Two quality attributes are in direct conflict and both stakeholders say theirs is non-negotiable. How do you resolve that?

Short answer

Express both attributes as measurable scenarios, then lay out the intermediate designs so the choice is between numbers rather than adjectives. Where the conflict is genuinely irreducible, escalate to whoever owns both consequences and record what was sacrificed, with a trigger for revisiting.

The interviewer is testing whether you can reason about quality attributes as trade-offs rather than slogans. Quality attributes often conflict: lower latency can reduce durability, stronger consistency can reduce availability, and tighter security can reduce usability. In architecture shorthand, each NFR needs a measurable scenario, and an NFR that conflicts with another NFR needs an explicit decision about which one wins in which context.