# CAT Model Paper 3 Questions and Answers with Explanation Part 3

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__Directions for questions 14 - 16: Answer the questions based on the given data__.

The following 8 teams will be taking part in the ICC world Cup 2015 in Australia.

Group A | ICC W/R | Group B | ICC W/R |

India | 1 | South Africa | 2 |

Australia | 4 | England | 3 |

Sri Lanka | 6 | Pakistan | 5 |

West Indies | 8 | New Zealand | 7 |

The format of the tournament is simple. The teams in each group play each other exactly once. The Top two teams qualify for the semi-finals, with the top team of group A playing second team of group B and vice versa. The winner of the S/F plays the finals. Each win gets the team 2 points there are no ties. In case of equal points, the team with higher Net run rate (NRR) is ranked higher.

Lalach Modi has launched a cricket betting website called doublematka. com which has calculated the following odds based on past data.

Sl. No | W/R diff | Odds |

1 | -5 to -7 | 5: 2 |

2 | -3 to -4 | 4: 3 |

3 | -2 to + 2 | 1: 1 |

4 | + 3 to + 4 | 3: 4 |

5 | + 5 to + 7 | 2: 5 |

W/R difference for a team is the difference of ranking between the Team and its opponent. For Example, to bet on India against West Indies the W/R Diff will be and to bet on West Indies against India it will be .

If the difference in world rankings is -6 and if you bet - 5 then you on winning you get back -5 plus - 2.

If the difference in world rankings is , and if you bet -3 and win you get back .

On every winning bet, doublematka. com takes a commission of 5 % on the winnings and pays the remaining to the winner.

Q: 14. If Rohan Tanhai bets $ 6000 on each group match of the West Indies, what is the maximum money that he can hope to win given that West Indies doesn՚t qualify for the Semi Finals?

(A)

(B)

(C)

(D)

Ans: B

Solution:

- Rohan Tanhai bets on WI in every match and exactly $ 6,000 each time. For him to make money WI has to win matches. But it is given that WI doesn՚t qualify for the SF stage. So best cases are that WI wins 2 matches and loses 1, in which case it is possible that WI doesn՚t qualify based on run rate.
- Secondly, to maximize Rohan՚s wins, WI wins should come against countries where the W/R difference is high, i.e.. , India and Australia (High W/R Diff, High odds, and hence greater winnings)

So

WI wins against India odds are . Hence winnings are

WI wins against Aus odds are 3: 4. Hence winnings are

WI loses against SL. Odds are 1: 1. Hence Loss of

Net Commission is of winnings

Net Winnings are

Hence,

Q: 15. Ranil Sattanayake is a compulsive gambler and die-hard Sri Lanka Fan. He bets $ 6,000 on Sri Lanka՚s first group match and doubles the bet amount in each successive match. If Sri Lanka wins the World Cup what is the minimum amount that Ranil would have won?

(A)

(B)

(C)

(D) None of these

Ans: A

Solution

- Ranil Sattanayake bets on SL in every match starting with a bet of $ 6,000 and doubling the bet in each match. Now Given SL wins the World Cup how do we minimize the winnings.
- Group Stage
- SL should qualify but win least matches. Hence SL should win 1 and lose 2 matches.
- Also, the lone win comes against WI so that winnings are minimum. Lastly the win should be first match so that bet size is minimum.

Hence

- SL Wins WI, Odds of Winnings
- SL Loss Ind, Odds of
- SL Loss to Aus, Odds of 3: 4,
- SF and Final
- SL has won the world cup implies that they have won both SF and Final. So, we can only reduce the winnings by ensuring the odds are lowest, i.e.. , 1: 1
- SF: SL Wins Pak/NZ, Odds of
- Final SL Wins WI/NZ/Pak, Odds of
- Commission on Winnings is
- Net Winnings for Ranil is

Hence, Option ()

Q: 16. Tarawala, a famous astrologer can see from the stars that either New Zealand or West Indies will win the tournament? If he starts with , then what is the maximum amount (approximate) he can win by the end of the tournament? (Assume that commission is not charged for Mr. Tarawala)

(A)

(B)

(C)

(D) None of these

Ans: B

Solution:

Tarawala knows that either WI or NZ will win the world cup. His maximum winnings will occur if he picks the winner and the winner wins all matches. The bet amount for the 1^{st} match would be . And for every successive match he will bet his winnings n + Original . Let us say he picks WI

Group Stage

WI Wins SL Odds of . Total money which is bet on next match

WI Wins Aus, Odds of . Total Money (bet on next match)

WI Wins Ind, Odds of . Total Money

SF and Final

To get the highest odds WI should play SA/Eng in the SF and then Ind/Eng/SA in the final.

So Total money at end of tournament (approx)

Total winnings . Approx choice is Mn

Q: 17. In the given figure, ABC is a right-angled triangle, right angled at A. A circle with centre X is inscribed within the triangle. Another circle with centre Y is drawn inside the triangle such that it touches AC, BC, and the larger circle. If the radii of two circles are 12 and 5 cm respectively, then find the length AC in cm.

(A)

(B)

(C)

(D)

Ans: C

Solution:

Joining both centres, if we extend the line it will meet C. Let the line AC touch the larger circle at S.

SQ is the direct common tangent for these circles.

SQ =

CYQ and CXS are similar triangles.

Or,

Therefore, while , applying dividend do to both sides, .

Since

Q: 18. + (n terms ) . Find the value of

(A)

(B)

(C)

(D)

Ans: C

Solution:

+

[1^{st} term of nth pair ] = 6

1^{st} term of nth pair

Hence, n is such that is the nth no of the series