Question

The "competitive edge" of a baseball team is defined by the formula $\sqrt{\frac{W}{L}}$, where $W$ represents the number of the team's wins and $L$ represents the number of the team's losses. This year, the GMAT All-stars had 3 times as many wins an done-half as many losses as they had last year. By what factor did their "competitive edge" increase?

• A. $\sqrt{12}$,
• B. $\sqrt{2}$,
• C. $\sqrt{6}$,
• D. $\sqrt{8}$,

Answer 1

The correct option is C $\sqrt{6}$,

Let $c=$ competitive edge

$c=\sqrt{\frac{W}{L}}$

Pick numbers to see what happens to the competitive edge when $W$ is tripled and $L$ is halved. If the original of $W$ is $4$ and the original value of $L$ is $2$, the original value of $c$ is $\sqrt{\frac{4}{2}}=\sqrt{2}$. If $W$ triples to $12$ and $L$ is halved to $1$, the new value of $c$ is $\sqrt{\frac{12}{1}}=\sqrt{12}$. The competitive edge has increased from $\sqrt{2}$ to $\sqrt{12}$. Therefore

$\frac{\sqrt{12}}{\sqrt{2}}=\sqrt{\frac{12}{2}}=\sqrt{6}$

The competitive edge has increased by a factor of $\sqrt{6}$,