A certain assistant professor in the Art History department at Univers

Question

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.

GMATCoachBen · Accepted Answer

The key here is if we want to minimize one variable, we need to maximize the other variables:

https://www.youtube.com/watch?v=OZLsNRPjbzs

Bunuel · Answer

We are given that 0.4R + 0.4T + 0.2S must be greater than or equal to 4: 0.4R + 0.4T + 0.2S ≥ 4 General rule for such problems: To maximize one quantity, minimize the others. To minimize one quantity, maximize the others. Minimizing S: To find the minimum value of S for which 0.4R + 0.4T + 0.2S ≥ 4 holds, we need to maximize R and T. Since the maximum value for both R and T is 5, we get 0.4(5) + 0.4(5) + 0.2S ≥ 4, which simplifies to S ≥ 0. Thus, the minimum value of S is 0. Minimizing R: To find the minimum value of R for which 0.4R + 0.4T + 0.2S ≥ 4 holds, we maximize T and S. Again, the maximum values for T and S are both 5: 0.4R + 0.4(5) + 0.2(5) ≥ 4. This simplifies to R ≥ 2.5. Thus, the minimum value of R is 2.5. GMAT-Club-Forum-oktaacqg.png

chetan2u · Answer

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. 
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.

033 · Answer

I didnt understand that why didnt we divide the equation by 3 i.e (.4x + .4y + .2z)/3 since it is weighted average

chetan2u · Answer

No, what you are doing is normal average.

Weighted average is due to amount/weight of each. Here it is 40%, 40% and 20%, and that is why we are multiplying R, S and T by 0.4, 0.4 and 0.2.

reeyab · Answer

In weighted averages you have to sum the weights and not the number of items

shvm_sin7 · Answer

Hi, I did not understand as to why did we maximize teaching and research score to find minimum service score? Should'nt we minimize the both so as to gete the bare minimum of service score required which will guarantee us a weighted score of atleast 4? Please help

GMATCoachBen

The key here is if we want to minimize one variable, we need to maximize the other variables:

krohatgi · Answer

But arents we searching for the weighted average - so wouldnt we need to divide the weighted sum by 3?

Shaunak3004 · Answer

Weighted Average = ((Wi*Xi), i=1...n)/((Wi), i=1...n).

Here we don't divide by total observations, but sum of the weights.

In this case here the sum = 0.4+0.4+0.2 = 1.0

This makes the equation for weighted average = ((Wi*Xi), i=1...n) only.

oorja31 · Answer

Does this question not require the 2 minimum values to be consistent with each other? I thought we need minimum values of both research and teaching at the same time and achieve the performance score of at least 4.

Bunuel · Answer

No, the question doesn't require the two minimums to work together. Each is solved independently.

You're asked for the minimum service score, so we assume research and teaching are maxed to see how low service can go. Then for minimum research, we assume teaching and service are maxed to find how low research can go.

It’s not about finding a single set of values that works together. It’s about finding the minimum possible for each one on its own, under the given constraint.

anshhh2705 · Answer

Nope, seems to be independent of one another.

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A certain assistant professor in the Art History department at Univers

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