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01 May 2018, 00:54
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
74% (02:05) correct
26%
(02:36)
wrong
based on 181
sessions
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Not Attempted Yet
In a survey of students at a certain college, participants were asked two questions. If 2/3 of those surveyed responded “Strongly Agree” to the first question, and of those respondents, 1/5 answered “Strongly Agree” to the second question, what portion of the survey participants did not answer “Strongly Agree” to both questions?
(A) 13/15
(B) 5/6
(C) 3/4
(D) 3/5
(E) 2/15
(A) 13/15
(B) 5/6
(C) 3/4
(D) 3/5
(E) 2/15
01 May 2018, 01:45
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Bunuel
Let, Total Population = x
Participants who answered "Strongly agree" to first question = (2/3)x
Participants who answered "Strongly agree" to first as well as second question = (1/5)*(2/3)x = (2/15)x
i.e Population that did not answer strongly agree to both question = x - (2/15)x = (13/15)x
Answer: option A
01 May 2018, 01:55
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Solution
Given:
• All participants were asked two questions
• \(\frac{2}{3}\)rd of those surveyed responded “Strongly Agree” to the first question
• Of those responded to the first question, \(\frac{1}{5}\)th answered “Strongly Agree” to the second question
To find:
• What portion of the survey participants did not answer “Strongly Agree” to both questions
Approach and Working:
• We can assume the total participants is r.
- o Participants who responded “Strongly Agree” to the 1st question = r * \(\frac{2}{3}\)
- o Of those participants who responded “Strongly Agree” to the 1st question, participants who responded “Strongly Agree” to the 2st question = r * \(\frac{2}{3} * \frac{1}{5} = r * \frac{2}{15}\)
• Portion of survey participants did not answer “Strongly Agree” to both questions = \({(13/15r)}/r = \frac{13}{15}\)
Hence, the correct answer is option A.
Answer: A
Note: rather than taking r as the total participants, if we assume the value of r as 15 or any multiples of 15 (because the lcm of denominators 3 and 5 is 15), the calculations will be much easier.
