The main goal of advertising is to increase sales, and using particula

Premises:
The main goal of advertising is to increase sales.
Using particular catch phrases in ads is one way advertisers have pursued this goal.
Many of these catch phrases were developed decades ago.
Many commercials still use these catch phrases.

Conclusion:
The catch phrases continue to boost sales to this day

What is the author's opinion in the whole argument? Something that is not given as a fact? He says that the catchphrases continue to boost sales to this day (that is why they are being used in commercials today also even though they are very old).
We do not know actually whether that is the reason catchphrases are still used in commercials. But since they still are used in commercials, the author is concluding from it that they must be boosting sales even today.


A. does not address the possibility that there are reasons decades-old catch phrases remain in commercials even if the catch phrases themselves do not continue to boost sales

Correct. The very old catchphrases could have been retained in commercials for a purpose other than boosting sales. Perhaps they remind the viewer of the long history of the company. Perhaps the viewer strongly associates the brand with that catchphrase (say 'Just do it' for Nike). Perhaps the catchphrases doesn't lead to sales anymore. Perhaps the commercial focuses on the modern mindset. But because the viewer strongly associates the brand with the catchphrase, the brand might be retaining it.
So just a place in the commercial does not mean that the catchphrase is still boosting sales.


B. fails to address the possibility that an advertising approach used in the past could still be effective simply because more-effective approaches have not yet been developed

The author does not suggest that there are no new approaches. He just says that the approach of old is still effective. He doesn't give a reason why it is still effective. Our point of contention is simply whether using catchphrases of old boosts sales today. Why it may or may not do so is beyond our scope.


C. illicitly infers that more effective catch-phrases will not be developed in the future merely from the fact that they have not yet been developed

He does not infer that more effective catch-phrases will not be developed in the future. Neither does he suggest that they have not yet been developed. It is possible that there are more effective catchphrases too but the company is using the old ones for a purpose (as we discussed in option (A))

D. illicitly infers that one of the primary means of pursuing advertising's main goal should not be reevaluated merely from the fact that that goal has persisted for decades

They are trying to confuse you here with non-sense.
The fact he gives is that catchphrases have persisted for decades, not the goal of increasing sales.
Also, from this fact he is not inferring that catchphrases should not be reevaluated. All he says is that they must be boosting sales because they are still being used. Whether they should be reevaluated or not, he doesn't infer.


E. overlooks the possibility that particularly effective catch phrases remain in consumers' memories even when they have not appeared in commericals for years­

When a catchphrases doesn't appear in commercials for years, it is out of scope for us. We are discussing the role of those catchphrases that HAVE persisted in commercials for years.

Answer (A)