuracy
Vocabulary: 55 sec/question, 75% accuracy
Tense/voice: 45 sec/question, 80% accuracy
Other: 60 sec/question, 70% accuracy

Use your Part 1 counts as the maximum available per subtype.

With a 15-minute limit (900 sec) and 60 sec overhead, choose how many to attempt in each subtype to maximize expected correct answers.

Show your formulation (e.g., bounded knapsack or greedy by expected-correct-per-second), your final attempt plan, expected correct, and any leftover time.

Compute counts and pacing for verbal section

Quick Overview

Verbal Section Allocation and Time Optimization

Part 1: Integer Allocation Closest to Target Mix

Part 2: Attempt Plan to Maximize Expected Correct

Solution

Comments (0)

Compute counts and pacing for verbal section

Quick Overview

Verbal Section Allocation and Time Optimization

Part 1: Integer Allocation Closest to Target Mix

Part 2: Attempt Plan to Maximize Expected Correct

Solution

Comments (0)