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04 Aug 2025, 11:47
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Column A: \(\frac{9M}{10}\)
Column B: \(\frac{4M}{5}\)
In a company survey, M employees evaluated both Proposal 1 and Proposal 2, selecting either 'agree' or 'disagree' for each.
• \(\frac{2}{5}\) of them agreed with Proposal 1, and of those, \(\frac{1}{4}\) also agreed with Proposal 2.
• Of those who disagreed with Proposal 1, \(\frac{2}{3}\) agreed with Proposal 2.
Select for Column A the expression that represents the number of employees who did not answer "agree" to both proposals, and select for Column B the expression that represents the number of employees who did not answer "disagree" to both proposals. Make only two selections, one in each column.
• \(\frac{2}{5}\) of them agreed with Proposal 1, and of those, \(\frac{1}{4}\) also agreed with Proposal 2.
• Of those who disagreed with Proposal 1, \(\frac{2}{3}\) agreed with Proposal 2.
Select for Column A the expression that represents the number of employees who did not answer "agree" to both proposals, and select for Column B the expression that represents the number of employees who did not answer "disagree" to both proposals. Make only two selections, one in each column.
| Column A | Column B | |
| \(\frac{M}{10}\) | ||
| \(\frac{M}{5}\) | ||
| \(\frac{2M}{5}\) | ||
| \(\frac{4M}{5}\) | ||
| \(\frac{9M}{10}\) |
ShowHide Answer
Official Answer
Column A: \(\frac{9M}{10}\)
Column B: \(\frac{4M}{5}\)
04 Aug 2025, 11:47
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Official Solution:
Column A
The number of employees who did not answer "agree" to both proposals means we must exclude those who answered {agree, agree}.
• Total employees: M
• Agreed with Proposal 1: \(\frac{2}{5} * M = \frac{2M}{5}\)
• Of these, agreed with Proposal 2: \(\frac{1}{4} * \frac{2M}{5} = \frac{2M}{20} = \frac{M}{10}\)
So, \(\frac{M}{10}\) employees agreed with both proposals.
Therefore, the number who did not agree with both \(= M - \frac{M}{10} = \frac{9M}{10}\)
Column B
The number of employees who did not answer "disagree" to both proposals means we must exclude those who answered {disagree, disagree}.
• Disagreed with Proposal 1: \(M - \frac{2M}{5} = \frac{3M}{5}\)
• Of these, agreed with Proposal 2: \(\frac{2}{3} * \frac{3M}{5} = \frac{6M}{15} = \frac{2M}{5}\)
• So, disagreed with Proposal 2: \(\frac{3M}{5} - \frac{2M}{5} = \frac{M}{5}\)
Thus, \(\frac{M}{5}\) employees disagreed with both proposals.
So, the number who did not disagree with both \(= M - \frac{M}{5} = \frac{4M}{5}\)
Correct answer:
Column A "\(\frac{9M}{10}\)"
Column B "\(\frac{4M}{5}\)"
Bunuel
Column A
The number of employees who did not answer "agree" to both proposals means we must exclude those who answered {agree, agree}.
• Total employees: M
• Agreed with Proposal 1: \(\frac{2}{5} * M = \frac{2M}{5}\)
• Of these, agreed with Proposal 2: \(\frac{1}{4} * \frac{2M}{5} = \frac{2M}{20} = \frac{M}{10}\)
So, \(\frac{M}{10}\) employees agreed with both proposals.
Therefore, the number who did not agree with both \(= M - \frac{M}{10} = \frac{9M}{10}\)
Column B
The number of employees who did not answer "disagree" to both proposals means we must exclude those who answered {disagree, disagree}.
• Disagreed with Proposal 1: \(M - \frac{2M}{5} = \frac{3M}{5}\)
• Of these, agreed with Proposal 2: \(\frac{2}{3} * \frac{3M}{5} = \frac{6M}{15} = \frac{2M}{5}\)
• So, disagreed with Proposal 2: \(\frac{3M}{5} - \frac{2M}{5} = \frac{M}{5}\)
Thus, \(\frac{M}{5}\) employees disagreed with both proposals.
So, the number who did not disagree with both \(= M - \frac{M}{5} = \frac{4M}{5}\)
Correct answer:
Column A "\(\frac{9M}{10}\)"
Column B "\(\frac{4M}{5}\)"
