question_answer

Directions: These questions consist of a question and two statements I and II given below them. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and choose the appropriate option.                                                                                                  [LIC (AAO) 2014]

There are 600 members in a club. Each of them like either one or more of the given cuisines; Chinese, Mexican and Italian. How many members like only Mexican cuisine?

I. 57% of the members like Italian cuisine. 18% of the members like only Chinese cuisine and 15% of the members like only Chinese and Mexican cuisine.

II. 58% of the members like either two or more of all of the given cuisines. 43% of the members do not like Mexican cuisine.

A) If the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.

B) If the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.

C) If the data either in statement I alone or in statement II alone are sufficient to answer the question.

D) If the data in both statements I and II together are not sufficient to answer the question.

E) If the data in both the statements I and II together are necessary to answer the question.

Correct Answer: E

Solution :

According to statement I,

Total members who like Italian

\[=600\times \frac{57}{100}=342\]

Members who like only Chinese cuisine

\[=600\times \frac{18}{100}=108\]

Members who like only Chinese and Mexican

\[=600\times \frac{15}{100}=90\]

According to statement II,

The members who I like either two or more of all cuisines

\[=600\times \frac{58}{100}=348\]

Members who do not like Mexican cuisine

\[=600\times \frac{43}{100}=258\]

By depicting given information in Venn diagram,

Member who like Italian but do not like Mexican

\[=342-258=84\]

Then, persons who like only Mexican cuisine

\[=600-(108+348+84)\]

\[=600-(540)=60\]

Both statements are necessary.