avohden 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.
SOURCE: GMAT HACKS - Question of the Day - 9/25/2013
Confusing question... the trick is separating due date (unknown) from her paid date (7 days ago)...
(1) Let's say DUE (-7) was her LAST day to pay without fees (being = 30 days prior to expiration)
+14 or +1 or any additional day would cause her to pay the fee.
BUT, she did not originally pay the fee, so NO.
----(PAID & DUE -7)-----(0)----(+7)-----(EXPIRES +23)Now let's say (-8) was her last day to pay without fees.
----(DUE -8)---(PAID -7)----(0)----(+7)----(EXPIRES +22)She already paid the fee since she was one day late, Answer is YES. So additional 14 days is meaningless since she was already 29 days prior to expiration.
Another way to put it... if d is her distance from PAID to EXPIRES, we are asked d < 30?
In the first case above, d = |-7|+23 = 30, so it would be NO
While in the second case d =|-7|+22 = 29, so it would be YES
Statement one just tells us d - 14 < 30. However, we don't know the original value of d so we can't say if d < 30.
So without knowing the due date we can't determine if she paid or not (adding 14 does nothing). (2) If she didn't pay a fee 3 days later, she obviously wouldn't have to pay it 7 days ago, definite YES.
(the distance between NO FEE and EXPIRES is at least 30)
Note, we still don't know when her due date is, we just know it's at least 34 days from expiration.
-----(PAID -7)---(NO FEE -3)---(0)----(EXPIRES ≥27)