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. $1000$
• E. $2000$

Answer 1

The correct option is C $200$

Because $y$ is a positive integer, $y$ percent is notated as $\frac{y}{100}$. According to the problem, $y=0.50\left(0.50x\right)$ and $\left(\frac{y}{100}\right)x=100$.
The first equation simplifies to $y=0.25x$, and multiplying the second equation by $100$ gives $xy=10,000$.
Substituting the simplified first equation into this second equation gives:
$x\left(0.25x\right)=10,000$
$0.25x^2=10,000$ simplify left side
$x^2=40,000$ divide both sides by $0.25$
$x=200$ solve for the value of $x$
The correct answer is C.