CAT 2026 Slot 2 DILR: Set 4: Set 4 – Women's Cricket Sixes with Solutions

4 questions: Q15, Q16, Q17, Q18. Solve each one here: tap the answer, press Check, then open the solution.

Puzzles

The set

SET 4: WOMEN'S CRICKET – SIXES IN EIGHT MATCHES
The management of a women's cricket team is evaluating four players—Zara, Meera, Tanya and Rhea—for selection in the national team. The following facts relate only to the sixes hit by these four players in the past eight matches, numbered 1 to 8. Together, the four players hit 12 sixes. Each player hit at least one six, and no two players hit the same total number of sixes.

FACTS:
1. Exactly one six was hit in every even-numbered match (2, 4, 6 and 8).
2. Tanya hit more sixes than Zara.
3. The player who hit the highest total number of sixes scored in exactly three matches, including Matches 4 and 8.
4. Zara hit exactly one six in Match 1 and exactly one six in each of three other consecutive matches. She hit no sixes in the remaining matches.
5. Matches 3 and 7 had an equal number of sixes, and this number was different from the number hit in either Match 1 or Match 5.
6. The match with the highest number of sixes was unique and was not Match 5.

Question 15CAT DILR set

MCQ · +3 / −1 · medium

Which of the following statement(s) is/are necessarily true?
Statement 1: Zara and Rhea never hit sixes in the same match.
Statement 2: Tanya and Rhea never hit sixes in the same match.

Answer and solution

Correct answer: A

Solution

Answer: A — Statement 2 only

1. Zara hits four sixes, one in Match 1 and one in each of three other consecutive matches. Four distinct positive player totals sum to 12 and Tanya exceeds 4; the only possibility is totals 1,2,4,5. Thus Tanya has 5 and is the highest scorer.
2. Tanya scores in exactly three matches, including 4 and 8. Each even match has exactly one six, so Tanya hits 1 in 4,1 in 8 and 3 in one odd match. Zara cannot score in 4 or 8.
3. The only permitted three-match consecutive block for Zara, avoiding 4 and 8 and excluding her separate Match 1, is 5,6,7. Hence Zara scores 1 in 1,5,6,7.
4. Tanya's three-six match cannot be 7 because equal Match 3 would require too many sixes. It cannot be 3 because equality with 7 would force at least two extra sixes in 7 plus one in 2, leaving Match 3 and 7 tied for maximum. It cannot be 5 because then Match 5 would be the unique maximum, forbidden. Therefore Tanya hits 3 in Match 1.
5. Now Match 1 already has 4 sixes and Matches 4,5,6,7,8 have 1 each. Three sixes remain for Meera and Rhea. Match 2 requires 1 and equality of Matches 3 and 7 requires at least 1 in Match 3.
6. The last remaining six must be in Match 5. Putting it in Match 1 leaves Match 5=Match 3=1, forbidden; putting it in 3 or 7 would break their equality. Thus totals are 4,1,1,1,2,1,1,1. The remaining players split the three single-six slots 2,3,5 in totals 1 and 2.
7. Tanya scores only in 1,4,8. Rhea scores in a subset of 2,3,5, so Tanya and Rhea never overlap. Zara scores in 5 and Rhea may score in 5; statement 1 is not guaranteed. Thus only statement 2 must be true.

G Strategy shortcut

Method: Player totals must be 1,2,4,5; place Tanya in 4/8 and Zara in 5/6/7, then use equality 3=7. Tanya scores only in 1,4,8. Rhea scores in a subset of 2,3,5, so Tanya and Rhea never overlap. Zara scores in 5 and Rhea may score in 5; statement 1 is not guaranteed. Thus only statement 2 must be true.
Verification: 1. Zara hits four sixes, one in Match 1 and one in each of three other consecutive matches. Four distinct positive player totals sum to 12 and Tanya exceeds 4; the only possibility is totals 1,2,4,5. Thus Tanya has 5 and is the highest scorer.
2. Tanya scores in exactly three matches, including 4 and 8. Each even match has exactly one six, so Tanya hits 1 in 4,1 in 8 and 3 in one odd match. Zara cannot score in 4 or 8.
3. The only permitted three-match consecutive block for Zara, avoiding 4 and 8 and excluding her separate Match 1, is 5,6,7. Hence Zara scores 1 in 1,5,6,7.
4. Tanya's three-six match cannot be 7 because equal Match 3 would require too many sixes. It cannot be 3 because equality with 7 would force at least two extra sixes in 7 plus one in 2, leaving Match 3 and 7 tied for maximum. It cannot be 5 because then Match 5 would be the unique maximum, forbidden. Therefore Tanya hits 3 in Match 1.
5. Now Match 1 already has 4 sixes and Matches 4,5,6,7,8 have 1 each. Three sixes remain for Meera and Rhea. Match 2 requires 1 and equality of Matches 3 and 7 requires at least 1 in Match 3.
6. The last remaining six must be in Match 5. Putting it in Match 1 leaves Match 5=Match 3=1, forbidden; putting it in 3 or 7 would break their equality. Thus totals are 4,1,1,1,2,1,1,1. The remaining players split the three single-six slots 2,3,5 in totals 1 and 2.
7. Tanya scores only in 1,4,8. Rhea scores in a subset of 2,3,5, so Tanya and Rhea never overlap. Zara scores in 5 and Rhea may score in 5; statement 1 is not guaranteed. Thus only statement 2 must be true.

G Strategy: Method: Player totals must be 1,2,4,5; place Tanya in 4/8 and Zara in 5/6/7, then use equality 3=7. Tanya scores only in 1,4,8. Rhea scores in a subset of 2,3,5, so Tanya and Rhea never overlap. Zara scores in 5 and Rhea may score in 5; statement 1 is not guaranteed. Thus only statement 2 must be true. Verification: 1. Zara hits four sixes, one in Match 1 and one in each of three other consecutive matches. Four distinct positive player totals sum to 12 and Tanya exceeds 4; the only possibility is totals 1,2,4,5. Thus Tanya has 5 and is the highest scorer. 2. Tanya scores in exactly three matches, including 4 and 8. Each even match has exactly one six, so Tanya hits 1 in 4,1 in 8 and 3 in one odd match. Zara cannot score in 4 or 8. 3. The only permitted three-match consecutive block for Zara, avoiding 4 and 8 and excluding her separate Match 1, is 5,6,7. Hence Zara scores 1 in 1,5,6,7. 4. Tanya's three-six match cannot be 7 because equal Match 3 would require too many sixes. It cannot be 3 because equality with 7 would force at least two extra sixes in 7 plus one in 2, leaving Match 3 and 7 tied for maximum. It cannot be 5 because then Match 5 would be the unique maximum, forbidden. Therefore Tanya hits 3 in Match 1. 5. Now Match 1 already has 4 sixes and Matches 4,5,6,7,8 have 1 each. Three sixes remain for Meera and Rhea. Match 2 requires 1 and equality of Matches 3 and 7 requires at least 1 in Match 3. 6. The last remaining six must be in Match 5. Putting it in Match 1 leaves Match 5=Match 3=1, forbidden; putting it in 3 or 7 would break their equality. Thus totals are 4,1,1,1,2,1,1,1. The remaining players split the three single-six slots 2,3,5 in totals 1 and 2. 7. Tanya scores only in 1,4,8. Rhea scores in a subset of 2,3,5, so Tanya and Rhea never overlap. Zara scores in 5 and Rhea may score in 5; statement 1 is not guaranteed. Thus only statement 2 must be true.

Question 16CAT DILR set

MCQ · +3 / −1 · medium

How many sixes were hit in Match 7?

Answer and solution

Correct answer: C

Solution

Answer: C — 1

1. Zara hits four sixes, one in Match 1 and one in each of three other consecutive matches. Four distinct positive player totals sum to 12 and Tanya exceeds 4; the only possibility is totals 1,2,4,5. Thus Tanya has 5 and is the highest scorer.
2. Tanya scores in exactly three matches, including 4 and 8. Each even match has exactly one six, so Tanya hits 1 in 4,1 in 8 and 3 in one odd match. Zara cannot score in 4 or 8.
3. The only permitted three-match consecutive block for Zara, avoiding 4 and 8 and excluding her separate Match 1, is 5,6,7. Hence Zara scores 1 in 1,5,6,7.
4. Tanya's three-six match cannot be 7 because equal Match 3 would require too many sixes. It cannot be 3 because equality with 7 would force at least two extra sixes in 7 plus one in 2, leaving Match 3 and 7 tied for maximum. It cannot be 5 because then Match 5 would be the unique maximum, forbidden. Therefore Tanya hits 3 in Match 1.
5. Now Match 1 already has 4 sixes and Matches 4,5,6,7,8 have 1 each. Three sixes remain for Meera and Rhea. Match 2 requires 1 and equality of Matches 3 and 7 requires at least 1 in Match 3.
6. The last remaining six must be in Match 5. Putting it in Match 1 leaves Match 5=Match 3=1, forbidden; putting it in 3 or 7 would break their equality. Thus totals are 4,1,1,1,2,1,1,1. The remaining players split the three single-six slots 2,3,5 in totals 1 and 2.
7. The forced totals show Match 7=1. Answer: C.

G Strategy shortcut

Method: Player totals must be 1,2,4,5; place Tanya in 4/8 and Zara in 5/6/7, then use equality 3=7. The forced totals show Match 7=1. Answer: C.
Verification: 1. Zara hits four sixes, one in Match 1 and one in each of three other consecutive matches. Four distinct positive player totals sum to 12 and Tanya exceeds 4; the only possibility is totals 1,2,4,5. Thus Tanya has 5 and is the highest scorer.
2. Tanya scores in exactly three matches, including 4 and 8. Each even match has exactly one six, so Tanya hits 1 in 4,1 in 8 and 3 in one odd match. Zara cannot score in 4 or 8.
3. The only permitted three-match consecutive block for Zara, avoiding 4 and 8 and excluding her separate Match 1, is 5,6,7. Hence Zara scores 1 in 1,5,6,7.
4. Tanya's three-six match cannot be 7 because equal Match 3 would require too many sixes. It cannot be 3 because equality with 7 would force at least two extra sixes in 7 plus one in 2, leaving Match 3 and 7 tied for maximum. It cannot be 5 because then Match 5 would be the unique maximum, forbidden. Therefore Tanya hits 3 in Match 1.
5. Now Match 1 already has 4 sixes and Matches 4,5,6,7,8 have 1 each. Three sixes remain for Meera and Rhea. Match 2 requires 1 and equality of Matches 3 and 7 requires at least 1 in Match 3.
6. The last remaining six must be in Match 5. Putting it in Match 1 leaves Match 5=Match 3=1, forbidden; putting it in 3 or 7 would break their equality. Thus totals are 4,1,1,1,2,1,1,1. The remaining players split the three single-six slots 2,3,5 in totals 1 and 2.
7. The forced totals show Match 7=1. Answer: C.

G Strategy: Method: Player totals must be 1,2,4,5; place Tanya in 4/8 and Zara in 5/6/7, then use equality 3=7. The forced totals show Match 7=1. Answer: C. Verification: 1. Zara hits four sixes, one in Match 1 and one in each of three other consecutive matches. Four distinct positive player totals sum to 12 and Tanya exceeds 4; the only possibility is totals 1,2,4,5. Thus Tanya has 5 and is the highest scorer. 2. Tanya scores in exactly three matches, including 4 and 8. Each even match has exactly one six, so Tanya hits 1 in 4,1 in 8 and 3 in one odd match. Zara cannot score in 4 or 8. 3. The only permitted three-match consecutive block for Zara, avoiding 4 and 8 and excluding her separate Match 1, is 5,6,7. Hence Zara scores 1 in 1,5,6,7. 4. Tanya's three-six match cannot be 7 because equal Match 3 would require too many sixes. It cannot be 3 because equality with 7 would force at least two extra sixes in 7 plus one in 2, leaving Match 3 and 7 tied for maximum. It cannot be 5 because then Match 5 would be the unique maximum, forbidden. Therefore Tanya hits 3 in Match 1. 5. Now Match 1 already has 4 sixes and Matches 4,5,6,7,8 have 1 each. Three sixes remain for Meera and Rhea. Match 2 requires 1 and equality of Matches 3 and 7 requires at least 1 in Match 3. 6. The last remaining six must be in Match 5. Putting it in Match 1 leaves Match 5=Match 3=1, forbidden; putting it in 3 or 7 would break their equality. Thus totals are 4,1,1,1,2,1,1,1. The remaining players split the three single-six slots 2,3,5 in totals 1 and 2. 7. The forced totals show Match 7=1. Answer: C.

Question 17CAT DILR set

MCQ · +3 / −1 · medium

Which of the following statement(s) is/are false?
Statement 1: In every match at least one player hit a six.
Statement 2: No two players hit sixes in the same number of matches.

Answer and solution

Correct answer: A

Solution

Answer: A — None of the statements

1. Zara hits four sixes, one in Match 1 and one in each of three other consecutive matches. Four distinct positive player totals sum to 12 and Tanya exceeds 4; the only possibility is totals 1,2,4,5. Thus Tanya has 5 and is the highest scorer.
2. Tanya scores in exactly three matches, including 4 and 8. Each even match has exactly one six, so Tanya hits 1 in 4,1 in 8 and 3 in one odd match. Zara cannot score in 4 or 8.
3. The only permitted three-match consecutive block for Zara, avoiding 4 and 8 and excluding her separate Match 1, is 5,6,7. Hence Zara scores 1 in 1,5,6,7.
4. Tanya's three-six match cannot be 7 because equal Match 3 would require too many sixes. It cannot be 3 because equality with 7 would force at least two extra sixes in 7 plus one in 2, leaving Match 3 and 7 tied for maximum. It cannot be 5 because then Match 5 would be the unique maximum, forbidden. Therefore Tanya hits 3 in Match 1.
5. Now Match 1 already has 4 sixes and Matches 4,5,6,7,8 have 1 each. Three sixes remain for Meera and Rhea. Match 2 requires 1 and equality of Matches 3 and 7 requires at least 1 in Match 3.
6. The last remaining six must be in Match 5. Putting it in Match 1 leaves Match 5=Match 3=1, forbidden; putting it in 3 or 7 would break their equality. Thus totals are 4,1,1,1,2,1,1,1. The remaining players split the three single-six slots 2,3,5 in totals 1 and 2.
7. Every match has at least one six. Tanya scores in 3 matches, Zara in 4, and Meera/Rhea in 1 and 2 matches. Both statements are true, so none is false.

G Strategy shortcut

Method: Player totals must be 1,2,4,5; place Tanya in 4/8 and Zara in 5/6/7, then use equality 3=7. Every match has at least one six. Tanya scores in 3 matches, Zara in 4, and Meera/Rhea in 1 and 2 matches. Both statements are true, so none is false.
Verification: 1. Zara hits four sixes, one in Match 1 and one in each of three other consecutive matches. Four distinct positive player totals sum to 12 and Tanya exceeds 4; the only possibility is totals 1,2,4,5. Thus Tanya has 5 and is the highest scorer.
2. Tanya scores in exactly three matches, including 4 and 8. Each even match has exactly one six, so Tanya hits 1 in 4,1 in 8 and 3 in one odd match. Zara cannot score in 4 or 8.
3. The only permitted three-match consecutive block for Zara, avoiding 4 and 8 and excluding her separate Match 1, is 5,6,7. Hence Zara scores 1 in 1,5,6,7.
4. Tanya's three-six match cannot be 7 because equal Match 3 would require too many sixes. It cannot be 3 because equality with 7 would force at least two extra sixes in 7 plus one in 2, leaving Match 3 and 7 tied for maximum. It cannot be 5 because then Match 5 would be the unique maximum, forbidden. Therefore Tanya hits 3 in Match 1.
5. Now Match 1 already has 4 sixes and Matches 4,5,6,7,8 have 1 each. Three sixes remain for Meera and Rhea. Match 2 requires 1 and equality of Matches 3 and 7 requires at least 1 in Match 3.
6. The last remaining six must be in Match 5. Putting it in Match 1 leaves Match 5=Match 3=1, forbidden; putting it in 3 or 7 would break their equality. Thus totals are 4,1,1,1,2,1,1,1. The remaining players split the three single-six slots 2,3,5 in totals 1 and 2.
7. Every match has at least one six. Tanya scores in 3 matches, Zara in 4, and Meera/Rhea in 1 and 2 matches. Both statements are true, so none is false.

G Strategy: Method: Player totals must be 1,2,4,5; place Tanya in 4/8 and Zara in 5/6/7, then use equality 3=7. Every match has at least one six. Tanya scores in 3 matches, Zara in 4, and Meera/Rhea in 1 and 2 matches. Both statements are true, so none is false. Verification: 1. Zara hits four sixes, one in Match 1 and one in each of three other consecutive matches. Four distinct positive player totals sum to 12 and Tanya exceeds 4; the only possibility is totals 1,2,4,5. Thus Tanya has 5 and is the highest scorer. 2. Tanya scores in exactly three matches, including 4 and 8. Each even match has exactly one six, so Tanya hits 1 in 4,1 in 8 and 3 in one odd match. Zara cannot score in 4 or 8. 3. The only permitted three-match consecutive block for Zara, avoiding 4 and 8 and excluding her separate Match 1, is 5,6,7. Hence Zara scores 1 in 1,5,6,7. 4. Tanya's three-six match cannot be 7 because equal Match 3 would require too many sixes. It cannot be 3 because equality with 7 would force at least two extra sixes in 7 plus one in 2, leaving Match 3 and 7 tied for maximum. It cannot be 5 because then Match 5 would be the unique maximum, forbidden. Therefore Tanya hits 3 in Match 1. 5. Now Match 1 already has 4 sixes and Matches 4,5,6,7,8 have 1 each. Three sixes remain for Meera and Rhea. Match 2 requires 1 and equality of Matches 3 and 7 requires at least 1 in Match 3. 6. The last remaining six must be in Match 5. Putting it in Match 1 leaves Match 5=Match 3=1, forbidden; putting it in 3 or 7 would break their equality. Thus totals are 4,1,1,1,2,1,1,1. The remaining players split the three single-six slots 2,3,5 in totals 1 and 2. 7. Every match has at least one six. Tanya scores in 3 matches, Zara in 4, and Meera/Rhea in 1 and 2 matches. Both statements are true, so none is false.

Question 18CAT DILR set

MCQ · +3 / −1 · medium

Which of the following is the correct sequence of sixes hit in Matches 1, 3, 5 and 7?

Answer and solution

Correct answer: C

Solution

Answer: C — 4, 1, 2, 1

1. Zara hits four sixes, one in Match 1 and one in each of three other consecutive matches. Four distinct positive player totals sum to 12 and Tanya exceeds 4; the only possibility is totals 1,2,4,5. Thus Tanya has 5 and is the highest scorer.
2. Tanya scores in exactly three matches, including 4 and 8. Each even match has exactly one six, so Tanya hits 1 in 4,1 in 8 and 3 in one odd match. Zara cannot score in 4 or 8.
3. The only permitted three-match consecutive block for Zara, avoiding 4 and 8 and excluding her separate Match 1, is 5,6,7. Hence Zara scores 1 in 1,5,6,7.
4. Tanya's three-six match cannot be 7 because equal Match 3 would require too many sixes. It cannot be 3 because equality with 7 would force at least two extra sixes in 7 plus one in 2, leaving Match 3 and 7 tied for maximum. It cannot be 5 because then Match 5 would be the unique maximum, forbidden. Therefore Tanya hits 3 in Match 1.
5. Now Match 1 already has 4 sixes and Matches 4,5,6,7,8 have 1 each. Three sixes remain for Meera and Rhea. Match 2 requires 1 and equality of Matches 3 and 7 requires at least 1 in Match 3.
6. The last remaining six must be in Match 5. Putting it in Match 1 leaves Match 5=Match 3=1, forbidden; putting it in 3 or 7 would break their equality. Thus totals are 4,1,1,1,2,1,1,1. The remaining players split the three single-six slots 2,3,5 in totals 1 and 2.
7. Read totals for Matches 1, 3, 5, 7 in that order: 4,1,2,1. Answer: C.

G Strategy shortcut

Method: Player totals must be 1,2,4,5; place Tanya in 4/8 and Zara in 5/6/7, then use equality 3=7. Read totals for Matches 1, 3, 5, 7 in that order: 4,1,2,1. Answer: C.
Verification: 1. Zara hits four sixes, one in Match 1 and one in each of three other consecutive matches. Four distinct positive player totals sum to 12 and Tanya exceeds 4; the only possibility is totals 1,2,4,5. Thus Tanya has 5 and is the highest scorer.
2. Tanya scores in exactly three matches, including 4 and 8. Each even match has exactly one six, so Tanya hits 1 in 4,1 in 8 and 3 in one odd match. Zara cannot score in 4 or 8.
3. The only permitted three-match consecutive block for Zara, avoiding 4 and 8 and excluding her separate Match 1, is 5,6,7. Hence Zara scores 1 in 1,5,6,7.
4. Tanya's three-six match cannot be 7 because equal Match 3 would require too many sixes. It cannot be 3 because equality with 7 would force at least two extra sixes in 7 plus one in 2, leaving Match 3 and 7 tied for maximum. It cannot be 5 because then Match 5 would be the unique maximum, forbidden. Therefore Tanya hits 3 in Match 1.
5. Now Match 1 already has 4 sixes and Matches 4,5,6,7,8 have 1 each. Three sixes remain for Meera and Rhea. Match 2 requires 1 and equality of Matches 3 and 7 requires at least 1 in Match 3.
6. The last remaining six must be in Match 5. Putting it in Match 1 leaves Match 5=Match 3=1, forbidden; putting it in 3 or 7 would break their equality. Thus totals are 4,1,1,1,2,1,1,1. The remaining players split the three single-six slots 2,3,5 in totals 1 and 2.
7. Read totals for Matches 1, 3, 5, 7 in that order: 4,1,2,1. Answer: C.

G Strategy: Method: Player totals must be 1,2,4,5; place Tanya in 4/8 and Zara in 5/6/7, then use equality 3=7. Read totals for Matches 1, 3, 5, 7 in that order: 4,1,2,1. Answer: C. Verification: 1. Zara hits four sixes, one in Match 1 and one in each of three other consecutive matches. Four distinct positive player totals sum to 12 and Tanya exceeds 4; the only possibility is totals 1,2,4,5. Thus Tanya has 5 and is the highest scorer. 2. Tanya scores in exactly three matches, including 4 and 8. Each even match has exactly one six, so Tanya hits 1 in 4,1 in 8 and 3 in one odd match. Zara cannot score in 4 or 8. 3. The only permitted three-match consecutive block for Zara, avoiding 4 and 8 and excluding her separate Match 1, is 5,6,7. Hence Zara scores 1 in 1,5,6,7. 4. Tanya's three-six match cannot be 7 because equal Match 3 would require too many sixes. It cannot be 3 because equality with 7 would force at least two extra sixes in 7 plus one in 2, leaving Match 3 and 7 tied for maximum. It cannot be 5 because then Match 5 would be the unique maximum, forbidden. Therefore Tanya hits 3 in Match 1. 5. Now Match 1 already has 4 sixes and Matches 4,5,6,7,8 have 1 each. Three sixes remain for Meera and Rhea. Match 2 requires 1 and equality of Matches 3 and 7 requires at least 1 in Match 3. 6. The last remaining six must be in Match 5. Putting it in Match 1 leaves Match 5=Match 3=1, forbidden; putting it in 3 or 7 would break their equality. Thus totals are 4,1,1,1,2,1,1,1. The remaining players split the three single-six slots 2,3,5 in totals 1 and 2. 7. Read totals for Matches 1, 3, 5, 7 in that order: 4,1,2,1. Answer: C.

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