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Goldman Sachs·Software Engineer·Technical Phone Screen·Intermediate

Intermediate
Jun 2026

Summary

Goldman Sachs data science interview with a math optimization problem that looks deceptively clean but has some real teeth if you haven't thought about it before.

Questions Asked (1)

Q1

Given that a + b + c + d = 63, find the maximum possible value of a*b + b*c + c*d.

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

I stared at this longer than I'd like to admit.

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AI HintsAI Generated

Suggested Approach

Recognize that the expression is not symmetric, so the maximum occurs at boundary values (some variables zero). Use calculus or inequalities to find the optimal assignment, then verify by testing extreme cases.

Pro tip: In interviews, after finding the answer, briefly discuss the method's time complexity and whether it scales to more variables, showing algorithmic thinking.

1. Understand the problem

Identify that a, b, c, d are likely non-negative (or positive) and the sum is fixed. The objective is to maximize a*b + b*c + c*d.

2. Analyze symmetry and boundaries

Note the expression is not symmetric; terms involve adjacent pairs. Consider setting some variables to zero to simplify.

3. Use optimization techniques

Apply Lagrange multipliers or inequalities (e.g., AM-GM) to find critical points. Alternatively, reduce variables using the constraint.

4. Solve and verify

Compute the maximum value and check if it satisfies the constraint. Test edge cases to ensure it's the global maximum.

5. Discuss generalization

Mention how the approach could be extended to more variables or different coefficients, demonstrating algorithmic thinking.

Key Points to Mention

  • Non-negativity assumption (if not stated, clarify).
  • Use of Lagrange multipliers or KKT conditions for constrained optimization.
  • Boundary analysis: setting some variables to zero often yields maximum.
  • Verification by testing extreme cases (e.g., d=0, a=0).
  • Time complexity of the method (constant time for fixed variables).
  • Generalization to n variables or different objective functions.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.