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# LRDI Questions [Difficult] Set 11

Four friends - A, B, C and D - play a game which involves money. They all start with different amounts, and at the end of 4 rounds, they end up with Rs. 1024 each. The results of each round are as given below:

In each round, the amount with the person who is ranked I becomes 4 times its value,the amount with the person who is ranked II becomes twice its value, the amount with the person who is ranked III remains the same, and the person who is ranked IV loses the amount that were gained by ranks I and II (such that the sum total of the amounts with the four of them remains constant in each round).

Q1. Who had the least amount before the game started?

1. A
2. B
3. C
4. D

Q2. At the end of which round did C have the least amount among all four?

1. Round 1
2. Round 2
3. Round 3
4. Round 4

Q3. What is the maximum amount that anyone had in any of the four rounds?

1. Rs. 2304
2. Rs. 1152
3. Rs. 1728
4. Rs. 2048

Q4. Who had the least amount at the end of round 3?

1. A
2. B
3. C
4. D

Since D was ranked 1 in round 4, his amount in round 3 should have been $\frac { 1 } { 4 } \times 1024 = 256 .$ since C was ranked II in round 4 his amount in round 3 should have been $\frac { 1 } { 2 } \times 1024 = 512$

Since B was ranked III in round 4, his amount in round 3 would have remained as 1024.

Since A was ranked IV in round 4, his amount in round 3 should have been 1024 +

(1024 - 256) + (1024 - 512) = 2304

We can do similar back calculations and find out how much each person had at the end of each round as follows:

 Amount with each person Round A B C D 4 1024 1024 1024 1024 3 2304 1024 512 256 2 2304 512 128 1152 1 1152 128 1664 1152 Initially 288 1568 1664 576

Using this, all the questions can be answered.

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