Staff employed in a UNESCO office in Paris are represented by four intersecting circles, one each for people who can read and write English, French, Spanish and Russian, as shown in the diagram above. Given: \(a = 40\), \(c = 2a\), \(e = \frac{1}{2}a\), \(g = 2e\). How many people know only Spanish?
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Only-Spanish is the region exclusive to the Spanish circle, given directly as e = (1/2)a.
We can also read this off directly from the given ratio without separately identifying the diagram region first.
The question defines four "only" quantities through the equations at the top of the diagram: $a = 40$ is the only-Russian count, $c = 2a$ is the only-English count, $e = \frac{1}{2}a$ is the only-Spanish count, and $g = 2e$ is the only-French count.
Since the question asks specifically for the only-Spanish count, we use the third equation directly: $e = \frac{1}{2}a$.
This matches option (B). As a quick sanity check, since $c = 2a = 80$ (only English) and $g = 2e = 40$ (only French), all four "only" values (40, 80, 20, 40) are positive whole numbers, which is consistent with them representing head counts of staff. $\boxed{20}$
