Discussion
The number of faces (F), edges (E) and vertices (V) of a polyhedron are 7, 15 and x, respectively. Then, the value of \((2F + 3E - 4x)\) is :
Answer: B
The value is 19.
Euler's formula for a polyhedron gives the number of vertices:
\[ \begin{aligned} F + V - E &= 2 \\ 7 + x - 15 &= 2 \Rightarrow x = 10 \\ 2F + 3E - 4x &= 14 + 45 - 40 = 19 \end{aligned} \]
A wrong value of x, for example from writing F + E - V = 2, leads to the other options.
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