CAT 2026 · Slot 2 · Expected paper

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CAT 2026 Slot 2 DILR Q16: CAT DILR set

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.

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.

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