A group of 580 people participated in a survey. Each of these people

Question

A group of 580 people participated in a survey. Each of these people indicated that they had either heard of brand A soda or had not heard of brand A soda, and each of these people indicated that they had either heard of brand B soda or had not heard of brand B soda. How many of the people surveyed indicated that they had heard of brand A soda and had not heard of brand B soda?

(1) There were 226 people who indicated that they had heard of exactly one of the two brands of soda.

(2) There were 187 people who indicated that they had not heard of either brand soda and there were 281 people who indicated that they had heard of brand B soda.

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RaghavKhanna · Answer

Number of people:
Only A = a
Only B = b
Both A and B = c
Neither A or B = d

=> a + b + c + d = 580

To find: a

St. 1: 
a + b = 226
Cannot determine 'a' from this
=>  St. 1 is insufficient.

St. 2: 
d = 187
b + c = 281
=> a + b + c + d = 580
=> a + 281 + 187 = 580
=> a = 112

=>  St. 2 is sufficient.

Answer: B

GMATinsight · Answer

Answer: Option B

The detailed Video explanation is as mentioned below

https://www.youtube.com/watch?v=VHytOr_AFng

yashikaaggarwal · Answer

To find : X(Know brand A but not B)
Let people who heard about only one brand = X and Y
Statement 1: x+y = 226
No information about x or y separately. (Insufficient)

Statement 2: neither know A nor B = 187
Know about brand B = 281
No information about x (Insufficient)

Together 1&2: Sufficient

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RaghavKhanna · Answer

Hey! For Statement 2, It is possible to find people who only know A because: 580 - 187 - 281 = No. of people who only know brand A Just check it once again!

GMATWhizTeam · Answer

Solution 
 Step 1: Analyse Question Stem 
 • Number of people participated in the survey = 580
• Let’s draw the Venn-diagram,
  https://www.dropbox.com/s/m74wj9rhqivq6ic/venn_01_07.jpg?dl=1 
• In the above Venn-diagram :
 o x = Number of people who had heard of only Brand A.
o y = Number of people who had heard of only Brand B.
o z = Number of people who had heard of Brand A as well as Brand B.
o n = Number of people who had neither heard of Brand A nor of Brand B. 
• Therefore,  x + y + z+ n = 580 ………..Eq.(i)  
We need to find the value of x.

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE 
 Statement 1:  There were 226 people who indicated that they had heard of exactly one of the two brands of soda.
 • According to this statement:  x + y = 226 
• However, we don’t the value of y so we cannot find x from this information. 
Hence, statement 1 is NOT sufficient and we can eliminate answer Options A and D.

Statement 2:  There were 187 people who indicated that they had not heard of either brand soda and there were 281 people who indicated that they had heard of brand B soda.
 • According to this statement:
 o   n = 187 
o  y + z = 281  
• Now, substituting the value of n and y + z in Eq.(i), we get,
 o  x + 281 + 187 = 580 
  ⟹ x = 580 – 281-187 
  ⟹ x = 112   
Hence, statement 2 is sufficient.
Thus, the correct answer is  Option B.

sambitspm · Answer

Kindly see the attachment. Now this question might take you some time as it takes time to formulate the matrix based on the complete context of the question.

TIME: 02:34
IMO B

rajatchopra1994 · Answer

Explanation:

Statement 1: x+y=226
2 variable, need value for one variable to solve equation
NOT sufficient

Statement 2: b = 187
y+a=281
x+y+a+b = 580
x+281+187=580
x=112
Sufficient.

IMO-B.

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A group of 580 people participated in a survey. Each of these people

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