Ten students Alex, Bryan, Charlie, Deepak, Elwin, Frank, George, Harish, Ian and Joseph are the only participants in an inter-college competition. They are all from three different colleges viz. Harvard, Stanford and Oxford. The number of participants from no two colleges is the same.

The following additional information is known:

- Exactly two of Bryan, Elwin and George are from Harvard.
- Frank and Alex are from different colleges and neither of them is from a college from where the maximum participants are.
- Charlie and Ian are from the same college.
- Derek, Harish and Joseph are from three different colleges.
- Harish is from Stanford and Derek is from the same college as Alex.

**Q1. **Which two of these are definitely from two different colleges?

- Elwin and Frank
- Bryan and Alex
- Ian and Derek
- George and Harish

**Q2. **Which of these students cannot be from the college from where the least number of participants are?

- Frank
- Joseph
- Derek
- Alex

**Q3. **If Joseph and Bryan are from different colleges, which of the below statements is definitely true?

- Bryan and Alex are from Oxford.
- Bryan is from the same college as Harish.
- Elwin and Ian are from the same college.
- None of the above

**Q4. **The colleges of how many of the 10 students can be definitely determined?

Ten students are Alex(A), Bryan(B), Charlie (C), Derek(0), Elwin(E), Frank(F), George(G), Harish(H), lan(I) and Joseph(J). D, H and J are from three different colleges. Also, two of B, E and 6 are from Harvard.

Therefore, there are at least 3 students from Harvard. If one of F or A is from Harvard, then two of the colleges will have the same number of participants.

Thus, neither F nor A is from Harvard. Also, it implies that most number of participants are from Harvard and there are at least two participants from each college. Thus, the only possibility is that there are 5 students from Harvard, and 3 and 2 students horn Stamford and Oxford (in any order).

From condition (v), Derek and Alex are from Oxford and Frank is from Stanford.

Thus, partial information about students is as below:

Harvard (5) | Stanford | Oxford |

J | H | D |

C | F | A |

I |

Two of B, E and G from Harvard.

**Q1. **As it can be seen from the table above, Ian and Derek are from different colleges. **Hence, [3].**

**Q2. **Joseph cannot be from a college from where the least number of participants are**. Hence, [2].**

**Q3. **From the given condition, George and Elwin are from Harvard. Thus, Elwin and Ian are from the same college**. Hence, [3].**

**Q4. **The colleges of 7 students out of 10 can be definitely determined. Therefore, the required **answer is 7.**