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Read the following scenario and answer the THREE questions that follow.
The enrolment of students (in 1000s) at each of the five universities named — MPU, JSU, LTU, PKU and TRU — during each of the eight years from 2014 to 2021 is represented in the following chart. The names of these universities are not shown in the chart, Stead they are labelled Unit 1, Unit 2, Unit 3, Unit 4 and Unit 5.
However, these four pieces of information are available:
W: The magnitudes of TRU's and MPU's net change in enrolment between 2014 and 2021 are the closest among any two universities.
X: LTU had the same enrolment in consecutive years at least twice between 2014 and 2021.
Y: The increase in JSU's enrolment from 2015 to 2019 is about 50% of TRU's total enrolment in 2020.
Z: The enrolment in one of LTU and PKU had a steady decline between 2014 and 2021, while the enrolment in the other had no decline between any two consecutive years in the same period.
Which amongst the pieces of information mentioned below, if removed, will notprevent us from uniquely identifying the five universities?
Using condition W :
The magnitudes of the net change in enrollment between 2014 and 2021 is closest among any two universities for TRU and MPU.
Going by the color of the lines the net change for different universities is:
Univ 1: 0.7
Univ 2: 4.4
Univ 3: 0.1
Univ 4: 0.2
Univ 5: 3.3
The closest among these are: Univ 3 and Univ 4. They can possibly be : (TRU/MPU)
Using condition X :
The university LTU must have the same enrollment in consecutive years at least twice :
LTU can either be Univ 3 or Univ 1 but since Univ 3 must be among TRU and MPU. LTU is university 1.
Using condition Y :
The increase in the enrollment of JSU between the years 2015 and 2019 is 50 percent of TRU's total enrollment in 2020.
Considering :
TRU = Univ 4
The enrollment is 5.
TRU = Univ 3
The enrollment is 0.7
For TRU as Univ 3, there is no university whose increase in enrollment between 2015 and 2019 is 50 percent of TRU.
Hence TRU = Univ 4.
Since the increase in enrollment for JSU is half of TRU. The increase must be half of 5 = 2.5
The only possible case is JSU = Univ 2.
MPU = Univ 3.
LTU = Univ 1
PKU = Univ 5.
All the universities can be uniquely determined without using the condition Z.
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