1. **State the problem:** We have 100 people surveyed about desserts. - 55 had cake. - 82 had ice cream. - 37 had both cake and ice cream. We need to find the correct Venn diagram representing these numbers. 2. **Recall the formula for union of two sets:** $$|A \cup B| = |A| + |B| - |A \cap B|$$ where $|A|$ is the number of people who had cake, $|B|$ is the number who had ice cream, and $|A \cap B|$ is the number who had both. 3. **Calculate the number of people who had either cake or ice cream or both:** $$|A \cup B| = 55 + 82 - 37 = 100$$ This matches the total number of people surveyed, so the data is consistent. 4. **Find the number of people who had only cake:** $$|A| - |A \cap B| = 55 - 37 = 18$$ 5. **Find the number of people who had only ice cream:** $$|B| - |A \cap B| = 82 - 37 = 45$$ 6. **Check the Venn diagram options:** - Option A shows: - Cake only: 18 - Both: 37 - Ice cream only: 45 - Option B shows cake as 55 and ice cream as 82, which are totals, not parts. - Options C and D have inconsistent numbers (74) which do not match calculations. 7. **Conclusion:** Option A correctly represents the data. **Final answer:** Option A is the correct Venn diagram.