A series of eight games, numbered G1 to G8, is organized as part of a college fest. In each game, only four players — A, B, C, D - participate and only one of them emerges as the winner. Five persons - P, Q, R, S, T - from among the audience took part in a contest wherein each person predicts the winner of each of the eight games in the series. 

A person gets Dollar 300 for the right prediction and loses Dollar 100 for a wrong prediction. The following table gives the predictions of each of the five persons as to who the winners would be. For example in game G1, R predicted player B to win, while both P and T predicted player C to win and both Q and S predicted player D to win.

At the end of the eight games, it turned out that if any person had predicted that a single player would win each of the eight games, he would not have gained or lost any amount. At the end of the series of eight games, Q received the maximum amount of Dollar 1600, while T neither gained nor lost any amount. Had R made one more correct prediction and Q made one more incorrect prediction, the amounts gained by them at the end of the games would have interchanged.

Q1. The amount gained by P at the end of the eight games is

  1. $800
  2. $1200
  3. $400
  4. Cannot be determined

Q2. How many correct predictions were made by S?

  1. 3
  2. 5
  3. 4
  4. 2

Q3. In how many of the games was the winner not a player predicted by any of the five persons?

  1. 2
  2. 0
  3. 1
  4. 3

Exactly two games each have the winner as A, B, C and D (since a person who makes the same prediction for all the games or loss no amount). 

Q got the maximum amount - He made six correct predictions and two incorrect predictions.

Also, as per the prediction of O, D was the winner in four games. However, as D is the winner in exactly two games, his predictions in exactly two of the four games — G1, G3, G5 and G7 must be wrong.

This means, Q made the right predictions in G2, G4, G5, G8. As the difference between the amounts gained by Q and that by K is Dollar 400, so the net amount gained by R at the end of the games must have been Dollar 1200 (5 correct predictions and 3 incorrect predictions).

Now the number of correct predictions (considering only G2, G4, G5 and G3) are Q — 4, R — 2 and T - 2. As T had only two correct predictions in the eight games, it means his predictions in each of G1, G3, G6 and G7 are wrong, i.e., the winner of G1, G3, G6 and G7 respectively are not C, C, D and C respectively.

So also as B has already won two games, he could not have won any of the four games.

Therefore, The possible winners of the four games are

As R has got only two of the predictions correct among G2, G4, G5 and G8, he would have got three of his predictions among G1, G3, G6 and G7 correct.

As R’s predictor of winner of G1 is B, which is not possible, his prediction in G3, G5 and G7 must be correct.

The players who won different games are as follows.

Q1. Amount gained by P at the end of eight games is =4 x300-4x 100 =1200-400 = 800 Choice (1)

Q2. The number of correct predictions made by S is 4. Choice (3)

Q3. In one game, i.e., G1, the winner was not a player predicted by any of the five persons. Choice (3)

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