CAT 2025 Lesson : Interpretative Tables - Case 5

Directions for Questions 18 to 20 : Answer the following questions based on the information given below:

For admission to various affiliated colleges, a university conducts a written test with four different sections, each with a maximum of 50 marks. The following table gives the aggregate as well as the sectional cut-off marks fixed by six different colleges affiliated to the university. A student will get admission only if he/she gets marks greater than or equal to the cut-off marks in each of the sections and his/her aggregate marks are at least equal to the aggregate cut-off marks as specified by the college.


[CAT 2008]

18) Bhama got calls from all colleges. What could be the minimum aggregate marks obtained by her?

(1) 180
(2) 181
(3) 196
(4) 176
(5) 184

19) Charlie got calls from two colleges. What could be the minimum marks obtained by him in a section?

(1) 0
(2) 21
(3) 25
(4) 35
(5) 41

20) Aditya did not get a call from even a single college. What could be the maximum aggregate marks obtained by him?

(1) 181
(2) 176
(3) 184
(4) 196
(5) 190

Solution

18)

If Bhama gets calls from all the colleges, then she has cleared the sectional cut-off marks and aggregate cut-off marks required for all the colleges. It is inferred that the aggregate marks will be greater than or equal to 180 as 180 is the aggregate cut-off marks for one college.

The lowest possible scores for all sections are taken (which will clear the cut-off marks) to get the minimum aggregate score. Then the lowest possible score for section A, B, C and D are 45, 45, 46 and 45.

Sum of the score of all sections = 45 + 45 + 46 + 45 = 181, which is greater than 180.

Answer: (2) 181

19)

Let us have aggregate cut-off marks as 175, such that Charlie get calls from only 2 colleges (College 2 and 3).

To get the minimum cut-off score in one section we need to maximise the score of other 3 sections. Let Charlie have scored lowest score in section A, then he can score maximum marks of 50 in other 3 sections. The sum of marks in 3 sections is 150, which means that he scores 25 (175 – 150) marks.

(Note: Charlie must score more than 45 in section B and more than 46 in section C)

Answer: (3) 25

20)

If Aditya has not cleared the sectional cut-off marks in any one section, then he will not get a call even if he scores full marks in the remaining sections.

Then, if Aditya scores 41 marks in section C, he will not clear cut-off marks of Section C for Colleges 1, 2, 3 and 5. If Aditya scores 43 marks in Section D, then he will not clear the cut-off marks in Section D for Colleges 4 and 6.

To maximise the aggregate marks obtained, Aditya must score 50 marks in each of section A and B. Then the marks scored by Aditya is 50 + 50 + 41 + 43 = 184.

Answer: (3) 184

Answer:
18) (2) 181
19) (3) 25
20) (3) 184