#amc10

［Math Knowledge Tip 2］ Best math plans for you——https://www.thethinkacademy.com/ThinkMatrix👈👈 Today we are going to learn about Prime Numbers and Composite Numbers✅✅ ⛵️Prime number：A number has only 1 and its own two factors, such a number is called a prime number. The smallest prime number is 2. ⛵️Composite Number：A number that has other factors besides 1 and itself is called a composite number. The smallest composite is 4. 🥰🥰Here are some tips for you: 1.0 and 1are not prime numbers, nor are they composite numbers. 2.The prime numbers within 100🍭🍭 #AMC8 #amc10 #math #AmericanMathmatics #AMC12 #maths #mathslearning #studying #amcexam #amc8exam #AmericanMathmaticsCompetition #studyingpartner #lovemathswithsip https://www.instagram.com/p/CmpGlCsyBpE/?igshid=NGJjMDIxMWI=

［Math Knowledge Tip 2］ Best math plans for you——https://www.thethinkacademy.com/ThinkMatrix👈👈 Today we are going to learn about Prime Numbers and Composite Numbers✅✅ ⛵️Prime number：A number has only 1 and its own two factors, such a number is called a prime number. The smallest prime number is 2. ⛵️Composite Number：A number that has other factors besides 1 and itself is called a composite number. The smallest composite is 4. 🥰🥰Here are some tips for you: 1.0 and 1are not prime numbers, nor are they composite numbers. 2.The prime numbers within 100🍭🍭 #AMC8 #amc10 #math #AmericanMathmatics #AMC12 #maths #mathslearning #studying #amcexam #amc8exam #AmericanMathmaticsCompetition #studyingpartner #lovemaths https://www.instagram.com/p/CmpGewayfI2/?igshid=NGJjMDIxMWI=

We can rewrite the fractions as (9a^2 + 14b^2) / 9ab. Therefore, 3|b. Since a and b are coprime, a|9a^2 + 14b^2, so a|14. Similarly, b|9. However, b cannot be 9 as 81a|9a^2 + 81*14 only has solutions when 3|a, which can’t happen when a|14. So, b=3, and a can be {1, 2, 7, 14}. Checking shows us that all 4 work, so the answer is A (4).

The maximum number of balls we can draw without drawing 15 of the same color comes from this scenario: we draw 14 red, 14 green, 14 yellow, 13 blue, 11 white, and 9 black. This gives us 75 balls. Drawing one more ball will guarantee us 15 of the same color, so the answer is B (76).

sorry for this bragging post I'm just really happy right now