having trouble understanding the question...

"The argument" means the Conclusion and how it is arrived.

Here the argument is "If servers regularly write "Thank You" in the bills the average income from tips will be significantly higher than it would otherwise be". In simple words, if servers write TY on bills they will get more tip from customers.

Correct Answer: Regularly seeing TY written on their bills would not lead restaurant patrons to revert to their earlier tipping habits.

For finding the assumption one should use the negation technique, i.e., take the negation and check the argument falls apart.

The negated correct answer will be "Regularly seeing TY written on the bills would lead restaurant patrons to revert to their earlier tipping habits." That is, they will stop paying extra tip. The argument falls apart using this assumption.

Hope you get my point.If not, please ask more question and I'll try to answer.

yumi2012 wrote:Servers wrote "Thank you" on randomly selected bills and tips on those bills were higher than bills without the "Thank you" message. Therefore if servers regularly wrote "Thank you" on restaurant bills, their average income from tips would be significantly higher than it otherwise would have been.

Which of the following is the assumption on which the argument relies?

Correct Answer: Regularly seeing TY written on their bills would not lead restaurant patrons to revert to their earlier tipping habits.

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What is "the argument" in the question referring to? Is it what the writer insists? (that regular "TY" note will increase tip income")

Or, is "the argument" against it?

An "argument" on the GMAT means a conclusion supported by one or more pieces of evidence. A conclusion is the opinion, fact, or idea that is the author's main idea. Evidence is anything offered to back up that main idea--often, but not necessarily, factual information.

In this case, "therefore" identifies the conclusion: servers should write "thank you" on checks all the time.

Now, we are asked to identify an "assumption" that underlies the conclusion. A GMAT argument will basically never be written watertight--that's intentional. Some evidence necessary to support the conclusion will always be omitted, and identifying that missing piece is part of the skill that the Critical Reasoning section is designed to test! Here, the major assumption is a simple one: that the "special" feeling generated by a thank-you won't get old and tired rapidly. Spot that, and we have our answer.

Hope this helps!