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Professors' Performance Analysis

XAT 2018 · Quantitative Ability & Data Interpretation · Hard · Data Interpretation

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Passage / data set

The graph below represent the performance of four professors, across years, measured on four variables: Percentage of time spent on research, teaching, feedback on (a scale of 10, right-hand side) and number of publications (right-hand side). Assume that the cumulative time spent per year on research and teaching activities are same for all four professors and each of them taught only one course of 90 classroom hours.

Question 1 of 3

Which of the following, shows the maximum year to year percentage growth in feedback?

  1. A.

    Professor Arithmetic during 2013-2014

  2. B.

    Professor Algebra during 2015-2016

  3. C.

    Professor Calculus during 2012-2013

  4. D.

    Professor Calculus during 2014-2015

Answer

C

Explanation

Percentage growth in feedback:

  • Prof. Arithmetic (2013-14): (6.5−4)/4=62.5%(6.5 - 4)/4 = 62.5\%
  • Prof. Algebra (2015-16): (8−5)/5=60%(8 - 5)/5 = 60\%
  • Prof. Calculus (2012-13): (7−4)/4=75%(7 - 4)/4 = 75\%
  • Prof. Calculus (2014-15): (9−5.5)/5.5=63.63%(9 - 5.5)/5.5 = 63.63\% Thus, Professor Calculus during 2012-2013 shows the maximum percentage growth in feedback. Hence, option C is correct.

Question 2 of 3

Count the number of instances in which "annual decreasing efforts in research" is accompanied with "annual increase in feedback"?

  1. A.

    5

  2. B.

    7

  3. C.

    9

  4. D.

    11

Answer

C

Explanation

Checking each professor for years where research % decreased and feedback score increased:

  • Prof. Arithmetic: 2 instances (2013-14, 2015-16)
  • Prof. Algebra: 3 instances (2011-12, 2014-15, 2015-16)
  • Prof. Geometry: 2 instances (2010-11, 2013-14)
  • Prof. Calculus: 2 instances (2010-11, 2014-15) Total instances = 2+3+2+2=92 + 3 + 2 + 2 = 9. Hence, option C is correct.

Question 3 of 3

Research efficiency is the ratio of cumulative number of publication for a period of 3 years to the cumulative number of hours spent on research activity in those 3 years. Which of the following professors is the least efficient researcher for the period 2015 to 2017?

  1. A.

    Professor Arithmetic

  2. B.

    Professor Algebra

  3. C.

    Professor Geometry

  4. D.

    Professor Calculus

Answer

A

Explanation

Research efficiency = PublicationsResearch Hours\frac{\text{Publications}}{\text{Research Hours}}.

  • Prof. Arithmetic: RE=890×(0.7+0.5+0.6)=818×9RE = \frac{8}{90 \times (0.7 + 0.5 + 0.6)} = \frac{8}{18 \times 9}
  • Prof. Algebra: RE=890×(0.3+0.4+0.25)=89.5×9RE = \frac{8}{90 \times (0.3 + 0.4 + 0.25)} = \frac{8}{9.5 \times 9}
  • Prof. Geometry: RE=890×(0.75+0.25+2)=812×9RE = \frac{8}{90 \times (0.75 + 0.25 + 2)} = \frac{8}{12 \times 9}
  • Prof. Calculus: RE=890×(0.55+0.55+0.4)=815×9RE = \frac{8}{90 \times (0.55 + 0.55 + 0.4)} = \frac{8}{15 \times 9} Prof. Arithmetic has the highest denominator, hence the lowest research efficiency. Hence, option A is correct.

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