Comprehension
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-offmarks 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.
Question: 1
Bhama got calls from all colleges. What could be the minimum aggregate marks obtained by her?
Bhama got calls from all colleges. What could be the minimum aggregate marks obtained by her?
Show Hint
To be called by every college she must meet the highest cut-off in each section and the highest aggregate cut-off.
Updated On: Nov 4, 2026
- 180
- 196
- 181
- 176
- 184
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Highest sectional cut-off over all six colleges:
Section A: 42, 43, 45, so 45. Section B: 42, 45, 41, so 45. Section C: 42, 45, 46, 43, so 46. Section D: 45, 44, so 45.
Step 2: Minimum total from the sections:
\(45+45+46+45=181\).
Step 3: Aggregate requirement:
The highest aggregate cut-off is 180 (College 5), and \(181\ge 180\), so the aggregate condition is automatically met.
Hence the least possible aggregate is 181 (180 is not possible since the sectional minima already add to 181).
Final Answer:
The correct option is (3): 181.
Section A: 42, 43, 45, so 45. Section B: 42, 45, 41, so 45. Section C: 42, 45, 46, 43, so 46. Section D: 45, 44, so 45.
Step 2: Minimum total from the sections:
\(45+45+46+45=181\).
Step 3: Aggregate requirement:
The highest aggregate cut-off is 180 (College 5), and \(181\ge 180\), so the aggregate condition is automatically met.
Hence the least possible aggregate is 181 (180 is not possible since the sectional minima already add to 181).
Final Answer:
The correct option is (3): 181.
Was this answer helpful?
0
0
Question: 2
Charlie got calls from two colleges. What could be the minimum marks obtained by him in a section?
Charlie got calls from two colleges. What could be the minimum marks obtained by him in a section?
Show Hint
Each section has maximum 50, so a low mark in one section must be compensated by 50s elsewhere. Use the smallest aggregate cut-off that two colleges together force.
Updated On: Nov 4, 2026
- 25
- 21
- 0
- 35
- 41
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Lower bound:
Only College 3 has an aggregate cut-off below 175 (it is 171); every other college needs at least 175. Charlie is called by two colleges, so at least one of them has aggregate cut-off \(\ge 175\); his total is therefore \(\ge 175\).
The other three sections can give at most \(3\times50=150\), so his lowest section mark is at least \(175-150=25\).
Step 2: Check that 25 is attainable:
Take marks A = 25, B = C = D = 50 (total 175).
College 2 (B \(\ge45\), C \(\ge45\), aggregate 175): yes. College 3 (C \(\ge46\), aggregate 171): yes.
College 1 needs A \(\ge42\), College 4 needs A \(\ge43\), College 5 needs A \(\ge45\): no. College 6 needs aggregate 176 and he has 175: no.
So he gets calls from exactly two colleges.
Final Answer:
The correct option is (1): 25.
Only College 3 has an aggregate cut-off below 175 (it is 171); every other college needs at least 175. Charlie is called by two colleges, so at least one of them has aggregate cut-off \(\ge 175\); his total is therefore \(\ge 175\).
The other three sections can give at most \(3\times50=150\), so his lowest section mark is at least \(175-150=25\).
Step 2: Check that 25 is attainable:
Take marks A = 25, B = C = D = 50 (total 175).
College 2 (B \(\ge45\), C \(\ge45\), aggregate 175): yes. College 3 (C \(\ge46\), aggregate 171): yes.
College 1 needs A \(\ge42\), College 4 needs A \(\ge43\), College 5 needs A \(\ge45\): no. College 6 needs aggregate 176 and he has 175: no.
So he gets calls from exactly two colleges.
Final Answer:
The correct option is (1): 25.
Was this answer helpful?
0
0
Question: 3
Aditya did not get a call from even a single college. What could be the maximum aggregate marks obtained by him?
Aditya did not get a call from even a single college. What could be the maximum aggregate marks obtained by him?
Show Hint
To find maximum aggregate without qualifying anywhere, miss one sectional cut-off per college while scoring high otherwise.
Updated On: Oct 28, 2026
- 181
- 176
- 184
- 196
- 190
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
To find the maximum aggregate marks obtained by Aditya such that he did not get a call from any college, consider the likely cut-off criteria for a call from colleges. If Aditya exceeded any expected cut-off, he would have received a call. Therefore, his marks must be strictly lower than the lowest of such cut-offs. Assuming the given options are potential aggregate marks: 181, 176, 184, 196, and 190, we need to find the maximum permissible limit that is below all necessary cut-offs.
| Option | Possible Status |
|---|---|
| 181 | Potential |
| 176 | Potential |
| 184 | Potential but does not exceed threshold |
| 196 | Unlikely, as it surpasses lower cut-offs |
| 190 | Possible, yet slightly higher |
Considering college cut-offs logically increase with aggregate marks, Aditya's scores likely align at the higher end of "not getting a call" thresholds. The highest permissible mark without attracting any college interest is therefore 184. As such, the correct option is 184.
Was this answer helpful?
0
0
Top CAT Questions
- Compare and contrast between Portia and Jessica characters in Merchant of Venice.
- In a triangle ABC,AB=AC=8cm. A circle drawn with BC as diameter passes through A. Another circle drawn with center at A passes through B and C. Then the area,in sq.cm,of the overlapping region between the two circles is
- The simple interest accrued on an amount of Rs.25,000 at the end of three years is Rs.7,500. What would be the compound interest accrued on the same amount at the same rate in the same period?
- What is the sum of all roots of the equation \(|x+4|^2–10|x+4|=24\)?
- A solid metal sphere is melted and smaller spheres of equal radii are formed. 10% of the volume of the sphere is lost in the process. The smaller spheres have a radius which is \(\frac{1}{9}\text{th}\) the larger sphere. If 10 litres of paint were needed to paint the larger sphere,how many litres are needed to paint all the smaller spheres?
View More Questions