Re: x and y are integers greater than 5 .
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12 Feb 2026, 07:47
1. Translate the sentence into an equation: The prompt states: " $\(x\)$ is $\(y\)$ percent of $\(x^2\)$." In mathematical terms, this is:
$$
\(x=\frac{y}{100} \cdot x^2\)
$$
2. Simplify the equation: Since the problem states $\(x>5\)$, we know $x$ is not zero. We can safely divide both sides by $x$ :
$$
\(1=\frac{y}{100} \cdot x\)
$$
Multiply both sides by 100:
$$
\(100=x \cdot y\)
$$
3. Apply the constraints: We are looking for two integers ( $x$ and $y$ ) that multiply to 100 , where both must be greater than 5 . Let's look at the factor pairs of 100 :
- $\(1 \times 100\)$ (Rejected: 1 is not $\(>5\)$ )
- $\(2 \times 50\)$ (Rejected: 2 is not $\(>5\)$ )
- $\(4 \times 25\)$ (Rejected: 4 is not $\(>5\)$ )
- $\(5 \times 20\)$ (Rejected: 5 is not greater than 5 ; it is equal to 5 )
- $\(10 \times 10\)$ (Accepted: Both 10 and 10 are greater than $\(\mathbf{5}\)$ )
Any other pair (like $\(20 \times 5\)$ or $\(25 \times 4\)$ ) would result in one of the numbers being 5 or less, which violates the rules of the question.
4. Compare the Quantities:
- Quantity A: $\(x=10\)$
- Quantity B: 10