Question

Many of the students at the International School speak French or German or both. Among the students who speak French, four times as many speak German as don't. In addition, ${\left(\frac{1}{6}\right)}^{th}$ of the students who don't speak German do speak only French. What fraction of the students speak German?
(A) Exactly 60 students speak French and German.

(B) Exactly 75 students speak neither French nor German.

• A. if the question can be answered by one of the statements alone but not by the other.
• B. if the question can be answered by using either statement alone.
• C. if the question can be answered by using both the statements together but cannot be answered using either statement alone
• D. if the question cannot be answered even by using both the statements A and B

Answer 1

The correct option is D

if the question cannot be answered even by using both the statements A and B

Let the total number of students be indicated as T
From the question stem, Among the students who speak French, four times as many speak German as don't. Thus, if the number of students who speak only French are indicated as "x", then the number of students who speak both French and German are indicated as "4x"
Let the number of students who do not speak French but speak German = "y" and let the number of students who don't speak both =z
It is also given that $\left(\frac{1}{6}\right)$ of the students who don't speak German do speak French
Thus, $\left(\frac{1}{6}\right)x(X+Z)=X$
From this, z = 5x

Using the both statements, we cannot answer the question.