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CAT 2019 PYQsData Interpretation & Logical Reasoning. Free, no login required.

Logical Reasoning

past year questions, CAT 2019

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past year questions, Logical Reasoning, CAT 2019

Hard

Ten players, as listed in the table below, participated in a rifle shooting competition comprising of 10 rounds. Each round had 6 participants. Players numbered 1 through 6 participated in Round 1, players 2 through 7 in Round 2,..., players 5 through 10 in Round 5, players 6 through 10 and 1 in Round 6, players 7 through 10, 1 and 2 in Round 7 and so on.

The top three performances in each round were awarded 7, 3 and 1 points respectively. There were no ties in any of the 10 rounds. The table below gives the total number of points obtained by the 10 players after Round 6 and Round 10.

Player No.Player NamePoints after Round 6Points after Round 10
1Amita818
2Bala25
3Chen36
4David66
5Eric310
6Fatima1010
7Gordon1717
8Hansa14
9Ikea217
10Joshin1417

The following information is known about Rounds 1 through 6:

  1. Gordon did not score consecutively in any two rounds.
  2. Eric and Fatima both scored in a round.

The following information is known about Rounds 7 through 10:

  1. Only two players scored in three consecutive rounds. One of them was Chen. No other player scored in any two consecutive rounds.
  2. Joshin scored in Round 7, while Amita scored in Round 10.
  3. No player scored in all the four rounds.

Which players scored points in the last round?

Solution

✅ Correct Option: 1
Slide 1/17

Understanding the set :-

  1. This logical reasoning set is based on a rifle shooting competition involving 10 players (named and numbered from 1 to 10).
  1. The competition consists of 10 rounds, and in each round, 6 players participate.
  1. The players rotate across rounds in a cyclical pattern, ensuring that all players participate in multiple rounds.
  1. Points are awarded based on performance in each round:

a) 1st place earns 7 points

b) 2nd place earns 3 points

c) 3rd place earns 1 point

(No ties occur in any round.)

  1. You're given a table of total scores for each player after Round 6 and after Round 10, and several logical conditions (clues) about the rounds and scores. These include rules like which players scored or didn’t score in consecutive rounds, or specific rounds where certain players scored.

The task involves using these clues and the scoring rules to deduce who scored in which rounds and reconstruct the scoring pattern across the competition.

123456T78910TT
AXXXX818
BXXXX25
CXXX3X6
DXX6XX6
EX3XXX10
F10XXXX10
GX17XXX17
HXX1XX4
IXXX2X17
JXXXX771417

For J :-

We know, J has scored 14 points in two rounds (round 5 and 6)

=> He would have scored 7 in both the rounds.

123456T78910TT
A7XXXX1818
BXXXX25
CXXX3X6
DXX6XX6
EX3XXX10
F10XXXX10
GX17XXX17
HXX1XX4
IXXX2X17
JXXXX771417

For A :-

We know, A has scored 8 in two rounds (round 1 and 6)

=> he would have scored a 7 and a 1.

But in round 6 ,J already have a 7.

=> A will get a 7, in round 1 and a 1, in round 6.

123456T78910TT
A7XXXX1818
B11XXXX25
CXXX3X6
DXX6XX6
EX3XXX10
F10XXXX10
GX17XXX17
HXX1XX4
IXXX2X17
JXXXX771417

For B :-

We know, B has scored 2 in two rounds (round 1 and 2)

=> he would have scored 1 in both the rounds.

123456T78910TT
A7XXXX1818
B11XXXX25
CXXX3X6
DXX6XX6
EX3XXX10
F10XXXX10
GX17XXX17
HXX1XX4
IXXX1102X17
JXXXX771417

For I :-

We know, I has scored 2 in three rounds (round 4, 5, and 6)

=> he would have scored 1 in two rounds and 0 in other.

But in round 6 ,A already have a 1.

=> I will get a 1, in round 4 and 5 and 0, in round 6.

123456T78910TT
A7XXXX1818
B11XXXX25
CXXX3X6
DXX6XX6
EX3XXX10
F10XXXX10
GX7070317XXX17
HXX10001XX4
IXXX1102X17
JXXXX771417

For G :-

We know, G has scored 17 in five rounds (round 2, 3, 4, 5, and 6)

=> he would have scored 7 in two rounds , 3 in one and 0 in other.

But in round 5 and 6 ,A already have a 7.

Therefore, G will 7 in any two of rounds 2, 3, 4.

But, clue 1 says,

Gordon did not score consecutively in any two rounds.

=> G will score 7 in round 2 and round 4 and 3 in round 6.

123456T78910TT
A7XXXX1818
B11XXXX25
C0XXX3X6
D0XX6XX6
E00300X3XXX10
F7010XXXX10
GX7070317XXX17
HXX10001XX4
IXXX1102X17
JXXXX771417

Now, clue 2 says,

Eric and Fatima both scored in a round.

Now, for both E and F to score, there should be two positions left

i.e., in round 1, 2, 4, 5 and 6 we already have found two players securing any of the two positions

=> Both E and F can't be in these rounds

Therefore, only round in which both of them can score is in round 3, where we have only H , scoring 1.

=> F will score 7 in round 3 and H -3.

123456T78910TT
A7XXXX1818
B11XXXX25
C0XXX3X6
D0XX6XX6
E00300X3XXX10
F00703010XXXX10
GX7070317XXX17
HXX10001XX4
IXXX1102X17
JXXXX771417

Round 5 :-

We only have one position - F left.

Therefore, he must score 3 in round 5.

123456T78910TT
A7XXXX1818
B11XXXX25
C0/33/00XXX3X6
D3/00/303XX6XX6
E00300X3XXX10
F00703010XXXX10
GX7070317XXX17
HXX10001XX4
IXXX1102X17
JXXXX771417

Similarly, in Round 4 :-

We only have one position - D left.

Therefore, he must score 3 in round 4.

Now, We can't say C and D in round 1 and 2, only thing we know, is they have score 3 in one round and 0 in another, in any order.

123456T78910TT
A7XXXX1818
B11XXXX25
C0/33/00XXX3X6
D3/00/303XX6XX6
E00300X3XXX10
F00703010XXXX10
GX70703170XXX17
HXX10001XX4
IXXX1102X17
JXXXX771417

Now, for Round 7 to 10.

For G ;

We know, G had scored a total of 17 in round 1 to 6.

And, he had scored 17 in TT as well.

=> He had not scored anything from round 7 to 10.

Therefore, his score in round 7 will be 0.

123456T78910TT
A7XXXX1818
B11XXXX25
C0/33/00XXX3X6
D3/00/303XX6XX6
E00300X3XXX710
F00703010XXXX10
GX70703170XXX17
HXX10001XX4
IXXX1102X17
JXXXX771417

For E;

We can see, He has played only in round 10.

And total difference is 10−3=710 - 3 = 7

=> he scored 7 in round 10.

123456T78910TT
A7XXXX1818
B11XXXX25
C0/33/00XXX3X6
D3/00/303XX6XX006
E00300X3XXX710
F00703010XXXX10
GX70703170XXX17
HXX10001XX4
IXXX1102X17
JXXXX771417

For D,

We know, D has played in only round 9 and 10.

But the difference between T and TT = 6−6=06 - 6 =0

=> He haven't scored anything in round 7 to 10.

123456T78910TT
A7XXXX1818
B11XXXX25
C0/33/00XXX3X1116
D3/00/303XX6XX006
E00300X3XXX710
F00703010XXXX10
GX70703170XXX17
HXX10001XX4
IXXX1102177X17
JXXXX771417

Clue 3 says,

Only two players scored in three consecutive rounds. One of them was Chen.

For C :-

We know, difference between T and TT for C is 6−3=36-3 = 3

Also, as the clue says, C has scored in three consecutive rounds.

=> C will score 1 in all the three rounds he had played.

Now, as the clue says, there are two people who has scored in three consecutive rounds.

so, other than Chen I will score in three consecutive rounds.

As, I have a difference of 17−2=1517 - 2 = 15

=> I will score 7, 7 and 1.

But, I can score 1 in only round 7. (as in round 8 and 9, C has already scored 1)

Therefore, C has scored 1 in round 7, and 7 in both round 8 and 9.

123456T78910TT
A7XXXX18718
B11XXXX25
C0/33/00XXX3X1116
D3/00/303XX6XX006
E00300X3XXX710
F00703010XXXX10
GX70703170XXX17
HXX10001XX4
IXXX1102177X17
JXXXX771417

For A,

Difference = 18−8=1018 - 8 = 10

=> A will score a 7 and a 3.

But, A can score 7 in only round 7

(as I has scored 7 in round 8 and 9 ,and E has scored 7 in round 10.)

123456T78910TT
A7XXXX18700318
B11XXXX2005
C0/33/00XXX3X1116
D3/00/303XX6XX006
E00300X3XXX710
F00703010XXXX10
GX70703170XXX17
HXX100010XX4
IXXX1102177X17
JXXXX7714300017

Clue 4 says,

Joshin scored in Round 7, while Amita scored in Round 10.

For J :-

J has difference = 17−14=317-14 = 3

=> J has scored 3 in round 7.

For A :-

we know A has scored 7 in round 7.

=> A has scored 3 in round round 10.

123456T78910TT
A7XXXX18700318
B11XXXX200305
C0/33/00XXX3X1116
D3/00/303XX6XX006
E00300X3XXX710
F00703010XXXX10
GX70703170XXX17
HXX1000103XX4
IXXX1102177X17
JXXXX7714300017

For H ;

Difference = 4−1=34-1 = 3

=> H has scored 3 in round 8.

=> B has scored in round 3 in round 9.

123456T78910TT
A7XXXX18700318
B11XXXX200305
C0/33/00XXX3X1116
D3/00/303XX6XX006
E00300X3XXX710
F00703010XXXX10
GX70703170XXX17
HXX1000103XX4
IXXX1102177X17
JXXXX7714300017

As shown Amita, Chen, Eric scored points in the last round.

More from this set:

Question 29

What were the scores of Chen, David, and Eric respectively after Round 3?

Question 30

Which three players were in the last three positions after Round 4?

Question 31

Which player scored points in maximum number of rounds?

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