Bunuel wrote:
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.
Solution
Step 1: Analyse Question Stem
• Number of people participated in the survey = 580
• Let’s draw the Venn-diagram,
• 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.