In the following figure, four overlapping shapes (rectangle, triangle, circle, and hexagon) are given. The sum of the numbers which belong to only two overlapping shapes is ________
In the following figure, four overlapping shapes (rectangle, triangle, circle, and hexagon) are given. The sum of the numbers which belong to only two overlapping shapes is ________
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Solution and Explanation
1: Belongs to {circle, rectangle, hexagon} → 3 shapes (Not counted)
2: Belongs to {circle, rectangle} → 2 shapes (Counted)
3: Belongs to {circle, rectangle, triangle} → 3 shapes (Not counted)
4: Belongs to {rectangle, hexagon} → 2 shapes (Counted)
5: Belongs to {circle, triangle} → 2 shapes (Counted)
6: Belongs to {circle, triangle, hexagon} → 3 shapes (Not counted)
7: Belongs to {circle, triangle} → 2 shapes (Counted)
8: Belongs to {circle, triangle, hexagon} → 3 shapes (Not counted)
9: Belongs to {circle, triangle, hexagon} → 3 shapes (Not counted)
So, the numbers that belong to only two shapes are: 2, 4, 5, 7
\[ \text{Required sum} = 2 + 4 + 5 + 7 = \boxed{18} \]
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