Logical Reasoning

Arrangements

Hard

10 players - P1, P2, ..., P10 - competed in an international javelin throw event. The number (after P) of a player reflects his rank at the beginning of the event, with rank 1 going to the topmost player. There were two phases in the event with the first phase consisting of rounds 1,2, and 3, and the second phase consisting of rounds 4, 5, and 6. A throw is measured in terms of the distance it covers (in meters, up to one decimal point accuracy), only if the throw is a 'valid' one. For an invalid throw, the distance is taken as zero. A player's score at the end of around is the maximum distance of all his throws up to that round. Players are re-ranked after every round based on their current scores. In case of a tie in scores, the player with a prevailing higher rank retains the higher rank. This ranking determines the order in which the players go for their throws in the next round.

In each of the rounds in the first phase, the players throw in increasing order of their latest rank, i.e. the player ranked 1 at that point throws first, followed by the player ranked 2 at that point and so on. The top six players at the end of the first phase qualify for the second phase. In each of the rounds in the second phase, the players throw in decreasing order of their latest rank i.e. the player ranked 6 at that point throws first, followed by the player ranked 5 at that point and so on. The players ranked 1, 2, and 3 at the end of the sixth round receive gold, silver, and bronze medals respectively.

All the valid throws of the event were of distinct distances (as per stated measurement accuracy). The tables below show distances (in meters) covered by all valid throws in the first and the third round in the event.

Distances covered by all the valid throws in the first round

Player	Distance (in m)
P1	82.9
P3	81.5
P5	86.4
P6	82.5
P7	87.2
P9	84.1

Distances covered by all the valid throws in the third round

Player	Distance (in m)
P1	88.6
P3	79.0
P9	81.4

The following facts are also known.

i. Among the throws in the second round, only the last two were valid. Both the throws enabled these players to qualify for the second phase, with one of them qualifying with the least score. None of these players won any medal.

ii. If a player throws first in a round AND he was also the last (among the players in the current round) to throw in the previous round, then the player is said to get a double. Two players got a double.

iii. In each round of the second phase, exactly one player improved his score. Each of these improvements was by the same amount.

iv. The gold and bronze medalists improved their scores in the fifth and the sixth rounds respectively. One medal winner improved his score in the fourth round.

v. The difference between the final scores of the gold medalist and the silver medalist, as well as the difference between the final scores of the silver medalist and the bronze medalist was $1.0$ m.

Who threw the last javelin in the event?

P10

✅ Correct Option: 1

Slide 1/11

Understanding the set :-

There are 10 players – P1, P2, … , P10 - competed in an international javelin throw event, where 1,2,3... after "p" is his rank.

Game was played in 2 phases -

a) First phase - rounds 1, 2, and 3 -

i) Players throw in increasing order of their rank

i.e., P1 throw first then P2...

ii) top six players at the end of the first phase qualify for the second phase.

b) Second phase - rounds 4, 5, 6 -

i) players throw in decreasing order of their latest rank

i.e., rank 6 throws first then rank 5...

player's score at the end of a round is the maximum distance of all his throws up to that round.

This is a games and tournament set:

In this kind of set, the first paragraph is most crucial to understand as that will be the one, which will explain all the rules of the game, which is going to be the base point to solve the set.

ROUND -1

Throw	Player
1	P1
2	P2
3	P3
4	P4
5	P5
6	P6
7	P7
8	P8
9	P9
10	P10

We know, In first three rounds, players throw in increasing order of their rank.

ROUND - 2 :

Player	Distance (in m)
P1	82.9
P3	81.5
P5	86.4
P6	82.5
P7	87.2
P9	84.1

Throw	Round 1	Round 2
1	P1	P7
2	P2	P5
3	P3	P9
4	P4	P1
5	P5	P6
6	P6	P3
7	P7	P2
8	P8	P4
9	P9	P8
10	P10	P10

This is a table given in the set,

It shows Distances covered by all the valid throws in the first round.

=> in the first round P2, P4, P8 and P10, had invalid throw

therefore, "0" score.

Therefore, their rank will change in round 2 according to their round 1 scores.

Throw	Round 1	Round 2
1	P1	P7 (0)
2	P2	P5 (0)
3	P3	P9 (0)
4	P4	P1 (0)
5	P5	P6 (0)
6	P6	P3 (0)
7	P7	P2 (0)
8	P8	P4 (0)
9	P9	P8
10	P10	P10

Clue 1 says,

Among the throws in the second round, only the last two were valid.

=> In second round, except last two (P8 and P10 ) all had scored '0'.

=> Their rank will change in round 3 as,

P8 and P10 will move up in the table and occupy some higher places, whereas some of the others may move down consequently.

ROUND -3 :-

Player	Distance (in m)
P1	88.6
P3	79.0
P9	81.4

Throw	Round 1	Round 2	Winner
1	P1	P7	P1
2	P2	P5	P7
3	P3	P9	P5
4	P4	P1	P9
5	P5	P6	P8/P10
6	P6	P3	P6
7	P7	P2	P3
8	P8	P4	P2
9	P9	P8	P4
10	P10	P10

In Round 3, we can see that P1 improved his score from 82.9 to 88.6.

The other 2 participants did not improve their scores.

Also after Round 3, P8 and P10 qualify, where one of P8 or P10 is at the sixth position.

So at the end of Round 3, we can say that P6, P3, P2, and P4 are at the bottom 4 positions(ranks).

One of P8 or P10 is at the sixth position.

And, P1 > P7 > P5 > P9.

The other person between P8/P10 can go anywhere between Rank 1 and Rank 5.

Case -1 :

Throw	Round 1	Round 2	Round 3
1	P1	P7	P10
2	P2	P5	P1
3	P3	P9	P7
4	P4	P1	P5
5	P5	P6	P9
6	P6	P3	P8
7	P7	P2	P6
8	P8	P4	P3
9	P9	P8	P2
10	P10	P10	P4

Case -2 :

Throw	Round 1	Round 2	Round 3
1	P1	P7	P1
2	P2	P5	P10
3	P3	P9	P7
4	P4	P1	P5
5	P5	P6	P9
6	P6	P3	P8
7	P7	P2	P6
8	P8	P4	P3
9	P9	P8	P2
10	P10	P10	P4

Now let us consider the two players who got a double.

Doubles happen in the transition between rounds.

1 -> 2 - Not possible

2 -> 3 - Possible if P10 reaches Rank 1 after round 2.

3 -> 4 - P8/P10 who is the last among qualifying will be the first to throw. So, here it definitely happens.

4 - > 5

AND 5 - > 6 not possible.

So, after Round 2, definitely, P10 reaches the top of the ranking.

P8 is at the bottom.

Hence, after Round 3, P10 either retains rank 1 or P1 surpasses him and P10 becomes Rank 2.

Throw	Round 1	Round 2	Round 3
1	P1	P7	P1
2	P2	P5	P10
3	P3	P9	P7
4	P4	P1	P5
5	P5	P6	P9
6	P6	P3	P8
7	P7	P2	P6
8	P8	P4	P3
9	P9	P8	P2
10	P10	P10	P4

Table before Round 4:

Player	Distance (in m)
P1	88.6
P7	87.2
P5	86.4
P9	84.1

Now, we know,

in each of the rounds in phase 2, only one player improves his score.

Also, P8 and P10 cannot win medals.

Hence, in case 1, three of P1, P7, P5 and P9 will improve their scores by x and reach the top 3 positions.

However, the top 3 positions' distances are in AP.

P1 - 88.6 + x

P7 - 87.2 + x

P5 - 86.4 + x

P9 - 84.1 + x

The differences do not satisfy the condition.

Hence, case 1 is invalidated.

Throw	Round 1	Round 2	Round 3
1	P1	P7	P1
2	P2	P5	P10
3	P3	P9	P7
4	P4	P1	P5
5	P5	P6	P9
6	P6	P3	P8
7	P7	P2	P6
8	P8	P4	P3
9	P9	P8	P2
10	P10	P10	P4

Player	Distance (in m)
P1	88.6
P7	87.2
P5	86.4
P9	84.1

Here, P1 definitely wins a medal, and P10 does not.

So, two of P7, P5 and P9 jumps above P10.

Now, if we have three different people increasing their scores or distances in each of the three rounds, again we would not get a difference of 1 among the Gold, Silver and Bronze medalists.

Hence, one of them increases his score twice and the other increases his score twice and none of them is P1.

Throw	Round 1	Round 2	Round 3
1	P1	P7	P1
2	P2	P5	P10
3	P3	P9	P7
4	P4	P1	P5
5	P5	P6	P9
6	P6	P3	P8
7	P7	P2	P6
8	P8	P4	P3
9	P9	P8	P2
10	P10	P10	P4

Player	Distance (in m)
P1	88.6
P7	87.2
P5	86.4
P9	84.1

Let us take the cases where P1 is individually the G, S and B medallists.

Case 1: P1 is a G medallist.

P1 - 88.6

The silver medalist is 87.6

and the bronze medalist is 86.6 metres.

However, P10 thrown for a distance that is greater than 87.2 metres. Hence, in this case, he would be the B medallist.

Hence, this is not the right case.

Throw	Round 1	Round 2	Round 3
1	P1	P7	P1
2	P2	P5	P10
3	P3	P9	P7
4	P4	P1	P5
5	P5	P6	P9
6	P6	P3	P8
7	P7	P2	P6
8	P8	P4	P3
9	P9	P8	P2
10	P10	P10	P4

At the end of round 6 :-

Player	Score
P7	89.6
P1	88.6
P5	87.6
P10	X
P9	84.1
P8	Y

Case 2: P1 is the S medallist.

P1 - 88.6

G - 89.6

B - 87.6

Now, if we see the differences 89.6 - 87.2 = 2.4

87.6 - 86.4 = 1.2

This satisfies the condition that P7 has increased his score twice to become the gold winner and P5 has increased it once to become the bronze winner.

Hence, P1 - Silver

P7 - Gold

P5 - Bronze

Throw	Round 1	Round 2	Round 3
1	P1	P7	P1
2	P2	P5	P10
3	P3	P9	P7
4	P4	P1	P5
5	P5	P6	P9
6	P6	P3	P8
7	P7	P2	P6
8	P8	P4	P3
9	P9	P8	P2
10	P10	P10	P4

At the end of round 6 :-

Player	Score
P7 (Gold)	89.6
P1 (Silver)	88.6
P5 (Bronze)	87.6
P10	X
P9	84.1
P8	Y

P7 (who won gold) will throw the last.

Question 1

Which two players got the double?

Question 2

Who won the silver medal?

Question 4

What was the final score (in m) of the silver-medalist?

Question 5

Which of the following can be the final score (in m) of P8?

Question 6

By how much did the gold medalist improve his score (in m) in the second phase?

Throw	Round 1	Round 2	Round 3
1	P1	P7	P10
2	P2	P5	P1
3	P3	P9	P7
4	P4	P1	P5
5	P5	P6	P9
6	P6	P3	P8
7	P7	P2	P6
8	P8	P4	P3
9	P9	P8	P2
10	P10	P10	P4

Throw	Round 1	Round 2	Round 3
1	P1	P7	P1
2	P2	P5	P10
3	P3	P9	P7
4	P4	P1	P5
5	P5	P6	P9
6	P6	P3	P8
7	P7	P2	P6
8	P8	P4	P3
9	P9	P8	P2
10	P10	P10	P4

Throw	Round 1	Round 2	Round 3
1	P1	P7	P1
2	P2	P5	P10
3	P3	P9	P7
4	P4	P1	P5
5	P5	P6	P9
6	P6	P3	P8
7	P7	P2	P6
8	P8	P4	P3
9	P9	P8	P2
10	P10	P10	P4

Throw	Round 1	Round 2	Round 3
1	P1	P7	P1
2	P2	P5	P10
3	P3	P9	P7
4	P4	P1	P5
5	P5	P6	P9
6	P6	P3	P8
7	P7	P2	P6
8	P8	P4	P3
9	P9	P8	P2
10	P10	P10	P4

Throw	Round 1	Round 2	Round 3
1	P1	P7	P1
2	P2	P5	P10
3	P3	P9	P7
4	P4	P1	P5
5	P5	P6	P9
6	P6	P3	P8
7	P7	P2	P6
8	P8	P4	P3
9	P9	P8	P2
10	P10	P10	P4

Throw	Round 1	Round 2	Round 3
1	P1	P7	P1
2	P2	P5	P10
3	P3	P9	P7
4	P4	P1	P5
5	P5	P6	P9
6	P6	P3	P8
7	P7	P2	P6
8	P8	P4	P3
9	P9	P8	P2
10	P10	P10	P4

Throw	Round 1	Round 2	Round 3
1	P1	P7	P1
2	P2	P5	P10
3	P3	P9	P7
4	P4	P1	P5
5	P5	P6	P9
6	P6	P3	P8
7	P7	P2	P6
8	P8	P4	P3
9	P9	P8	P2
10	P10	P10	P4

Throw	Round 1	Round 2	Round 3
1	P1	P7	P10
2	P2	P5	P1
3	P3	P9	P7
4	P4	P1	P5
5	P5	P6	P9
6	P6	P3	P8
7	P7	P2	P6
8	P8	P4	P3
9	P9	P8	P2
10	P10	P10	P4

Throw	Round 1	Round 2	Round 3
1	P1	P7	P1
2	P2	P5	P10
3	P3	P9	P7
4	P4	P1	P5
5	P5	P6	P9
6	P6	P3	P8
7	P7	P2	P6
8	P8	P4	P3
9	P9	P8	P2
10	P10	P10	P4

Throw	Round 1	Round 2	Round 3
1	P1	P7	P1
2	P2	P5	P10
3	P3	P9	P7
4	P4	P1	P5
5	P5	P6	P9
6	P6	P3	P8
7	P7	P2	P6
8	P8	P4	P3
9	P9	P8	P2
10	P10	P10	P4

Throw	Round 1	Round 2	Round 3
1	P1	P7	P1
2	P2	P5	P10
3	P3	P9	P7
4	P4	P1	P5
5	P5	P6	P9
6	P6	P3	P8
7	P7	P2	P6
8	P8	P4	P3
9	P9	P8	P2
10	P10	P10	P4

Throw	Round 1	Round 2	Round 3
1	P1	P7	P1
2	P2	P5	P10
3	P3	P9	P7
4	P4	P1	P5
5	P5	P6	P9
6	P6	P3	P8
7	P7	P2	P6
8	P8	P4	P3
9	P9	P8	P2
10	P10	P10	P4

Throw	Round 1	Round 2	Round 3
1	P1	P7	P1
2	P2	P5	P10
3	P3	P9	P7
4	P4	P1	P5
5	P5	P6	P9
6	P6	P3	P8
7	P7	P2	P6
8	P8	P4	P3
9	P9	P8	P2
10	P10	P10	P4

Throw	Round 1	Round 2	Round 3
1	P1	P7	P1
2	P2	P5	P10
3	P3	P9	P7
4	P4	P1	P5
5	P5	P6	P9
6	P6	P3	P8
7	P7	P2	P6
8	P8	P4	P3
9	P9	P8	P2
10	P10	P10	P4

Who threw the last javelin in the event?

Solution

More from this set:

Keyboard Shortcuts

CAT Past Year Questions (Topic-Wise)

Throw	Round 1	Round 2	Round 3
1	P1	P7	P10
2	P2	P5	P1
3	P3	P9	P7
4	P4	P1	P5
5	P5	P6	P9
6	P6	P3	P8
7	P7	P2	P6
8	P8	P4	P3
9	P9	P8	P2
10	P10	P10	P4

Throw	Round 1	Round 2	Round 3
1	P1	P7	P1
2	P2	P5	P10
3	P3	P9	P7
4	P4	P1	P5
5	P5	P6	P9
6	P6	P3	P8
7	P7	P2	P6
8	P8	P4	P3
9	P9	P8	P2
10	P10	P10	P4

Throw	Round 1	Round 2	Round 3
1	P1	P7	P1
2	P2	P5	P10
3	P3	P9	P7
4	P4	P1	P5
5	P5	P6	P9
6	P6	P3	P8
7	P7	P2	P6
8	P8	P4	P3
9	P9	P8	P2
10	P10	P10	P4

Throw	Round 1	Round 2	Round 3
1	P1	P7	P1
2	P2	P5	P10
3	P3	P9	P7
4	P4	P1	P5
5	P5	P6	P9
6	P6	P3	P8
7	P7	P2	P6
8	P8	P4	P3
9	P9	P8	P2
10	P10	P10	P4

Throw	Round 1	Round 2	Round 3
1	P1	P7	P1
2	P2	P5	P10
3	P3	P9	P7
4	P4	P1	P5
5	P5	P6	P9
6	P6	P3	P8
7	P7	P2	P6
8	P8	P4	P3
9	P9	P8	P2
10	P10	P10	P4

Throw	Round 1	Round 2	Round 3
1	P1	P7	P1
2	P2	P5	P10
3	P3	P9	P7
4	P4	P1	P5
5	P5	P6	P9
6	P6	P3	P8
7	P7	P2	P6
8	P8	P4	P3
9	P9	P8	P2
10	P10	P10	P4

Throw	Round 1	Round 2	Round 3
1	P1	P7	P1
2	P2	P5	P10
3	P3	P9	P7
4	P4	P1	P5
5	P5	P6	P9
6	P6	P3	P8
7	P7	P2	P6
8	P8	P4	P3
9	P9	P8	P2
10	P10	P10	P4