A health club charges an annual $10 renewal fee for all memb

Official Explanation

Answer: B - Statement (1) is insufficient. If it were 40 days before expiration this would be true, and it would also be true if it were 20 days before expiration. Those two days provide different answers to the question.

Statement (2) is sufficient. If she wouldn't have paid a fee 3 days later, "3 days later" must refer to no later than 31 days before expiration. That means she renewed her membership no later than 34 days before expiration. No matter when she renewed before that point, she didn't pay a renewal fee. Choice (B) is correct.

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Please comment on the following explanation,

Statement 1:
Because t

Please comment on the following explanation,

Statement 1:
If Eileen had renewed her membership 14 days later, she would have paid the renewal fee.
Reasoning:
On the 15th day itself she needs to pay the fee; therefore if today is 8/10/2013, she pays on 1/10/2013 (7 days ago); then the date she needs to pay $10 will be on 15/10/2013.
If she needs to pay on the first day of the 14 days, then even if she pays on 1/10/13 and today is the 14th day, 8/10/2013; the last day that she would not have to pay will be 23/9/2013.

Statement 2:
If Eileen had renewed her membership 3 days later, she would not have paid the renewal fee.
Reasoning:
If she needs to pay on the 4th day; assuming that the date 8/10/13, she needs to pay; then 7 days ago she definitely need not have to pay.

This is not correct. All we know is the following:

- Pay 30 days before expiration, no fee.
- Pay later, there is fee. Now we could have paid 10 days before expiration, 10 days after expiration or a year after expiration, the fee will be there.
Knowing that we need to pay the fee on 15/10/2013 tells us nothing about when we don't need to pay the fee. Perhaps the expiration date is 1/10/2013 or 15/10/2013 or 30/10/2013 or 14/11/2013. We know that the expiration is not 15/11/2013 or later because in that case we wouldn't need to pay the fee on 15/10/2013.

Also, in the above given explanation, I don't know how 23/9/2013 appeared. 15 days prior to today has no significance. In fact, in this question, today has no significance.

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.

some difficulty to visualize the first one.

thanks

In statement 1: Eileen would have to pay renewal fee. So 14 days later date of renewal will be in less than or equal 30 days duration.
So consider total 40 days remaining to expire the member ship. So if she renew member ship after 14 days she has to pay renewal fee.(Made by statement 1)
if she renewed her membership 7 days ago she had not paid any renewal fee.
Next thought :

So consider total 20 days remaining to expire the member ship. So if she renew member ship after 14 days she has to pay renewal fee.(Made by statement 1)
if she renewed her membership 7 days ago she had to pay renewal fee.

So statement 1 gives two answer-- Insufficient.

Statement 2:Eileen would not have to pay renewal fee. So 3 days later, date of renewal will be in greater than 30 days duration.
So 34 days are remaining to renew the membership and if she does it 7 days ago there will be no renewal fee.

So B is Sufficient.

Thanks

I'm diving in

B

atleast 30 days

1)14 days later she would have paid
PS-using month as acronym for aleast 30 days below

2 cases
a)7+14=21(so she can be in that last month and will have to pay)
b)maybe the last month started in between 14 days ..so she wouldn't pay

insuff


2)after 3 days from now she won't have to pay.

that means 7 days before also she didn't pay.

so suff


B

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)

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