Problem Solving

BTGmoderatorDC wrote:ADVANCED PURCHASE DISCOUNTS FOR AIRLINE TRAVEL
days prior to departure-------------------percentage discount
0~6 days----------------------------------------0%
7~13 days--------------------------------------10%
14~29 days--------------------------------------25%
30 days or more---------------------------------40%

The table above shows the discount structure for advanced purchase of tickets at a particular airline.A passenger bought a ticket at this airline for $1,050. The ticket agent informed her that，had she purchased the ticket one day later， she would have paid $210 more.How many days before her departure did she purchase her ticket?

A. 6 days
B. 7 days
C. 13 days
D. 14 days
E. 29 days

OA D

Source: Manhattan GMAT

Plug In The Answers. But first, take 30 seconds to comprehend the information provided by the question stem.

Had she purchased the ticket one day later, she would have purchased the ticket one day closer to the date of her departure, so the number of days prior to her departure would decrease by 1.
Since she would have paid more had she purchased the ticket one day later, the day on which she purchased the ticket must have been the first day on which a greater percentage discount applied.
Thus, she must have purchased the ticket 7 days, 14 days, or 30 days prior to her departure. Based on the information in the table, these are the only possible answers, so eliminate choices A, C, and E.

Now, Plug In either of the remaining answers. Since 25% is an easy percentage to work with, begin with choice D.
If she purchased the ticket 14 days prior to her departure, then she received a 25% discount, and $1,050 is 75% of the ticket price. Therefore, the full price of the ticket is $1,050/0.75 = $1,400.
Had she purchased the ticket one day later, 13 days prior to her departure, she would have received a 10% discount, so she would have paid $1,400 - $140 = $1,260.
According to the question stem, she would have paid $210 more had she purchased the ticket one day later. Since $1,260 - $1,050 = $210, Choice D is a match for all of the information in the question stem.

The correct answer is choice D.