Question

The product of two composite numbers is 96, and their quotient is 6. What is the smaller number?

a) 8
b) 12
c) 16
d) 24

Answer 1

To find the smaller composite number, we set up equations based on the given product and quotient, solve them algebraically, and conclude that the smaller number is 16, which is option c.

Step-by-step explanation:

The question asks us to find the smaller of two composite numbers that multiply to 96 and have a quotient of 6. To find these numbers, we follow these steps:

1. Let's assume the two numbers are a and b, where a > b, and according to the problem, ab = 96 and a/b = 6.
2. From the quotient, we can express a as 6b.
3. We can then plug this into the product equation to get 6b * b = 96, which simplifies to 6b2 = 96.
4. Solving for b, we divide both sides by 6 to get b2 = 16.
5. Since b is a composite number, the square root of 16 is 4, but 4 is not a composite number. However, if a = 24 (another factor of 96 that when divided by 4 gives us the quotient 6), then b will indeed be 4's multiple and a composite number, which is 16.

The smaller number is 16, which is option c.