The table above shows the discount structure for advanced purchase of

Question

https://gmatclub.com/forum/download/file.php?id=64239 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 2021-10-19_17-59-59.png

sanjitscorps18 · Answer

Relatively tough question!!

If the ticket is purchased on 6th, 13th or the 29th day before departure, a day later their prices would not change as the bracket of discount does not change. Considering this, we are looking at only Option B and Option D.

The passenger bought a ticket at $1,050. A day later, it would have costed $210 more.

Considering the below ranges (10% and 25%) for purchase by the customer

1. If $1,050 was bought at 10% discount the original price of ticket would be 10/9 x $1,050
Difference = 10/9 x $1,050 - $1,050 = 116
Not the discount we are looking at hence moving forward

2. If $1,050 was bought at 25% discount the original price of ticket would be 4/3 x $1,050
Price of ticket with 10% discount = 4/3 x 9/10 x $1,050 = 1260
Here 1260 - 1050 = 210

Hence, the ticket was purchased on 14th day prior to departure at $1,050 and on the 13th day it would have become $1260

IMHO it should be Option D

pleasefix · Answer

I agree with your reasoning to discard the 3 options.

However I believe your reasoning at 1. is the wrong way around. The $210 dollar is the extra discount she got, we need to compare it with the 0% discount instead of with the 25% discount.

Thus if she bought the ticket at 7 days, the original price was indeed 10/9 x $1,050 = +- 1160 . Which means her benefit of buying earlier was 10% of that (1/10)*(10/9)*1050 = +- $116.

$116 is not $210. Hence B is wrong.

Based on this you can already note D as the correct answer.

sanjitscorps18 · Answer

Totally agree !! I've edited my answer.

Fdambro294 · Answer

1 day later means she would have bought the ticket 1 day closer to departure and the price would have increased.

This price increase is equivalent to a fractional increase of:

$210 / $1050 = 21 / 105 = 3 / 15 = 1/5

1/5th increase in price.

0 to 6 days ——— 0% discount ——— P = price

7 to 14 days out ——- 10% discount ——- 90%(P)

14 to 29 days out ———25% discount ——— 75%(P)

30 days or more out ——— 40% discount ———> 60%(P)

We need to figure out which price increase is equivalent to a +(1/5)th fractional increase

From 7 to 6 days the fractional price increase is:

P - (90%P)
_________
(90% * P)

+(1/9) wrong

From 14 days out to 13 days out the fractional price increase is:

(90%X) - (75%X)
______________
(75% * X)

15%
___
75%

+(1/5) fractional price increase

She must have bought her ticket

14 days out

Posted from my mobile device

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The table above shows the discount structure for advanced purchase of

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