During the application vetting process, the Cest La Vie hiring manage

Question

The figure below shows what is known regarding the Spanish and French language abilities of applicants for a marketing job at C’est La Vie Advertising.

During the application vetting process, the C’est La Vie hiring manager only records applicants who either do not speak French or do not speak either French or Spanish, as shown in the figure If a successful applicant must be fluent in both French and Spanish, choose from each drop-down menu the option that creates the most accurate statement based on the provided information.

The maximum possible number of qualified applicants is . However, if the number of applicants speaking only French was 1/7 of those speaking only Spanish, the number of qualified applicants would be .

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Official Answer

Dropdown 1: 20 Dropdown 2: 15

MHBS · Answer

S N S TOTAL
F 15 35/5 = 5 20
N F 35 25 60
 80
So 20 & 15

Bismuth83 · Answer

1. Both parts of the question ask us about   the number of qualified applicants  . Let that be    Q   .

2. We can draw out a chart using information from the Venn diagram.

Speak French  
  Don't Speak French  
 
   Speak Spanish  
  ?  
  35  
 
   Don't Speak Spanish  
  ?  
  25

3. Since we know about 60 (or 35 + 25) of the applicants, then there are 20 left. Let     the number of people who speak both languages     be    B   . Then, the number of people who speak only French are 20 -    B   . Because both numbers have to be larger than zero, 0  \leq     B     \leq  20.

Speak French  
  Don't Speak French  
 
   Speak Spanish  
   B   
  35  
 
   Don't Speak Spanish  
  20 -    B   
  25

4. We know that since a qualified applicant has to know both languages, the number of them is more than or equal to the number of qualified applicants. In other words:    Q     \leq     B   .

5. The first part of the question asks us about what is the  maximum value  of    Q    with    no other restrictions   . We know that    Q     \leq     B     \leq  20. So,  max{    Q    } = 20 .

6. The second part of the question introduces a new restriction that says that the number of applicants speaking only French was 1/7 of those speaking only Spanish. In other words: 20 -    B    =  \frac{1}{7} * 35 = 5 \rightarrow     B    = 15.

7. Now we know that    Q     \leq     B   , which means    Q     \leq     B    = 15. So,  max{    Q    } = 15 .

8. Our answer will then be   20 and 15  .

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I believe that the 2nd part of the question should clarify that they're asking for the maximum number of qualified applicants.

ajay0520 · Answer

why should we believe that contenstant knows atleast one language? what if there are some contenstant who can not speak both language.

Bismuth83 · Answer

There are applicants that know neither French nor Spanish. From the diagram in the problem, we have:

Speak French  
  Don't Speak French  
 
   Speak Spanish  
  ?  
  35  
 
   Don't Speak Spanish  
  ?  
  25

So, we have 25 applicants who don't speak either language.

Bunuel · Answer

The manager only records applicants who either do not speak French or do not speak either French or Spanish, so the manager does NOT record applicants who speak French (that is, anyone who speaks French only ( ? ) or who speaks both French and Spanish ( ? )), which are represented by the region inside Do Not Speak Spanish but outside Do Not Speak French ( ? ) and the region outside both circles ( ? ). https://gmatclub.com/forum/download/file.php?id=87785 From the diagram, 12 symbols are inside “Do Not Speak French”, so 60 applicants do not speak French . Since there are 80 total applicants, 20 applicants speak French . The maximum possible number fluent in both is therefore 20 (this happens if none of the 20 speak only French). Also, the “only Spanish” region (which is the region inside “Do Not Speak French” but outside “Do Not Speak Spanish”, meaning applicants who do not speak French but do speak Spanish) has 7 symbols, so 35 applicants speak only Spanish . If “only French” ( ? ) is 1/7 of that, then only French is 5, so qualified (both) is 20 minus 5, which is 15. Maximum possible qualified applicants: 20 With the 1/7 condition: 15 GMAT-Club-Forum-c4illcwu.png

egmat · Answer

The diagram shows who DOESN'T speak languages, not who does

The circles are labeled:
- "Do Not Speak Spanish" (left circle)
- "Do Not Speak French" (right circle)

Hence , the  overlap  region (center) represents applicants who do NOT speak Spanish AND do NOT speak French -  exactly the people you're asking about

Counting from the diagram: 
- Inside "Do Not Speak French" circle:  12 symbols  =  60 applicants  don't speak French
- Inside "Do Not Speak Spanish" circle:  7 symbols  =  35 applicants  don't speak Spanish
- Overlap (both circles):  5 symbols  =  25 applicants  speak NEITHER language

Therefore: 
- Total applicants:  80 
- Don't speak French only: 60 - 25 =  35  (speak Spanish, not French)
- Don't speak Spanish only: 35 - 25 =  10  (speak French, not Spanish)
- Speak neither:  25 
-  Remaining (speak French) = 80 - 60 =  20

Part 1: Maximum qualified applicants 
Qualified = speaks BOTH French AND Spanish
Maximum occurs when ALL  20  French speakers also speak Spanish.
  Answer: 20

Part 2: With the 1/7 constraint 
Only French speakers = (1/7) x Only Spanish speakers
Only French = (1/7) x 35 =  5 
Qualified (both) = 20 - 5 =  15 
  Answer: 15

During the application vetting process, the Cest La Vie hiring manage

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	Speak French	Don't Speak French
Speak Spanish	?	35
Don't Speak Spanish	?	25

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Prep Toolkit

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