Question: What is the highest number of wins for a team in the first stage in spite of which it would be eliminated at the end of first stage?
Explanation:
We need to find, maximum value of x, such that despite winning x matches, a team gets definitely eliminated at the end of the first stage.
If x = 4; the team can reach in second stage.
{For example: Let A, B, C, D, E, F, G, and H are the eight teams. A wins matches against B, C, D, E, F, G(i.e. 6 matches); B wins matches against C, D(i.e. wins 2 matches);; C wins matches against D, E(i.e. wins 2 matches); D wins match against E; E wins match against B; F wins matches against B, C, D, E(i.e. wins 4 matches); G loose only one match against A (i.e. wins 6 matches); and H loose only one match against G (i.e. wins 6 matches).}
If x = 3; the team can reach in second stage.
{For example: Let A, B, C, D, E, F, G, and H are the eight teams. A wins matches against B, C, D, E, F, G(i.e. 6 matches); B wins matches against C, D; C wins matches against D, E; D wins match against E and F(i.e. wins 2 matches); E wins match against B; F wins matches against B, C, E(i.e. wins 3 matches); G loose only one match against A (i.e. wins 6 matches); and H loose only one match against G (i.e. wins 6 matches).}
If x = 2; the team can reach in second stage.
{For example: Let A, B, C, D, E, F, G, and H are the eight teams. A wins matches against B, C, D, E, F, G(i.e. 6 matches); B wins matches against C, D; C wins matches against D, E; D wins match against E and F(i.e. wins 2 matches); E wins match against B and F(i.e. wins 2 matches); F wins matches against B, C,(i.e. wins 2 matches); G loose only one match against A (i.e. wins 6 matches); and H loose only one match against G (i.e. wins 6 matches).}
Thus, for x = 2, 3 and 4; we definitely cannot say that the team will not reach the second stage.
We can say that the value of x must be 1, because only four teams reach the second stage and it is not possible that more than two teams win exactly one match each.
Hence, option (a).