Question

Staff employed in a UNESCO office in Paris are represented by four intersecting circles, one each for people who can read and write Russian, English, French and Spanish. The strength of people in some regions is given: \(a = 40, \quad c = 2a, \quad e = \frac{1}{2}a, \quad g = 2E\)

How many people can read and write any one language except French?

• A. 100
• B. 160
• C. 140
• D. 120

Hint:

Add the three regions that mean 'only one language' and are not French.

Answer 1

The Correct Option is C

Step 1: Identify the regions that mean "exactly one language, and not French".
In the four-circle diagram, region a is the part of the Russian circle that does not touch English, French or Spanish, so a counts people who know only Russian. In the same way, region c is the part of the English circle lying outside all the other circles, the only-English group, and region e is the part of the Spanish circle lying outside all the other circles, the only-Spanish group. Region g is the only-French group.

Step 2: Work out the values.
We are told \(a = 40\). Using \(c = 2a\), \(c = 2 \times 40 = 80\). Using \(e = \frac{1}{2}a\), \(e = \frac{1}{2} \times 40 = 20\).

Step 3: Add the three "only" groups that are not French.
"Any one language except French" means a person knows exactly one of the four languages, and that language is not French. So we add the only-Russian, only-English and only-Spanish counts: \(a + c + e = 40 + 80 + 20 = 140\). Region g, the only-French group, is left out because the question excludes French.

Final Answer:
140 people can read and write any one language except French. \[ \boxed{140} \]