Group QuestionAnswer the following question based on the information g...
Let a be the number of students who have taken the XAT examination, secured 96 percentile or more, have work experience of more than 3 years but are not university toppers.
b : (XAT, at least 96 percentile, University topper, Work experience)
c : (XAT, less than 96 percentile, University topper, Work experience)
d: (CAT, at least 96 percentile, not a University topper, Work experience)
e : (CAT, at least 96 percentile, University topper, Work experience)
/: (CAT, less than 96 percentile, University topper, Work experience)
g : (CAT, less than 96 percentile, not a University topper, Work experience)
h : (CAT, at least 96 percentile, not a University topper, Fresher)
i: (CAT, at least 96 percentile, University topper, Fresher)
j : (CAT, less than 96 percentile, University topper, Fresher)
k: (CAT, less than 96 percentile, not a University topper, Fresher)
/: (XAT, at least 96 percentile, not a University topper, Fresher)
m : (XAT, at least 96 percentile, University topper, Fresher)
n : (XAT, less than 96 percentile, University topper, Fresher)
o : (XAT, less than 96 percentile, not a University topper, Fresher)
v Every student who has been absorbed by the institute must have secured at least 96 percentile in the examination he or she has taken, or must be a University topper,
g — k — o - 0
Total number of students = 80
From (I), there were 45 university toppers.
Therefore, the remaining 35 students were not university toppers, i.e. a + d + h +1 = 80 — 45 = 35 ... (i)
Also, of these 45 university toppers, 33.33% (i.e. 15 students) were freshers while 66.66% (i.e. 30 students) had taken the CAT examination. This means that the remaining 30 students had work experience of more than 3 years, and that 15 students had taken the XAT examination.
-j + n= 15 (ii)
and b + c + e + /= 30 ... (iii)
ande+f+j = 30 ... (iv)
andb + c + n=5 ... (v)
From (VII), we have e + /= 20 ... (vi)
Using (iv) and (vi), we have j = 10 ... (vii)
Using (ii) and (vii), we have n - 5 ... (viii)
From (V), 30 students had appeared for XAT and of these 15 were freshers.
•*•/ + «= 15 ... (ix)
and a + b + c= 15 ... (x)
Using (viii) and (ix), we have j = l = 10
Also, using (viii) and (v), we have b + c = 10 ... (xi)
Using (x) and (xi), we have a = 5 ... (xii)
From (VIII), there were 40 students who had a work experience greater than 3 years. ••• a + b + c + d+ e+ /= 40 ... (ix)
Using (x) and (vi), we have d = 5
Using (i) and the values of a, d and l obtained above, we have h = 15
From (VI), we have b + e = 15. Using this result with b + c = 10, we have e = c + 5
••• We have,
The number of students that the college has absorbed who had work experience, were also university top 10 rankers, had taken the CAT examination and had secured more than 96 percentile in the examination they had taken was c + 5.
v The value of c cannot be computed,
••• The answer cannot be determined.
Hence, option 4.