Question 1177473
It's helpful to solve this kind of problem with a Venn Diagram. Here's how we can approach this:

**1. Draw a Venn Diagram**

Draw three overlapping circles representing broccoli, carrots, and green beans.

**2. Fill in the Diagram**

* **28 kids only liked green beans:** Place "28" in the green beans only section.
* **40 kids liked broccoli and green beans:** Since 73 like broccoli total, and 40 like broccoli and green beans, 73 - 40 = 33 like only broccoli and green beans. Of those, 12 also like carrots. So, place "12" in the broccoli-carrot-green bean overlap, and 33 - 12 = 21 in the broccoli-green bean overlap.
* **79 kids liked exactly 2 of these vegetables:** We've already accounted for 12 who like broccoli and carrots, and 21 who like broccoli and green beans. So, 79 - 12 - 21 = 46 must like carrots and green beans only.
* **12 kids liked broccoli and carrots, but not green beans:** Place "12" in the broccoli-carrot overlap.
* **34 kids only liked carrots:** Place "34" in the carrots only section.
* **104 kids liked carrots or green beans, but not broccoli:** This includes those who like only carrots, only green beans, and the overlap between carrots and green beans. We've already accounted for 28 + 46 = 74, so 104 - 74 = 30 must like carrots only.

**3. Calculate the Remaining Values**

* **Total who like carrots:** 30 (carrots only) + 12 (broccoli-carrot) + 46 (carrot-green bean) + 12 (all three) = 100
* **Total who like any vegetable:** Add up all the numbers in the Venn diagram.
* **Those who dislike carrots:** 200 (total) - 100 (like carrots) = 100

**Answers**

1. **How many kids liked carrots, but not green beans?** 30 (carrots only) + 12 (broccoli-carrot) = 42
2. **How many kids liked exactly 1 of the three vegetables?** 30 (carrots only) + 28 (green beans only) + 12 (broccoli and carrots only) = 70
3. **How many kids do not like carrots?** 100