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.)

**Q3.** Madhuri got calls from all the six colleges. What is the minimum marks she could have scored?

Accepted Answer

B. 178

She must clear the maximum cutoff in every specified section, plus the highest overall cutoff.
- Section I: max(40, 41, 43) = 43 → s1 ≥ 43
- Section II: max(40, 45, 43) = 45 → s2 ≥ 45
- Section III: max(42, 43, 45) = 45 → s3 ≥ 45
- Section IV: max(43, 45, 42, 40) = 45 → s4 ≥ 45
- Overall: max overall cutoff = 175 (E's)
Minimum total = 43 + 45 + 45 + 45 = 178 (≥ 175 ✓, so overall cutoff is satisfied automatically). Verification confirms all 6 colleges call her.

Answer

179

Answer

180

Answer

175