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A survey was conducted to find out the number of languages spoken by the 210 employees of a company. It was found that 60 employees did not speak English, 150 employees did not speak German and 170 employees did not speak French. If there were 20 employees who did not speak German or English and 20 employees who did not speak French or English, what was the maximum number of employees who spoke only English? Assume that each of the employees spoke at least one language and no employee spoke any language other than English, French and German.
  • a)
    110
  • b)
    120
  • c)
    130
  • d)
    140
  • e)
    150
Correct answer is option 'C'. Can you explain this answer?
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A survey was conducted to find out the number of languages spoken by t...
Given
  • Number of employees = 210
  • Number of employees who did not speak English = 60
    • So, number of employees who spoke English = 210 – 60 = 150
  • Number of employees who did not speak German = 150
    • So, number of employees who spoke German = 210 – 150 = 60
  • Number of employees who did not speak French = 170
    • So, number of employees who spoke French = 210 – 170 = 40
  • Number of employees who did not speak German or English = 20
    • So, these employees must speak only French (because it’s given that each employee speaks at least one language)
  • Number of employees who did not speak French and English = 20
    • So, these employees must speak only German (because it’s given that each employee speaks at least one language)
To Find: Maximum number of employees who spoke only English
Approach
 
  1. To find the maximum number of employees who spoke only English, we will first analyse the relation between total number of employees and number of employees who speak only English.
    1. Total number of employees = number of employees (who only speak English + who only speak French + who only speak German + who speak both German & French + who speak both German & English + who speak both French & English + who speak all the three languages + who speak none of the languages)
    2. Number of employees who only speak English = (Total number of employees) – (number of employees (who only speak French + who only speak German + who speak both German & French + who speak both German & English + who speak both French & English + who speak all the three languages + who speak none of the languages)
    3. As we need to maximize the number of employees who spoke only English, we need to minimize the number of employees who spoke English as well as some other language.
    4. So, of the employees who speak more one language we would maximize the number of employees who spoke only French and German
       
  2. Now, we know the number of employees who spoke French and German and also the number of employees who spoke only  French and German.
     
  3. We will use this information to maximize the number of employees who spoke only French and German.
 
Working Out
  1. As there are 40 employees who spoke French and 20 employees who only spoke French,              
    1. Number of employees who spoke French and some other language = 40 – 20 = 20
  2. Similarly, as there are 60 employees who spoke German and 20 employees who spoke only German,
    1. Number of employees who spoke German and some other language = 60 – 20 = 40
  3. Total number of employees who spoke more than 1 language
    1. Number of employees who spoke English + Number of employees who spoke French + Number of employees who spoke German – Total number of employees = 150 + 60 + 40 – 210 = 40
  4. As there are 40 employees who spoke more than 1 language, we will try to distribute maximum number of these employees into the number of employees who spoke French and German only.
    1. As there are 20 employees who spoke French and some other language and there are 40 employees who spoke German and some other language, the maximum number of employees who spoke French and German = 20
  5. So, that still leaves us with 40 – 20 = 20 employees who spoke German and some other language.
    1. The only possibility is for these employees to speak German and English
  6. So, there are 20 employees who spoke English and some other language
  7. As there are 150 employees who spoke English, there can be a maximum of 150 – 20 = 130 employees who spoke only English.
 
Answer: C
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Most Upvoted Answer
A survey was conducted to find out the number of languages spoken by t...
To solve this problem, we can use a Venn diagram. Let's break down the information given step by step:

Step 1: Draw a Venn diagram with three overlapping circles representing English (E), German (G), and French (F). Label the overlapping regions as EG, EF, and FG, and the region outside all three circles as O.

Step 2: Fill in the given information:
- 60 employees do not speak English, so write 60 in the region outside the E circle (O).
- 150 employees do not speak German, so write 150 in the region outside the G circle (O).
- 170 employees do not speak French, so write 170 in the region outside the F circle (O).
- 20 employees do not speak German or English, so write 20 in the region outside both the E and G circles (O).
- 20 employees do not speak French or English, so write 20 in the region outside both the E and F circles (O).

Step 3: Calculate the number of employees who speak at least two languages:
- The number of employees who do not speak English (O) can be found by adding the number of employees who do not speak German (150) and the number of employees who do not speak French (170), and then subtracting the number of employees who do not speak German or English (20). So, O = 150 + 170 - 20 = 300.
- The number of employees who speak at least two languages is the complement of O, which is the total number of employees minus O. So, the number of employees who speak at least two languages is 210 - 300 = -90. However, since it is not possible to have a negative number of employees, we can conclude that all employees speak at least two languages.

Step 4: Calculate the number of employees who speak only English:
- The number of employees who speak only English is the difference between the total number of employees (210) and the number of employees who speak at least two languages (-90). So, the number of employees who speak only English is 210 - (-90) = 300.

Step 5: Calculate the maximum number of employees who speak only English:
- Since the total number of employees who speak only English is 300, we need to subtract the number of employees who speak only English from the total number of employees (300) to find the maximum number of employees who speak only English. So, the maximum number of employees who speak only English is 300 - 210 = 90.

Therefore, the maximum number of employees who speak only English is 90, which corresponds to option C.
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A survey was conducted to find out the number of languages spoken by the 210 employees of a company. It was found that 60 employees did not speak English, 150 employees did not speak German and 170 employees did not speak French. If there were 20 employees who did not speak German or English and 20 employees who did not speak French or English, what was the maximum number of employees who spoke only English? Assume that each of the employees spoke at least one language and no employee spoke any language other than English, French and German.a)110b)120c)130d)140e)150Correct answer is option 'C'. Can you explain this answer?
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A survey was conducted to find out the number of languages spoken by the 210 employees of a company. It was found that 60 employees did not speak English, 150 employees did not speak German and 170 employees did not speak French. If there were 20 employees who did not speak German or English and 20 employees who did not speak French or English, what was the maximum number of employees who spoke only English? Assume that each of the employees spoke at least one language and no employee spoke any language other than English, French and German.a)110b)120c)130d)140e)150Correct answer is option 'C'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A survey was conducted to find out the number of languages spoken by the 210 employees of a company. It was found that 60 employees did not speak English, 150 employees did not speak German and 170 employees did not speak French. If there were 20 employees who did not speak German or English and 20 employees who did not speak French or English, what was the maximum number of employees who spoke only English? Assume that each of the employees spoke at least one language and no employee spoke any language other than English, French and German.a)110b)120c)130d)140e)150Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A survey was conducted to find out the number of languages spoken by the 210 employees of a company. It was found that 60 employees did not speak English, 150 employees did not speak German and 170 employees did not speak French. If there were 20 employees who did not speak German or English and 20 employees who did not speak French or English, what was the maximum number of employees who spoke only English? Assume that each of the employees spoke at least one language and no employee spoke any language other than English, French and German.a)110b)120c)130d)140e)150Correct answer is option 'C'. Can you explain this answer?.
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