Question

In a class of 30 students 19 are studying French, 12 are studying Spanish and

7 are studying both French and Spanish. How many students are not taking any

foreign language?​

Answer 1

Step-by-step explanation:

There are 30 students. Nineteen are French, 12 are studying Spanish and 7 are studying both French and Spanish. How many students are not taking any foreign language?

The only possible answer, the way this question is formulated, is “we don’t know”. Of the 30 students, 19 are French — we have no idea whether they’re studying a foreign language or not. 12 are studying Spanish, but we don’t know if that’s the only language they’re studying, so that doesn’t help us any, and 7 are studying both French and Spanish, which leaves us with at least 23 students who are not studying both these languages simultaneously, but could be studying Chinese for all we know.

If we start from the assumption that French and Spanish are the only languages on offer, then we know that either 19 students are taking at least one of them (12 who are studying Spanish treated as a separate group from the 7 studying both Spanish and French), which leaves 11 non-language studying students, or else, of the 12 Spanish-taking students, 7 are also taking French, in which case we only have 12 language-students, and the remaining 18 are non-language students.

Now, if the 19 who “are French” are really “students of French”, the maths remains the same, only the numbers change, and we see that we must allow for overlap because otherwise we don’t have enough students (because 19+12+7 is more than 30): 19 studying French, of which 7 are also taking Spanish, and 12 studying Spanish, of which 7 are also taking French, which gives us: 12 students of French alone; 5 students of Spanish alone, and 7 students of both: 12+5+7=24, which means that 6 students remain not learning either.