Of the 220 restaurants in a certain city, how many serve neither shrim

Question

Of the 220 restaurants in a certain city, how many serve neither shrimp nor crab?

(1) 94 serve shrimp and 72 serve crab.
(2) 42 serve both shrimp and crab.

Gladiator59 · Answer

This is a two-overlapping sets problem.

1) We know shrimp = 94 and crab = 72. Entire crab could have overlap with shrimp or non could.  Hence insufficient  as we do not know how many are  both

2) We know how many are both shrimp and crab but no info about either individually.  Hence insufficient

(1) + (2) together.  It is sufficient as we now have all the info

Shrimp = 94. Crab = 72. Both = 42. Hence either shrimp or crab or both = 94 + 72 - 42 = 124.
Hence : neither + 124 = 220
neither = 220 - 124 = 96

Hence  Option (C)  is our answer.

Best,
Gladi

EgmatQuantExpert · Answer

Solution

Given:  
• Total number of restaurants in the city = 220

To find:  
• Out of 220 restaurants, how many serve neither shrimp nor crab

Approach and Working:

Analysing Statement 1 
• As per the information given in Statement 1, 94 restaurants serve shrimp and 72 restaurants serve crab.
• From this, we cannot say if there is any restaurant which serves both.
 o Therefore, from statement 1, we cannot conclude.

Analysing Statement 2 
• As per the information given in Statement 2, 42 restaurants serve both shrimp and crab.
• From this, we cannot find out how many such restaurants are there which serve only shrimp or only crab.
 o Therefore, from statement 2, we cannot conclude.

Combine both statements 
• Combining the information given in the statements, we know 94 serve shrimp, 72 serve crab and 42 serve both.
• Therefore (94 – 42) = 52 serve only shrimp and (72 – 42) = 30 serve only crab.
• Number of restaurants serving at least one of shrimp and crab = 52 + 30 + 42 = 124
• Therefore, Number of restaurants serving none of shrimp and crab = 220 – 124 = 96
 https://e-gmat.com/blogs/wp-content/uploads/2018/04/1-3-e1524544680755.png 
Hence, by combining the statements we can find out the answers.
The correct answer is option C.

Answer: C

PP777 · Answer

Given: Total restaurants in a certain city= 220

To find: of these 220 restaurants, how many serve neither shrimp nor crab
 
1) Serve shrimp = 94
 serve crab= 72
Not sufficient
2) Serve both shrimp and crab= 42
Not sufficeint

1) + 2) Either shrimp or crab = 94 + 72 - 42 = 124
 Neither shrimp nor crab = 220 -124 = 96
Sufficient

Correct Answer = C

push12345 · Answer

Total-neither=A+B-both

To calculate neither both statements r required

So B is answer

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Of the 220 restaurants in a certain city, how many serve neither shrim

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GMAT Data Sufficiency (DS) Questions

Of the 220 restaurants in a certain city, how many serve neither shrim

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