CAT 2008 — DILR Question 1
Answer the following question 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.
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Aditya did not get a call from even a single college. What could be the maximum aggregate marks obtained by him?
Answer & solution
- A
181
- B
176
184
- D
196
- E
190
Since Aditya didn’t get a call from any of the colleges, so for each college, he either didn’t clear one of the sectional cut-offs or he didn’t clear the aggregate cut-off or both.
If he didn’t clear one of the sectional cut-offs, then for that section he scored less marks than the least cut-off among the given cut-offs of all the colleges.
For example, for section A, it is given that the cut-offs for colleges 1, 4 and 5 are 42, 43 and 45 respectively. The least cut-off among them is 42.
So, in order to not clear the sectional cut-off of section A for colleges 1, 4 and 5, he should have scored less than 42.
Similarly,
For colleges 1, 2 and 6, Aditya’s Section B marks < 41
For colleges 1, 2, 3 and 5, Aditya’s Section C marks < 42
For colleges 4 and 6, Aditya’s Section D marks < 44
If he scores less in Section C and D, he would not get calls for any colleges. Also in order to maximise the score we would assume that he got just one less than the cut-off in section C and D and he scored maximum marks (50) in other sections.
∴ Maximum marks obtained by Aditya such that he doesn’t get any calls = 41 + 43 + 50 + 50 = 184
Hence, option (c).