QuestionDecember 14, 2025

12. Bruce says that if a number is a product of 6, then it is not a product of 3. What would you say to Bruce?

12. Bruce says that if a number is a product of 6, then it is not a product of 3. What would you say to Bruce?
12. Bruce says that if a number is a product of 6, then it is not a
product of 3. What would you say to Bruce?

Solution
4.1(287 votes)

Answer

Every product of 6 is also a product of 3; Bruce is incorrect. Explanation 1. Define "product of 6" and "product of 3" A "product of 6" means a multiple of 6; a "product of 3" means a multiple of 3. 2. Analyze the relationship Every multiple of 6 (6, 12, 18, ...) can be written as 6n = 3 \times 2n, so it is also a multiple of 3. 3. Conclusion Bruce's statement is incorrect because every product of 6 is also a product of 3.

Explanation

1. Define "product of 6" and "product of 3"<br /> A "product of 6" means a multiple of 6; a "product of 3" means a multiple of 3.<br />2. Analyze the relationship<br /> Every multiple of 6 ($6, 12, 18, ...$) can be written as $6n = 3 \times 2n$, so it is also a multiple of 3.<br />3. Conclusion<br /> Bruce's statement is incorrect because every product of 6 is also a product of 3.
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