Question

A small school has three foreign language classes, one in French, one in Spanish, and one in German. How many of the 34 students enrolled in the Spanish class are also enrolled in the French class?(1) There are 27 students enrolled in the French class,and 49 students enrolled in either the French class,the Spanish class,or both of these classes.
(2) One half of the students enrolled in the Spanish class are enrolled in more than one foreign language class.

Answer 1

Answer:

Statement 1 is sufficient

And the solution is 12

Statement 2 is insufficient

Step-by-step explanation:

Statement 1 : There are 27 students enrolled in the French class,and 49 students enrolled in either the French class,the Spanish class,or both of these classes.

Let S = number of Spanish-only students

F = number of French-only students

B = number of students taking both, which is the number the prompt question wants.

Given that;

S + B = 34

F + B = 27

S + F + B = 49

The equations above are from the question and statement 1.

Solving for B, we have;

(S + B) + (F + B) = 34 + 27

B + S + B + F = 61

S + B + F = 49

B + 49 = 61

B = 61 - 49 = 12

Therefore statement 1 is sufficient to give a specific and numerical solution to the question.

Statement 2: One half of the students enrolled in the Spanish class are enrolled in more than one foreign language class.

The statement 2 states that half of the students enrolled in the Spanish class are also enrolled in one foreign language but did not specify which proportion or fraction of them are enrolled in german or french therefore a specific numerical solution cannot be derived from this statement.

Hence, statement 2 is insufficient.