Total workers from two preferences and a known intersection: In an office, 72% prefer cold drink and 44% prefer tea. Everyone prefers at least one, and 40 workers prefer both. Find the total number of workers.

Introduction / Context:
When percentages of two categories and their overlap are given, the percentage of the union is p(cold) + p(tea) − p(both). If “everyone prefers at least one,” the union is 100%. Knowing the numeric overlap count lets us solve for the total population N from an overlap percentage.

Given Data / Assumptions:

• p(cold) = 72%
• p(tea) = 44%
• Everyone prefers at least one ⇒ union = 100%
• |both| = 40 workers

Concept / Approach:
Compute overlap percentage by inclusion–exclusion: p(both) = p(cold) + p(tea) − 100% = 72% + 44% − 100% = 16%. If 16% of N equals 40, then N = 40 / 0.16.

Step-by-Step Solution:
p(both) = 16%0.16 * N = 40N = 40 / 0.16 = 250

Verification / Alternative check:
Check counts: 72% of 250 = 180, 44% of 250 = 110, overlap 40; union = 180 + 110 − 40 = 250 (100%), consistent with “everyone prefers at least one.”

Why Other Options Are Wrong:
210, 220, 240 do not make 16% equal 40; 40 is the overlap count, not the total N.

Common Pitfalls:
Forgetting to subtract the overlap when combining percentages or treating 40 as a percentage instead of a count.

Final Answer:
250