CAT 2003 Slot 1 — QA Question 51
Each question is followed by two statements, A and B. Answer each question using the following instructions
Choose 1 if the question can be answered by using one of the statements alone but not by using the other statement alone.
Choose 2 if the question can be answered by using either of the statements alone.
Choose 3 if the question can be answered by using both statements together but not by either statement alone.
Choose 4 if the question cannot be answered on the basis of the two statements.
In each question there are two statements: A and B.
Choose 1 if the question can be answered by one of the statements alone but not by the other.
Choose 2 if the question can be answered by using either statement alone.
Choose 3 if the question can be answered by using both the statements together but cannot be answered using either statement alone.
Choose 4 if the question cannot be answered even by using both the statements A and B.
A game consists of tossing a coin successively. There is an entry fee of Rs. 10 and an additional fee of Re. 1 for each toss of the coin. The game is considered to have ended normally when the coin turns heads on two consecutive throws. In this case the player is paid Rs. 100. Alternatively, the player can choose to terminate the game prematurely after any of the tosses. Ram has incurred a loss of Rs. 50 by playing this game. How many times did he toss the coin?
A. The game ended normally.
B. The total number of tails obtained in the game was 138.
Answer & solution
- A
1
2
- C
3
- D
4
Let the number of tosses be x.
Total amount spent by Ram after x tosses = (10 + x × 1) = Rs. (10 + x)
We know that Ram incurs a loss of Rs. 50.
∴ We have two cases to evaluate:
i. If the game ends normally then Ram's net loss = Rs. (10 + x) − Rs. 100
ii. If he quits prematurely his loss = Rs. (10 + x)
From statement A,
Ram's net loss = (10 + x) − 100
∴ 50 = (10 + x) − 100
∴ x = 140
∴ Statement A is alone sufficient.
From statement B,
Ram gets 138 tails.
If his game ends prematurely, his loss = 10 + x = 50
∴ x = 40
This is not possibe as the number of tails > 40
∴ His game must have ended normally.
∴ 10 + x – 100 = 50
∴ x = 140
∴ Statement B is also sufficient.
Hence, option (b).