Tobacco Survey Analysis

The question asks us to make a logical inference based *only* on the provided survey data about tobacco users. We are given two key pieces of information:

• 65% of tobacco users were advised to stop consuming tobacco.
• 3 out of 10 tobacco users attempted to stop using tobacco.

Let's convert the second piece of information into a percentage: 3 out of 10 is equal to $\frac{3}{10} \times 100\% = 30\%$. So, 30% of all tobacco users attempted to stop.

Evaluating Inference Options

Option 1 Inference: Majority of Advised Users Attempted

This statement claims that more than 50% of the 65% of users who were advised actually attempted to stop. We know only 30% of *all* users attempted to stop. It's possible that the 30% who attempted are all within the 65% advised group, or that some are from the 35% not advised. We cannot be certain that *more than half* of the advised group attempted, as the total attempts (30%) might not be that high relative to the advised group (65%). Therefore, this inference cannot be made with certainty.

Option 2 Inference: Majority of Advised Users Did Not Attempt

Let's analyze this logically. Let '$T$' represent the total number of tobacco users surveyed.

• Number of users advised = $0.65 \times T$
• Number of users who attempted = $0.30 \times T$

Let '$x$' be the percentage of *advised* users who attempted to stop. The number of advised users who attempted is $\frac{x}{100} \times (0.65 \times T)$.

The total number of users who attempted ($0.30 \times T$) cannot be more than the number of users who were advised and attempted. So, the attempts from the advised group must be less than or equal to the total attempts:

$$ \frac{x}{100} \times (0.65 \times T) \le 0.30 \times T $$

We can simplify this by dividing both sides by $T$ (assuming $T > 0$):

$$ \frac{x}{100} \times 0.65 \le 0.30 $$

Now, let's solve for the maximum possible value of $x$:

$$ \frac{x}{100} \le \frac{0.30}{0.65} $$ $$ \frac{x}{100} \le \frac{30}{65} = \frac{6}{13} $$ $$ x \le \frac{6}{13} \times 100 $$ $$ x \le 46.15\% \text{ (approximately)} $$

This calculation shows that the percentage ($x$) of advised users who attempted to stop is at most about 46.15%. Since 46.15% is less than 50%, it means that *less than a majority* of advised users attempted to stop.

If less than a majority (i.e., $\le 46.15\%$) of advised users attempted to stop, then the percentage of advised users who did not attempt to stop must be greater than $100\% - 46.15\% = 53.85\%$.

Since 53.85% is more than 50%, this means a majority of tobacco users who were advised to stop did not attempt to do so. This statement can be logically inferred with certainty.

Option 3 Inference: Success Rate Approximation

The survey states that 30% of users *attempted* to stop. It does not provide any information about the success rate of these attempts. We cannot infer how many successfully stopped.

Option 4 Inference: Success Rate Approximation

Similarly, the survey states that 65% were *advised* to stop. This number relates to the advice given, not the outcome (successful cessation). We cannot infer the success rate from this information.

Conclusion

Based purely on the provided data, the only statement that can be logically inferred with certainty is that a majority of tobacco users who were advised to stop consuming tobacco did not attempt to do so.