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24 Oct 2023, 11:19
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Minimum service score: 0
Minimum research score: 2.5
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:
68% (02:34) correct
32%
(02:39)
wrong
based on 1227
sessions
History
Date
Time
Result
Not Attempted Yet
A certain assistant professor in the Art History department at University X is being evaluated for promotion. One of the requirements is a performance score of at least 4.0. The performance score is the weighted average of 3 component scores: one for research, one for teaching, and one for service, with the scores for research and teaching each weighted 40% and the score for service weighted 20%. Each component score is between 0.0 and 5.0, inclusive.
Consistent with the given information, select for Minimum service score the least possible score the professor can receive for service and still achieve a performance score of at least 4.0, and select for Minimum research score the least possible score the professor can receive for research and still achieve a performance score of at least 4.0. Make only two selections, one in each column.
Consistent with the given information, select for Minimum service score the least possible score the professor can receive for service and still achieve a performance score of at least 4.0, and select for Minimum research score the least possible score the professor can receive for research and still achieve a performance score of at least 4.0. Make only two selections, one in each column.
| Minimum service score | Minimum research score | |
| 0 | ||
| 0.5 | ||
| 1 | ||
| 1.5 | ||
| 2 | ||
| 2.5 |
ShowHide Answer
Official Answer
Minimum service score: 0
Minimum research score: 2.5
18 Jan 2024, 11:54
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The key here is if we want to minimize one variable, we need to maximize the other variables:
02 Nov 2023, 00:53
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parkhydel
Attention: This question is sourced from the GMAT Prep Focus practice test; solving it before taking the practice test can inflate your score.
A certain assistant professor in the Art History department at University X is being evaluated for promotion. One of the requirements is a performance score of at least 4.0. The performance score is the weighted average of 3 component scores: one for research, one for teaching, and one for service, with the scores for research and teaching each weighted 40% and the score for service weighted 20%. Each component score is between 0.0 and 5.0, inclusive.
Consistent with the given information, select for Minimum service score the least possible score the professor can receive for service and still achieve a performance score of at least 4.0, and select for Minimum research score the least possible score the professor can receive for research and still achieve a performance score of at least 4.0. Make only two selections, one in each column.
Let the score for research, teaching and service be given by R, T and S.
The above tells us that the total score = 0.4R+0.4T+0.2S and it has to be at least 4.
\(0.4R+0.4T+0.2S \geq 4.............4R+4T+2S \geq 40...........2R+2T+S \geq 20\)
Now, Minimum score in any festoon would mean maximising the other two.
Minimum S:
Let R and T be 5 => \(2*5+2*5+S \geq 20........S\geq 0\)
Thus 0 is the answer.
Minimum R:
Let S and T be 5 => \(2*R+2*5+5 \geq 20........2*R \geq 5.....R\geq 2.5\)
Thus 2.5 is the answer.
