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30 Apr 2025, 10:48
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
89% (02:11) correct
11%
(02:01)
wrong
based on 36
sessions
History
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Not Attempted Yet
A cultural survey asked individuals whether they were interested in either of two traditional art forms: folk music and regional dance. Each respondent indicated an interest in at least one of the two. What percent of the respondents indicated interest only in regional dance?
(1) Among all respondents, the ratio of those interested in regional dance to those interested in folk music was 5 to 4.
(2) Among those interested in folk music, one-fourth also expressed interest in regional dance.
Gentle note to all experts and tutors: Please refrain from replying to this question until the Official Answer (OA) is revealed. Let students attempt to solve it first. You are all welcome to contribute posts after the OA is posted. Thank you all for your cooperation!
(1) Among all respondents, the ratio of those interested in regional dance to those interested in folk music was 5 to 4.
(2) Among those interested in folk music, one-fourth also expressed interest in regional dance.
Gentle note to all experts and tutors: Please refrain from replying to this question until the Official Answer (OA) is revealed. Let students attempt to solve it first. You are all welcome to contribute posts after the OA is posted. Thank you all for your cooperation!
10 May 2025, 16:45
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Official Solution:
A cultural survey asked individuals whether they were interested in either of two traditional art forms: folk music and regional dance. Each respondent indicated an interest in at least one of the two. What percent of the respondents indicated interest only in regional dance?
Since each respondent indicated interest in at least one of the two, the total number of respondents is given by \(Total = Folk + Dance - Both\). We are asked to find the value of \(\frac{Dance - Both}{Total} * 100\).
(1) Among all respondents, the ratio of those interested in regional dance to those interested in folk music was 5 to 4.
This tells us that the number of regional dance fans is \(5x\) and the number of folk music fans is \(4x\) for some positive value \(x\). However, we do not know how many respondents are interested in both art forms. Therefore, we cannot determine how many are interested only in regional dance or the total number of respondents. Not sufficient.
(2) Among those interested in folk music, one-fourth also expressed interest in regional dance.
This tells us that the number of people interested in both is one-fourth of the number of folk music fans. But this alone is not of much help. Not sufficient.
(1)+(2) From (1), the number of folk music fans is \(4x\), and from (2) one-fourth of folk music fans also like regional dance, so the number of people interested in both is \(x\). Since \(Total = 5x + 4x - x = 8x\) and \(Only\ dance = Dance - Both = 5x - x = 4x\), then required percent = \(\frac{4x}{8x}*100 = 50%\).
Answer: C
A cultural survey asked individuals whether they were interested in either of two traditional art forms: folk music and regional dance. Each respondent indicated an interest in at least one of the two. What percent of the respondents indicated interest only in regional dance?
Since each respondent indicated interest in at least one of the two, the total number of respondents is given by \(Total = Folk + Dance - Both\). We are asked to find the value of \(\frac{Dance - Both}{Total} * 100\).
(1) Among all respondents, the ratio of those interested in regional dance to those interested in folk music was 5 to 4.
This tells us that the number of regional dance fans is \(5x\) and the number of folk music fans is \(4x\) for some positive value \(x\). However, we do not know how many respondents are interested in both art forms. Therefore, we cannot determine how many are interested only in regional dance or the total number of respondents. Not sufficient.
(2) Among those interested in folk music, one-fourth also expressed interest in regional dance.
This tells us that the number of people interested in both is one-fourth of the number of folk music fans. But this alone is not of much help. Not sufficient.
(1)+(2) From (1), the number of folk music fans is \(4x\), and from (2) one-fourth of folk music fans also like regional dance, so the number of people interested in both is \(x\). Since \(Total = 5x + 4x - x = 8x\) and \(Only\ dance = Dance - Both = 5x - x = 4x\), then required percent = \(\frac{4x}{8x}*100 = 50%\).
Answer: C
General Discussion
05 May 2025, 23:38
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Bunuel
Let's assume that the following participants responded -
Only Music = x
Only Dance = y
Music + Dance = z
Question
\(\frac{y}{(x+y+z)}\) = ?
Statement 1
(1) Among all respondents, the ratio of those interested in regional dance to those interested in folk music was 5 to 4.
\(\frac{y+z}{x+z} = \frac{5}{4}\)
\(4y + 4z = 5x + 5z\)
\(4y - 5x = z\)
We cannot use this expression to find the value of \(\frac{y}{(x+y+z)}\), hence the statement alone is not sufficient. Eliminate A, and D.
Statement 2
(2) Among those interested in folk music, one-fourth also expressed interest in regional dance.
\(z = \frac{1}{4} (x+z)\)
\(3z = x\)
We cannot use this expression to find the value of \(\frac{y}{(x+y+z)}\), hence the statement alone is not sufficient. Eliminate B.
Combined
From (1) → \(4y - 5x = z\)
From (2) → \(3z = x\)
\(4y - 15z = z\)
\(4y = 16z\)
\(y = 4z\)
\(\frac{y}{(x+y+z)}\) =
\(\frac{4z}{(3z+4z+z)}\)
\(\frac{4z}{8z}\)
\(\frac{1}{2}\)
Option C
