The "competitive edge" of a baseball team is defined by the formula `sqrt(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 and one-half as many losses as they had last year. By what factor did their "Competitive edge" increase ?

Answer

To find the factor by which the "Competitive edge" of the GMAT All-Stars increased, we will follow these steps:

### Step 1: Define Variables
Let \( W \) be the number of wins last year and \( L \) be the number of losses last year. We can denote:
- Wins last year: \( W = X \)
- Losses last year: \( L = Y \)

### Step 2: Calculate Competitive Edge Last Year
The competitive edge for last year can be calculated using the formula:
\[ \text{Competitive Edge}_{\text{last year}} = \sqrt{\frac{W}{L}} = \sqrt{\frac{X}{Y}} \]

### Step 3: Determine Wins and Losses This Year
According to the problem:
- This year, the team has 3 times as many wins as last year:
\[ W_{\text{this year}} = 3X \]
- This year, the team has half as many losses as last year:
\[ L_{\text{this year}} = \frac{1}{2}Y \]

### Step 4: Calculate Competitive Edge This Year
Now, we can calculate the competitive edge for this year:
\[ \text{Competitive Edge}_{\text{this year}} = \sqrt{\frac{W_{\text{this year}}}{L_{\text{this year}}}} = \sqrt{\frac{3X}{\frac{1}{2}Y}} = \sqrt{\frac{3X \cdot 2}{Y}} = \sqrt{\frac{6X}{Y}} \]

### Step 5: Relate the Two Competitive Edges
Now we can express the competitive edge this year in terms of last year's competitive edge:
\[ \text{Competitive Edge}_{\text{this year}} = \sqrt{6} \cdot \sqrt{\frac{X}{Y}} = \sqrt{6} \cdot \text{Competitive Edge}_{\text{last year}} \]

### Step 6: Determine the Factor of Increase
To find the factor by which the competitive edge increased, we compare the two:
\[ \text{Factor of Increase} = \frac{\text{Competitive Edge}_{\text{this year}}}{\text{Competitive Edge}_{\text{last year}}} = \sqrt{6} \]

### Final Answer
Thus, the competitive edge of the GMAT All-Stars increased by a factor of \( \sqrt{6} \).

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