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30 Mar 2022, 09:00
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
74% (02:32) correct
26%
(02:42)
wrong
based on 309
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A survey included two questions, each of which could be answered with either Yes or No. A total of 100 respondents took the survey, and every respondent answered both questions. How many respondents answered both questions with a Yes?
(1) Of the respondents who answered Yes to the first question, 40% answered Yes to the second question.
(2) Of the respondents who answered Yes to at least one question, 30% answered Yes to both questions.
(1) Of the respondents who answered Yes to the first question, 40% answered Yes to the second question.
(2) Of the respondents who answered Yes to at least one question, 30% answered Yes to both questions.
12 Apr 2022, 11:15
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Bunuel
Please refer to the attached tables:
Attachment:
A tale of two questions.png [ 11.95 KiB | Viewed 4418 times ]
The above info. is what we can deduce from the stem
We need the value of \(x\)
(1) Of the respondents who answered Yes to the first question, \(40\%\) answered Yes to the second question.
Attachment:
A tale of two questions 1.png [ 12.21 KiB | Viewed 4387 times ]
\(x= .40a \)
Since we do not have the value of \(a\) we cannot find \(x.\)
INSUFF.
(2) Of the respondents who answered Yes to at least one question, \(30\%\) answered Yes to both questions.
Attachment:
A tale of two questions 2.png [ 12.93 KiB | Viewed 4306 times ]
\(x = .30(a+c)\)
Since we do not have the value of \(a+c \) we cannot get \(x\).
INSUFF.
\(1+2 \)
\(.30(a+c) = .40a\)
\(a=3c\)
We do not know \(a\) or \(c\) hence using this we still cannot get the value of \(x.\)
INSUFF.
Ans E
Hope it's clear.
13 Apr 2022, 07:21
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Step 1: Analyse Question Stem
We can represent the data given in the question in terms of a Venn diagram, since we have an overlapping region (that of people answering YES for both questions).
13th Apr 2022 - Post 3.png [ 20.83 KiB | Viewed 4198 times ]
In the Venn diagram, the sum of the four regions inside the diagram should be 100 i.e.,
a + b + c + n = 100
We need to find the value of the overlapping region (or the intersection of the two sets) i.e. the value of c.
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE
Statement 1: Of the respondents who answered Yes to the first question, 40% answered Yes to the second question.
The number of respondents who answered Yes to the first question = a + c
Of these, 40% answered YES to the second question also; therefore, c = 40% of (a + c)
or c =\(\frac{ 2}{5}\) (a+c).
We have no information about the other two regions, b and n. Therefore, we cannot find the value of c uniquely since we do not have sufficient number of independent equations.
Statement 1 alone is insufficient. Answer options A and D can be eliminated.
Statement 2: Of the respondents who answered Yes to at least one question, 30% answered Yes to both questions.
The number of respondents who answered Yes to at least one question = a + b + c
Of these, 30% responded Yes to both questions; therefore, c = 30% of (a+b+c)
We have no information about n. Therefore, we cannot find the value of (a + b + c) and hence the value of c.
Statement 2 alone is insufficient. Answer option B can be eliminated.
Step 3: Analyse Statements by combining
From statement 1: c = 2/5 (a+c).
From statement 2: c = 30% of (a+b+c)
Combining the information, we can get an equation in terms of a, b and c. However, we have no information about n and hence cannot find out the values of any of the variables uniquely.
The combination of statements is insufficient. Answer option C can be eliminated.
The correct answer option is E.
We can represent the data given in the question in terms of a Venn diagram, since we have an overlapping region (that of people answering YES for both questions).
Attachment:
13th Apr 2022 - Post 3.png [ 20.83 KiB | Viewed 4198 times ]
In the Venn diagram, the sum of the four regions inside the diagram should be 100 i.e.,
a + b + c + n = 100
We need to find the value of the overlapping region (or the intersection of the two sets) i.e. the value of c.
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE
Statement 1: Of the respondents who answered Yes to the first question, 40% answered Yes to the second question.
The number of respondents who answered Yes to the first question = a + c
Of these, 40% answered YES to the second question also; therefore, c = 40% of (a + c)
or c =\(\frac{ 2}{5}\) (a+c).
We have no information about the other two regions, b and n. Therefore, we cannot find the value of c uniquely since we do not have sufficient number of independent equations.
Statement 1 alone is insufficient. Answer options A and D can be eliminated.
Statement 2: Of the respondents who answered Yes to at least one question, 30% answered Yes to both questions.
The number of respondents who answered Yes to at least one question = a + b + c
Of these, 30% responded Yes to both questions; therefore, c = 30% of (a+b+c)
We have no information about n. Therefore, we cannot find the value of (a + b + c) and hence the value of c.
Statement 2 alone is insufficient. Answer option B can be eliminated.
Step 3: Analyse Statements by combining
From statement 1: c = 2/5 (a+c).
From statement 2: c = 30% of (a+b+c)
Combining the information, we can get an equation in terms of a, b and c. However, we have no information about n and hence cannot find out the values of any of the variables uniquely.
The combination of statements is insufficient. Answer option C can be eliminated.
The correct answer option is E.
