Pugalenthi wrote:A health club charges an annual $10 renewal fee for all memberships that are not renewed at least 30 days before they would expire. If Eileen renewed her membership 7 days ago, was she charged the renewal fee?
(1) If Eileen had renewed her membership 14 days later, she would have paid the renewal fee.
(2) If Eileen had renewed her membership 3 days later, she would not have paid the renewal fee.
Dear Pugalenthi,
Hello! I'm happy to help with this.
Prompt:
A health club charges an annual $10 renewal fee for all memberships that are not renewed at least 30 days before they would expire. If Eileen renewed her membership 7 days ago, was she charged the renewal fee?
A convoluted prompt. We need to figure out the relationship of her renewal date to the date when fees begin, 30 days before membership would expire.
Statement #1:
If Eileen had renewed her membership 14 days later, she would have paid the renewal fee.
Let "Fee Day" be that day, 30 days before expiration --- on Fee Day and after, Ellen would have to have paid the $10 renewal fee. Given the information of this statement, we can construct two scenarios:
scenario I
Ellen pays ... [a few days] ... Fee Day ...[a few more days] ... the 14th day after Ellen pays
scenario II
Fee Day .... [a couple days] ... Ellen pays ... [13 more days] ... the 14th day after Ellen pays
Both scenarios satisfy the constraint given in the statement, but in the first, Ellen would not have to play the the $10 renewal fee, and in the second, she would. This statement allows for scenarios that answer the prompt question either way, so by itself, this statement is
insufficient.
Statement #2:
If Eileen had renewed her membership 3 days later, she would not have paid the renewal fee.
This allows for only one scenario
Ellen pays (A) ... [2 days] ... 3 days after Ellen pays (B) ... [a couple days] .... Fee Day (C)
Since she would not pay 3 days later, that the 3-days-later day must be before Fee Day, and of course when Ellen actually paid has to be before 3 days after she paid. A is before B, and B is before C, so this necessarily means that A is before C. Therefore, when she paid is before Fee day, so she did not have to play the $10 renewal fee. This statement allows for a definitive answer to the prompt question, so by itself, this statement is
sufficient.
Answer =
B
Does that make sense?
Here's another DS practice question that, in its formal structure, is quite similar to this, although on the surface it looks like a different kind of question.
https://gmat.magoosh.com/questions/921
When you submit your answer, the following page will have the complete video explanation. Each of Magoosh's 800+ GMAT questions has its own video explanation.
Let me know if you have any further questions.
Mike
