The management of a university hockey team was evaluating performance of four women players - Amla, Bimla, Harita and Sarita for their possible selection in the university team for next year. For this purpose, the management was looking at the number of goals scored by them in the past 8 matches, numbered 1 through 8. The four players together had scored a total of 12 goals in these matches. In the 8 matches, each of them had scored at least one goal. No two players had scored the same total number of goals. The following facts are known about the goals scored by these four players only. All the questions refer only to the goals scored by these four players. Only one goal was scored in every even numbered match. Harita scored more goals than Bimla. The highest goal scorer scored goals in exactly 3 matches including Match 4 and Match 8. Bimla scored a goal in Match 1 and one each in three other consecutive matches. An equal number of goals were scored in Match 3 and Match 7, which was different from the number of goals scored in either Match 1 or Match 5. The match in which the highest number of goals was scored was unique and it was not Match 5. Which of the following statement(s) is/are true? Statement-1: Amla and Sarita never scored goals in the same match. Statement-2: Harita and Sarita never scored goals in the same match. Option 1: None of the statements Option 2: Statement-1 only Option 3: Both the statements Option 4: Statement-2 only

Answer: Both the statements. Solution: Understanding the set :- This is a logical grid puzzle — each clue slices away part of the possible distribution until only one arrangement remains. 1) Structure of the matches :- a) Matches 1–8 → total of 12 goals by 4 players. b) Each player scored at least 1 goal. c) No two players have the same total goals. 2) the facts gives you: a) Fixed totals in even matches. b) Equality constraint between matches 3 and 7. c) Inequalities between players’ total goals. d) Positional constraints for top scorer and for Bimla. e) Uniqueness condition for the highest-scoring match. Now, lets make a table where we can use all these clues to find the final answer. —--, A, B, H, S, Total, M1, M2, M3, M4, M5, M6, M7, M8, Total, 12, In this table M1, M2, M3, M4, M5, M6, M7, M8 - are all the 8 matches And, A, B, H, S are all 4 players Amla, Bimla, Harita and Sarita respectively. Also, we are given the total number of goals in all the 8 matches by all the 4 players is 12. —--, A, B, H, S, Total (2), M1, M2, M3, M4, M5, M6, M7, M8, Total (1), 12, We are given, There was a total of 12 goals in these matches and each of them had scored at least one goal. No two players had scored the same total number of goals. Therefore the possibilities of the total number of goals by players in these matches is i.e., the possible values in total (1) - 1) 1, 2, 3, 6 2) 1, 2, 4, 5 —--, A, B, H, S, Total (2), M1, 1, M2, M3, M4, M5, M6, M7, M8, Total (1), 1/2, 4, 5, 2/1, 12, Using statement 4, Bimla scored a goal in Match 1 and one each in three other consecutive matches. => Bimla has a minimum score 4 goals. But, clue 2 says, Harita scored more goals than Bimla. Now if we consider case 1 - 1, 2, 3, 6 then, since Bimla has a score > or equal to 4 => Bimla score will be 6 but then Harita's score can't be more then Bimla therefore, this case is rejected And therefore, we can say that, total scores will be 1, 2, 4, 5 From which Bimla's total score will be - 4 (and she will score 1 goal in match 1) and, Harita's score will be greater then Bimla = 5 and, Amla and Sarita score will be 1 or 2. —--, A, B, H, S, Total (2), M1, 1, M2, 1, M3, M4, 1, M5, M6, 1, M7, M8, 1, Total (1), 1/2, 4, 5, 2/1, 12, Using statement 1, Only one goal was scored in every even numbered match Therefore, Total (2) score in M2, M4, M6, M8 = 1 —--, A, B, H, S, Total (2), M1, 1, M2, 1, M3, M4, -, -, 1, -, 1, M5, M6, 1, M7, M8, -, -, 1, -, 1, Total (1), 1/2, 4, 5, 2/1, 12, Clue 3 says, The highest goal scorer scored goals in exactly 3 matches including Match 4 and Match 8. We know, highest goal scorer is Harita => Harita scored goal in M4, M8, and one other But, we know the total score in M4 and M8 is 1 each. => Harita will score 1 goal each in M4 and M8 and 3 goals in one of the matches. —--, A, B, H, S, Total (2), M1, 1, M2, -, 1, M3, -, M4, -, -, 1, -, 1, M5, 1, M6, -, 1, -, -, 1, M7, 1, M8, -, -, 1, -, 1, Total (1), 1/2, 4, 5, 2/1, 12, Now, we know Bimla score 1 goal each in 3 consecutive matches The only 3 consecutive places left is M5, M6, and M7 Therefore, Bimla scored 1 score each in M5, M6, M7. —--, A, B, H, S, Total (2), M1, 1, M2, -, 1, M3, -, x, M4, -, -, 1, -, 1, M5, 1, M6, -, 1, -, -, 1, M7, 1, x, M8, -, -, 1, -, 1, Total (1), 1/2, 4, 5, 2/1, 12, Clue 5 says, An equal number of goals were scored in Match 3 and Match 7 Let that be 'x' Also, x is different from the number of goals scored in either Match 1 or Match 5. But Clue 6 says, The match in which the highest number of goals was scored was unique and it was not Match 5. Now, only Unique scoring matches are 1 and 5 from which 5 is not the highest scoring match => Match 1 had highest number of goals. —--, A, B, H, S, Total (2), M1, 1, 4, M2, -, 1, M3, -, 1, M4, -, -, 1, -, 1, M5, 1, 2, M6, -, 1, -, -, 1, M7, -, 1, -, -, 1, M8, -, -, 1, -, 1, Total (1), 1/2, 4, 5, 2/1, 12, Let the total number of goals in M1 = y and total number of goals in M8 = z => x + x + y + z = 12 -1 -1- 1- 1 => 2x +y+ z = 8 If x=1, then y +z =6 therefore possible solutions for y and z will be 2 and 4 only If x=2, then y+z=4 therefore possible solutions for y and z will be 1 and 3 only but since highest goals scored is in Match 1 so then no. of goals scored in match 1 must be 3 Harita must have scored 3 goals in match 1 as Harita scored 5 goals in exactly 3 matches. Therefore, we can see this is not possible because then the no. of goals scored in Match 1 becomes 4. Therefore the only possible solution is x=1, y=4 and z=2 —--, A, B, H, S, Total (2), M1, -, 1, 3, -, 4, M2, -, -, 1, M3, -, -, 1, M4, -, -, 1, -, 1, M5, 1, -, 2, M6, -, 1, -, -, 1, M7, -, 1, -, -, 1, M8, -, -, 1, -, 1, Total (1), 1/2, 4, 5, 2/1, 12, We know, Harita has scored total of 5 goals, From which 1 goal each was scored in M4 and M8 => only match where she can score 3 goals is M1 —--, A, B, H, S, Total (2), M1, -, 1, 3, -, 4, M2, -, -, 1, M3, -, -, 1, M4, -, -, 1, -, 1, M5, 1, -, 2, M6, -, 1, -, -, 1, M7, -, 1, -, -, 1, M8, -, -, 1, -, 1, Total (1), 1/2, 4, 5, 2/1, 12, This is the final table we can make, In LRDI sets it is many times possible that you may not be able to fill whole of the table, in that case you should not give up thinking that you are unable to solve the set, instead you should move to the questions and try them and find out how much of them you can solve using the table you have formed. —--, A, B, H, S, Total (2), M1, -, 1, 3, -, 4, M2, -, -, 1, M3, -, -, 1, M4, -, -, 1, -, 1, M5, 1, -, 2, M6, -, 1, -, -, 1, M7, -, 1, -, -, 1, M8, -, -, 1, -, 1, Total (1), 1/2, 4, 5, 2/1, 12, Statement 1 : Total 3 vacant spaces are available where a total of 3 goals are to be scored. Now, the combination of Amla and Sarita goals is 2 or 1. Therefore, if Amla scores a goal then Sarita cannot score a goal and if Sarita scores a goal then Amla cannot.So, this is true. Statement 2: Harita's goals have already been scored as she is the highest goal scorer and the places where Harita is not scoring goal are the places where Sarita would score the goal. Hence, this statement is also true. Therefore both the statements are true : Option 3

Logical Reasoning

Arrangements

Medium

The management of a university hockey team was evaluating performance of four women players - Amla, Bimla, Harita and Sarita for their possible selection in the university team for next year. For this purpose, the management was looking at the number of goals scored by them in the past 8 matches, numbered 1 through 8. The four players together had scored a total of 12 goals in these matches. In the 8 matches, each of them had scored at least one goal. No two players had scored the same total number of goals.

The following facts are known about the goals scored by these four players only. All the questions refer only to the goals scored by these four players.

Only one goal was scored in every even numbered match.

Harita scored more goals than Bimla.

The highest goal scorer scored goals in exactly 3 matches including Match 4 and Match 8.

Bimla scored a goal in Match 1 and one each in three other consecutive matches.

An equal number of goals were scored in Match 3 and Match 7, which was different from the number of goals scored in either Match 1 or Match 5.

The match in which the highest number of goals was scored was unique and it was not Match 5.

Which of the following statement(s) is/are true?

Statement-1: Amla and Sarita never scored goals in the same match.

Statement-2: Harita and Sarita never scored goals in the same match.

None of the statements

Statement-1 only

Both the statements

Statement-2 only

✅ Correct Option: 3

Slide 1/12

Understanding the set :-

This is a logical grid puzzle — each clue slices away part of the possible distribution until only one arrangement remains.

Structure of the matches :-

a) Matches 1–8 → total of 12 goals by 4 players.

b) Each player scored at least 1 goal.

c) No two players have the same total goals.

the facts gives you:

a) Fixed totals in even matches.

b) Equality constraint between matches 3 and 7.

c) Inequalities between players’ total goals.

d) Positional constraints for top scorer and for Bimla.

e) Uniqueness condition for the highest-scoring match.

Now, lets make a table where we can use all these clues to find the final answer.

	A	B	H	S	Total
M1
M2
M3
M4
M5
M6
M7
M8
Total					$12$

In this table M1, M2, M3, M4, M5, M6, M7, M8 - are all the 8 matches

And, A, B, H, S are all 4 players Amla, Bimla, Harita and Sarita respectively.

Also, we are given the total number of goals in all the 8 matches by all the 4 players is 12.

	A	B	H	S	Total (2)
M1
M2
M3
M4
M5
M6
M7
M8
Total (1)					$12$

We are given,

There was a total of 12 goals in these matches

and each of them had scored at least one goal. No two players had scored the same total number of goals.

Therefore the possibilities of the total number of goals by players in these matches is

i.e., the possible values in total (1) -

$1, 2, 3, 6$
$1, 2, 4, 5$

	A	B	H	S	Total (2)
M1		1
M2
M3
M4
M5
M6
M7
M8
Total (1)	1/2	4	5	2/1	$12$

Using statement 4,

Bimla scored a goal in Match 1 and one each in three other consecutive matches.

=> Bimla has a minimum score 4 goals.

But, clue 2 says,

Harita scored more goals than Bimla.

Now if we consider case 1 - $1, 2, 3, 6$

then, since Bimla has a score > or equal to 4

=> Bimla score will be 6

but then Harita's score can't be more then Bimla

therefore, this case is rejected

And therefore, we can say that,

total scores will be $1, 2, 4, 5$

From which Bimla's total score will be - 4 (and she will score 1 goal in match 1)

and, Harita's score will be greater then Bimla = 5

and, Amla and Sarita score will be 1 or 2.

	A	B	H	S	Total (2)
M1		1
M2					1
M3
M4					1
M5
M6					1
M7
M8					1
Total (1)	1/2	4	5	2/1	$12$

Using statement 1,

Only one goal was scored in every even numbered match

Therefore, Total (2) score in M2, M4, M6, M8 = 1

	A	B	H	S	Total (2)
M1		1
M2					$1$
M3
M4	-	-	1	-	$1$
M5
M6					$1$
M7
M8	-	-	1	-	$1$
Total (1)	$1/2$	$4$	$5$	$2/1$	$12$

Clue 3 says,

The highest goal scorer scored goals in exactly 3 matches including Match 4 and Match 8.

We know, highest goal scorer is Harita

=> Harita scored goal in M4, M8, and one other

But, we know the total score in M4 and M8 is 1 each.

=> Harita will score 1 goal each in M4 and M8 and 3 goals in one of the matches.

	A	B	H	S	Total (2)
M1		1
M2		-			$1$
M3		-
M4	-	-	1	-	$1$
M5		1
M6	-	1	-	-	$1$
M7		1
M8	-	-	1	-	$1$
Total (1)	$1/2$	$4$	$5$	$2/1$	$12$

Now, we know Bimla score 1 goal each in 3 consecutive matches

The only 3 consecutive places left is M5, M6, and M7

Therefore, Bimla scored 1 score each in M5, M6, M7.

	A	B	H	S	Total (2)
M1		1
M2		-			$1$
M3		-			$x$
M4	-	-	1	-	$1$
M5		1
M6	-	1	-	-	$1$
M7		1			$x$
M8	-	-	1	-	$1$
Total (1)	$1/2$	$4$	$5$	$2/1$	$12$

Clue 5 says,

An equal number of goals were scored in Match 3 and Match 7

Let that be $'x'$

Also, $x$ is different from the number of goals scored in either Match 1 or Match 5.

But Clue 6 says,

The match in which the highest number of goals was scored was unique and it was not Match 5.

Now, only Unique scoring matches are 1 and 5

from which 5 is not the highest scoring match

=> Match 1 had highest number of goals.

	A	B	H	S	Total (2)
M1		1			$4$
M2		-			$1$
M3		-			$1$
M4	-	-	1	-	$1$
M5		1			$2$
M6	-	1	-	-	$1$
M7	-	1	-	-	$1$
M8	-	-	1	-	$1$
Total (1)	$1/2$	$4$	$5$	$2/1$	$12$

Let the total number of goals in M1 = $y$

and total number of goals in M8 = $z$

=> $x + x + y + z = 12 -1 -1- 1- 1$

=> $2x +y+ z = 8$

If $x=1$ ,

then $y +z =6$

therefore possible solutions for $y$ and $z$ will be 2 and 4 only

If $x=2$ ,

then $y+z=4$

therefore possible solutions for $y$ and $z$ will be 1 and 3 only

but since highest goals scored is in Match 1

so then no. of goals scored in match 1 must be 3

Harita must have scored 3 goals in match 1 as Harita scored 5 goals in exactly 3 matches.

Therefore, we can see this is not possible because then the no. of goals scored in Match 1 becomes 4.

Therefore the only possible solution is $x=1, y=4$ and $z=2$

	A	B	H	S	Total (2)
M1	-	1	3	-	$4$
M2		-	-		$1$
M3		-	-		$1$
M4	-	-	1	-	$1$
M5		1	-		$2$
M6	-	1	-	-	$1$
M7	-	1	-	-	$1$
M8	-	-	1	-	$1$
Total (1)	$1/2$	$4$	$5$	$2/1$	$12$

We know, Harita has scored total of 5 goals,

From which 1 goal each was scored in M4 and M8

=> only match where she can score 3 goals is M1

	A	B	H	S	Total (2)
M1	-	1	3	-	$4$
M2		-	-		$1$
M3		-	-		$1$
M4	-	-	1	-	$1$
M5		1	-		$2$
M6	-	1	-	-	$1$
M7	-	1	-	-	$1$
M8	-	-	1	-	$1$
Total (1)	$1/2$	$4$	$5$	$2/1$	$12$

This is the final table we can make,

In LRDI sets it is many times possible that you may not be able to fill whole of the table,

in that case you should not give up thinking that you are unable to solve the set, instead you should move to the questions and try them and find out how much of them you can solve using the table you have formed.

	A	B	H	S	Total (2)
M1	-	1	3	-	$4$
M2		-	-		$1$
M3		-	-		$1$
M4	-	-	1	-	$1$
M5		1	-		$2$
M6	-	1	-	-	$1$
M7	-	1	-	-	$1$
M8	-	-	1	-	$1$
Total (1)	$1/2$	$4$	$5$	$2/1$	$12$

Statement 1 : Total 3 vacant spaces are available where a total of 3 goals are to be scored.

Now, the combination of Amla and Sarita goals is 2 or 1.

Therefore, if Amla scores a goal then Sarita cannot score a goal and if Sarita scores a goal then Amla cannot.So, this is true.

Statement 2: Harita's goals have already been scored as she is the highest goal scorer and the places where Harita is not scoring goal are the places where Sarita would score the goal.

Hence, this statement is also true.

Therefore both the statements are true : Option 3

Question 1

How many goals were scored in Match 7?

Question 2

Which of the following is the correct sequence of goals scored in matches 1, 3, 5 and 7?

Question 4

Which of the following statement(s) is/are false?

Statement-1: In every match at least one player scored a goal.

Statement-2: No two players scored goals in the same number of matches.

Question 5

If Harita scored goals in one more match as compared to Sarita, which of the following statement(s) is/are necessarily true?

Statement-1: Amla scored goals in consecutive matches.

Statement-2: Sarita scored goals in consecutive matches.

Which of the following statement(s) is/are true? Statement-1: Amla and Sarita never scored goals in the same match. Statement-2: Harita and Sarita never scored goals in the same match.

Solution

More from this set:

Keyboard Shortcuts

CAT Past Year Questions (Topic-Wise)

Which of the following statement(s) is/are true?

Statement-1: Amla and Sarita never scored goals in the same match.

Statement-2: Harita and Sarita never scored goals in the same match.