You are confusing 'edges' with 'vertices'.

Face: is the flat surface of a solid figure. A face of a solid figure can be a square, a rectangle, a triangle or a circle.
Edge: is the line segment two faces of a solid meet.
Corner (vertex): is a corner where three or more edges of a solid meet.

You can ignore the diagram completely (as I did when I solved it) because the question tells you that you get a figure with "2 pyramids each with a square base that they share". Imagine what one pyramid looks like - a square with triangles attached to each side and the tips of the triangles stuck together. Imagine how would you have two pyramids with a common base. There would be 4 triangles on the lower side of the square too and their tips would be stuck together. So in all, the figure would have 8 faces (4 triangles + 4 triangles) and 12 edges ( 4 edges where the top triangles join, 4 edges where the bottom triangles join and 4 edges of the square).
All in all you will have 8 + 12 = 20 faces + edges

You can ignore the diagram completely (as I did when I solved it) because the question tells you that you get a figure with "2 pyramids each with a square base that they share". Imagine what one pyramid looks like - a square with triangles attached to each side and the tips of the triangles stuck together. Imagine how would you have two pyramids with a common base. There would be 4 triangles on the lower side of the square too and their tips would be stuck together. So in all, the figure would have 8 faces (4 triangles + 4 triangles) and 12 edges ( 4 edges where the top triangles join, 4 edges where the bottom triangles join and 4 edges of the square).
All in all you will have 8 + 12 = 20 faces + edges

You can ignore the diagram completely (as I did when I solved it) because the question tells you that you get a figure with "2 pyramids each with a square base that they share". Imagine what one pyramid looks like - a square with triangles attached to each side and the tips of the triangles stuck together. Imagine how would you have two pyramids with a common base. There would be 4 triangles on the lower side of the square too and their tips would be stuck together. So in all, the figure would have 8 faces (4 triangles + 4 triangles) and 12 edges ( 4 edges where the top triangles join, 4 edges where the bottom triangles join and 4 edges of the square).
All in all you will have 8 + 12 = 20 faces + edges

VeritasKarishma

Why is the face of the square base not being counted? we can also assume the pyramid to be on the same side of the square base and hence 1 should be added to its face.

Hi Karishma,

I guess the figure should be given. Otherwise, there is one more scenario where two pyramids share the same base yet their peak points are both above (or below) the base. In that scenario, the number of edges + the number of faces is 9 + 12 = 21.

If my explanation is not clear/wrong, please let me know.

Thanks.

Yes, i agree we can ignore when the structure is on opposite side of the base. But what i wrote above is when they are on the same side of the base.
Isn't that a possibility?

VeritasKarishma

Why is the face of the square base not being counted? we can also assume the pyramid to be on the same side of the square base and hence 1 should be added to its face.

Since they share the base, the pyramids have to be on the opposite sides of the square and will hide the square. If they were on the same side, we will have overlapping triangles and hence get only one pyramid.

Check this diagram again: https://gmatclub.com/forum/when-the-fig ... l#p1787756

VeritasKarishma

I get your point and understood the diagram. But the question does not state that the sides are equal. Hence, what i felt there is still a possibility of pyramid of different edgle lenght on the same side of square base. Plz. let me know what did i miss ?