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06 Aug 2026, 11:14
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A training program gave a final exam to all participants. Each participant was either an intern or a full-time employee. Was the percentage of interns who passed the exam greater than the percentage of all participants who passed the exam?
(1) The percentage of full-time employees who passed the exam was greater than the percentage of all participants who passed the exam.
(2) Less than \(\frac{2}{5}\) of all participants who passed the exam were interns, and less than \(\frac{3}{5}\) of all participants who failed the exam were full-time employees.
(1) The percentage of full-time employees who passed the exam was greater than the percentage of all participants who passed the exam.
(2) Less than \(\frac{2}{5}\) of all participants who passed the exam were interns, and less than \(\frac{3}{5}\) of all participants who failed the exam were full-time employees.
06 Aug 2026, 11:14
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Official Solution:
A training program gave a final exam to all participants. Each participant was either an intern or a full-time employee. Was the percentage of interns who passed the exam greater than the percentage of all participants who passed the exam?
(1) The percentage of full-time employees who passed the exam was greater than the percentage of all participants who passed the exam.
The overall passing percentage is between the interns’ passing percentage and the full-time employees’ passing percentage.
Since the full-time employees’ passing percentage was greater than the overall passing percentage, the interns’ passing percentage must have been less than the overall passing percentage.
So the answer is NO.
Sufficient.
(2) Less than \(\frac{2}{5}\) of all participants who passed the exam were interns, and less than \(\frac{3}{5}\) of all participants who failed the exam were full-time employees.
Less than \(\frac{2}{5}\) of those who passed were interns. Therefore, more than \(\frac{3}{5}\) of those who passed were full-time employees.
Less than \(\frac{3}{5}\) of those who failed were full-time employees. Therefore, more than \(\frac{2}{5}\) of those who failed were interns.
Thus, interns made up a smaller percentage of the passing group than of the failing group. Therefore, interns had a lower passing percentage than full-time employees.
The overall passing percentage is between the interns’ passing percentage and the full-time employees’ passing percentage. Therefore, the interns’ passing percentage was lower than the overall passing percentage.
So the answer is NO.
Sufficient.
Answer: D.
Answer: D
A training program gave a final exam to all participants. Each participant was either an intern or a full-time employee. Was the percentage of interns who passed the exam greater than the percentage of all participants who passed the exam?
(1) The percentage of full-time employees who passed the exam was greater than the percentage of all participants who passed the exam.
The overall passing percentage is between the interns’ passing percentage and the full-time employees’ passing percentage.
Since the full-time employees’ passing percentage was greater than the overall passing percentage, the interns’ passing percentage must have been less than the overall passing percentage.
So the answer is NO.
Sufficient.
(2) Less than \(\frac{2}{5}\) of all participants who passed the exam were interns, and less than \(\frac{3}{5}\) of all participants who failed the exam were full-time employees.
Less than \(\frac{2}{5}\) of those who passed were interns. Therefore, more than \(\frac{3}{5}\) of those who passed were full-time employees.
Less than \(\frac{3}{5}\) of those who failed were full-time employees. Therefore, more than \(\frac{2}{5}\) of those who failed were interns.
Thus, interns made up a smaller percentage of the passing group than of the failing group. Therefore, interns had a lower passing percentage than full-time employees.
The overall passing percentage is between the interns’ passing percentage and the full-time employees’ passing percentage. Therefore, the interns’ passing percentage was lower than the overall passing percentage.
So the answer is NO.
Sufficient.
Answer: D.
Answer: D
