CAT 1999 | Question: 109

Question

Answer the question based on the following information.

Recently, Ghosh Babu spent his winter vacation on Kyakya Island. During the vacation, he visited the local casino where he came across a new card game. Two players, using a normal deck of $52$ playing cards, play this game. One player is called the ‘dealer’ and the other is called the ‘player’. First, the player picks a card at random from the deck. This is called the base card. The amount in rupees equal to the face value of the base card is called the base amount. The face values of ace, king, queen and jack are ten. For other cards the face value is the number on the card. Once the ‘player’ picks a card from the deck, the ‘dealer’ pays him the base amount. Then the ‘dealer’ picks a card from the deck and this card is called the top card. If the top card is of the same suit as the base card, the ‘player’ pays twice the base amount to the ‘dealer’. If the top card is of the same colour as the base card (but not the same suit), then the ‘player’ pays the base amount to the ‘dealer’. If the top card happens to be of a different colour than the base card, the ‘dealer’ pays the base amount to the ‘player’.

Ghosh Babu played the game four times. First time he picked eight of clubs and the ‘dealer’ picked queen of clubs. Second time, he picked ten of hearts and the ‘dealer’ picked two of spades. Next time, Ghosh Babu picked six of diamonds and the ‘dealer’ picked ace of hearts. Lastly, he picked eight of spades and the ‘dealer’ picked jack of spades. Answer the following question based on these four games.

The initial money Ghosh Babu had (before the beginning of the game sessions) was Rs. X. At no point did he have to borrow any money. What is the minimum possible value of X?

• A. $16$
• B. $8$
• C. $100$
• D. $24$

Answer 1

answer is B)

let $\text{x}=8$ (initial amount)

first time = player  got  $=> 8$ of clubs ...dealer pays $\text{Rs.} \; 8$ (base amount) to player(ghosh)

now total amount of player $ = \text{Rs.} \; 8$ (initial) + $\text{Rs.} \; 8$(base amount) $ = \text{Rs.} \; 16$

first time = dealer got same suit as player  so player has to return twice of base amount(i.e $\text{Rs.} \; 8)= >  2*8  = 16$

player can return it without borrowing from anyone becoz he has $\text{Rs.} \; 16$ so he paid to dealer

 amount available with player  $= 16 - 16 = \text{Rs.} \; 0$

second time = player  got  $=> 10$ of hearts ...dealer pays $\text{Rs.} \; 10$ (base amount) to player(ghosh)

now total amount of player $\text{Rs.} \; 0 + \text{Rs.} \; 10$ (base amount) $ = \text{Rs.} \; 10$

second time = dealer got different color from  player  ..so dealer has to pay base amount(i.e $  \text{Rs.} \; 10$ ) to player

 amount available with player $= 10+10 = \text{Rs.} \; 20$

third time = player  got  $=> 6$ of diamonds ...dealer pays $\text{Rs.} \; 6$ (base amount) to player(ghosh)

now total amount of player $ = \text{Rs.} \; 20 + \text{Rs.} \; 6$ (base amount) = $\text{Rs.} \; 26$

third  time = dealer got same color but different suit from  player  ..so player has to pay base amount(i.e $\text{Rs.} \;6$) to dealer

 amount available with player $= 26-6 = \text{Rs.} \; 20$

fourth time = player  got  $=> 8$ of spades ...dealer pays $\text{Rs.} \; 8$ (base amount) to player(ghosh)

now total amount of player $= \text{Rs.} \; 20 +\text{Rs.} \; 8$ (base amount) $= \text{Rs.} \; 28$

fourth time = dealer got same suit as player  so player has to return twice of base amount(i.e $\text{Rs.} \; 8 )= >  2 *8  = 16$

player can return it without borrowing from anyone becoz he has $\text{Rs.} \; 28$ so he paid to dealer

 amount available with player $= 28 - 16 = \text{Rs.} \; 12 \dots$ still available wid player so $\text{Rs.} \; 8$ is enough