World Cup Special – Few maths questions

My colleague mentioned that he had asked his class 1-2 questions on numbers related to the WC. Just thought it might be a good idea to follow that.

1. Australia, in one of their matches, scored a total that is the lowest multiple of 11 with exactly 10 factors. Against who was this?

2. In one of the matches, the top-scorer (who scored a century) for the team batting first scored 3/8th the team’s runs, but the team still did not cross 300. The HCF of the team’s score and the top-scorers score is a prime number. Which match was this?

3. A ‘minnow’ scored a total that can be made a perfect square if it is multiplied by 23. If they had scored 1 more, then their score multiplied by 13 would have yielded a perfect square. What was their score? Bonus point, what match was this?

4. In a particular match, team A batting first scored twice a perfect square. Team B batting second, also scored twice a perfect square. The total score of both the teams put together was also a perfect square. What match are we talking about here?

5. Team scored a three digit score ‘abc’ in a match. a and b are prime numbers. a + 2b and a + 2c are also prime. b + 2a and b + 2c are also primes. a + c and b + c are also primes. Two digit numbers ‘ab’ and ‘ba’ are both primes. Which match was this?

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