Of the members in a certain club, 70text{ percent} are women. Is the average (arithmetic mean) age of the members...

## Understanding the Question

We need to determine: Is the average age of ALL club members greater than 45 years?

### Given Information
- 70% of club members are women
- 30% of club members are men
- We need a definitive Yes or No answer

### What We Need to Determine
The overall average age is a weighted average that combines:
- Women's average age (weighted by 70%)
- Men's average age (weighted by 30%)

For sufficiency, we need enough information to determine with certainty whether this weighted average exceeds 45.

### Key Insight
Since women make up 70% of the club, they have the dominant influence on the overall average. The men, at only 30%, have limited ability to shift the average significantly. This 70/30 imbalance will be crucial to our analysis.

## Analyzing Statement 1

**Statement 1**: The average age of the men in the club is 68 years.

Now we know:
- Men's average age: 68 years
- Men's proportion: 30%
- Women's average age: Unknown
- Women's proportion: 70%

### Testing Different Scenarios
Since women represent 70% of the club, their unknown average age controls the outcome:

- **If women averaged 30 years**: 
  - The 70% of women at age 30 would pull the average down significantly
  - The 30% of men at age 68 can only pull it up so much
  - Result: Overall average would be BELOW 45

- **If women averaged 50 years**: 
  - With 70% at age 50 and 30% at age 68
  - Result: Overall average would be ABOVE 45

Since different values for women's average age lead to different answers (sometimes Yes, sometimes No), we cannot determine with certainty whether the average exceeds 45.

**Statement 1 is NOT sufficient.**

## Analyzing Statement 2

**Let's forget Statement 1 completely and analyze Statement 2 independently.**

**Statement 2**: The average age of the women in the club is 65 years.

Now we know:
- Women's average age: 65 years
- Women's proportion: 70%
- Men's average age: Unknown
- Men's proportion: 30%

### The Power of the 70% Majority

Here's where the 70/30 split becomes decisive. Women represent 70% of the club with an average age of 65. 

Let's consider the absolute worst-case scenario for the overall average:
- What if all the men were newborns (age 0)?
- Women's contribution: 70% × 65 = 45.5
- Men's contribution: 30% × 0 = 0
- Overall average: 45.5

Since 45.5 > 45, we already exceed our threshold even in this impossible scenario!

In reality, the men must have some positive average age, which would only increase the overall average further above 45.

**No matter what the men's average age is**, the women's 70% dominance at 65 years **guarantees** the overall average exceeds 45.

**Statement 2 is sufficient.** **[STOP - Sufficient!]**

## The Answer: B

Statement 2 alone is sufficient because the 70% majority at 65 years guarantees the average exceeds 45, regardless of the men's ages.

Statement 1 alone is not sufficient because knowing only the minority group's average (30% at 68 years) leaves too much uncertainty about the dominant group's impact.

**Answer: B** - Statement 2 alone is sufficient, but Statement 1 alone is not sufficient.