Question

People in a club either speak French or Russian or both. Find the number of people in a club who speak only French.
A. There are 300 people in the club and the number of people who speak both French and Russian is 196.
B. The number of people who speak only Russian is 58.

• A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
• B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
• C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• D. Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Answer 1

The correct option is C BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Using both the given statements, we obtain the Venn diagram as shown below:

People speaking only french = Total number of people - (People speaking only Russian + People speaking both Russian and French)

= 300 - (196 + 58)

= 300 - 254

= 46

Since both the statements are required to find out the number of French speakers, hence option (c) is the correct answer.