#Approach 1:Let's assume that actual price of the ticket = T
Conference Ticket Advance Discounts:
5-29 days in advance -> 15% Discount
Ticket price in this time window = 85 % of T
30-59 days in advance -> 30% Discount
Ticket price in this time window = 70 % of T
60-89 days in advance -> 40% Discount
Ticket price in this time window = 60% of T
Helen bought a ticket for $252. Let's say after discount she paid X % of T = 252 ----(1)
If she had bought it 1 day later, she would have paid $306.
That means, one day after, the discount slab will change and she needs pay 306 $ after discount. we can assume that Y % of T = 306----(2)
On dividing eq 1/ eq 2,
Y % of T/X % of T = 306/252
Y/X = 34/28 = 17/14
On multiplying the ratio 17/14 by a 5, it becomes Y/X = 85/70
i.e Y is 85 % and X is 70%
X % of T = 252 => 70 % of T = 252
Y % of T = 306 => 80 % of T = 306
So we can conclude that she bought the ticket 30 days in advance. That's why she got 30 % discount and she paid 70 % of ticket price.
One day after, it would be 29 days in advance and the discount will change to 15 % and she need to pay 85 % of the ticket price.
#Approach 2:Since the price change from $ 252 to $ 306 after 1 day, we can conclude the discount slab should change after 1 day.
From this conclusion, we can eliminate the options C and E as the discount % will not change even after 1 day.
Example: Option C : 59
If she bought the ticket 59 days in advance , she gets 30 % discount.
One day after that it would be 58 days in advance but discount % is same for 30-59 days in advance. So the buying price will not change even after 1 day. Hence it could be eliminated. Similarly Option E also can be eliminated.
Lets try back solving method to eliminate the other options .
If option A is the right answer, she bought the ticket 5 days in advance and paid $ 252
i.e 85 % ticket price = 252
One day after, there is no discount and she need to pay full amount of 306 $. So we need to cross check whether ticket price is 306 $ or not
85 % ticket price = 252
Ticket price = (252/85) * 100 . we can easily figure out that Ticket price is less than 300 $ ≠ 306 $ . Hence Option A is eliminated.
If option B is the right answer, she bought the ticket 30 days in advance and paid $ 252
i.e 70 % of ticket price = 252
One day after, the discount % is 15 % and she need to pay 85 % of ticket price. So we need to cross check whether 85 % of ticket price is 306 $ or not.
70 % of ticket price = 252
85 % of ticket price = (252/70)*85 = (36/10)*85 = 18 * 17 = 306
Ureeekaa!!Since the values match, Option B would be the correct answer.Thanks,
Clifin J Francis,
GMAT SME _________________