Six colleges – A, B, C, D, E and F – jointly conducted an entrance exa…

Question

Six colleges – A, B, C, D, E and F – jointly conducted an entrance examination. The exam had four sections – I, II, III and IV. The following table gives the sectional cut-off marks specified by the colleges and the overall cut-off marks. A student will get a call from a college only if he/she scores at least the sectional and overall cut-off marks specified by that college. The maximum marks in each section is 50.

| Section → College ↓ | I | II | III | IV | Overall |
|---|---|---|---|---|---|
| A | 40 | – | – | 43 | 160 |
| B | – | 40 | 42 | 45 | 168 |
| C | 41 | – | 43 | – | 165 |
| D | – | 45 | – | 42 | 170 |
| E | 43 | – | 45 | – | 175 |
| F | – | 43 | – | 40 | 167 |

(A '–' means no cutoff is specified for that section by that college.)

**Q2.** Ram got a call from only one college. What is the maximum marks he could have scored?

Accepted Answer

B. 177

Ram should aim for the college whose constraints, when met, can be paired with section failures that lock out the other five.
Qualifying for C only: C requires I ≥ 41, III ≥ 43, overall ≥ 165. Try s1 = 50, s2 = 42, s3 = 44, s4 = 41:
- A: IV = 41 < 43 ✗ fails
- B: IV = 41 < 45 ✗ fails
- C: I = 50, III = 44, total = 177 ≥ 165 → call ✓
- D: II = 42 < 45 ✗ fails
- E: III = 44 < 45 ✗ fails
- F: II = 42 < 43 ✗ fails
(Trying to qualify for D or E always drags C or F in too because their cut-offs are dominated; B-only and A-only configurations top out lower in the option set.)
Maximum total = 50 + 42 + 44 + 41 = 177.

Answer

164

Answer

160

Answer

185