Question

In survey of 100 students in the institute of Language Studies at Addis Ababa University,

the numbers of students studying various languages were found to be English 28,
Amharic 30, Afan Oromo 42, English and Afan Oromo 10, English and Amharic 8,
Amharic and Afan Oromo 5, and all the three languages 3. How many students
a. were studying none of the languages?
b. had Afan Oromo as their only language?
c. studied Amharic if they studied Afan Oromo?​

Answer 1

From the given information, we can determine the number of students studying different languages and answer the questions.

Step-by-step explanation:

From the information given, we can create a Venn diagram to represent the number of students studying each language:

a. To find the number of students studying none of the languages, we need to subtract the total number of students studying each language from the total number of students (100). So, 100 - (28 + 30 + 42 + 10 + 8 + 5 + 3) = 100 - 136 = -36 students. However, it is not possible to have a negative number of students, so we can conclude that there were no students studying none of the languages.

b. To find the number of students who had Afan Oromo as their only language, we need to subtract the number of students studying Afan Oromo and other languages from the total number of students studying Afan Oromo. So, 42 - (10 + 5 + 3) = 24 students had Afan Oromo as their only language.

c. To find the number of students who studied Amharic if they studied Afan Oromo, we need to subtract the number of students studying Amharic and other languages from the total number of students studying Afan Oromo. So, 42 - (5 + 3) = 34 students studied Amharic if they studied Afan Oromo.

Answer 2

a. 17

b. 30

c. 5

Step-by-step explanation:

English (E) = 28 - 15 (10+8-3) = 13

Amharic (A) = 30 - 10 (8+5-3) = 20

Afan Oromo (AO) = 42 - 12(10+5-3) = 30

E+AO = 10

E + A = 8

A + AO = 5

A + AO + E = 3

a. 13 people spoke just English+ 20 people who just spoke Amharic + 30 people who just spoke Afan Oromo+ The multilingual people (10+8+5-3=20) which is 83, so that means that 17 learned no language.

b. 42 People learned Afan Oromo, but only 30 of them learned that language separately. 10 People learned it along with English, and 5 learned it with Amharic. However, 3 of those people were the same, so 12 people of those 42 spoke multiple languages. Therefore, only 30 people spoke just Afan Oromo.

c. This one is kinda just a trick question, they want you to overthink it because of the 3 who learned all, but it's just 5 like it says in the question.