Question

Positive integer \( y \) is 50 percent of 50 percent of positive integer \( x \), and \( y \) percent of \( x \) equals 100. What is the value of \( x \)?

• A. 50
• B. 100
• C. 200
• D. 1,000
• E. 2,000

Hint:

In problems involving percentages, express the percentage as a decimal and set up equations to solve for the unknowns.

Answer 1

The Correct Option is D

Step 1: Express the relationship between \( y \) and \( x \).
We are given that \( y = 50% \times 50% \times x = 0.5 \times 0.5 \times x = 0.25x \). Also, we know that \( y% \times x = 100 \), meaning: \[ \frac{y}{100} \times x = 100 \] Substitute \( y = 0.25x \) into the equation: \[ \frac{0.25x}{100} \times x = 100 \] Simplify the equation: \[ 0.0025x^2 = 100 \] Solving for \( x \): \[ x^2 = \frac{100}{0.0025} = 40,000 \quad \implies \quad x = \sqrt{40,000} = 200 \] \[ \boxed{1000} \]