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Helen paid $252 for a conference ticket. If she had purchas

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GMAT Club Legend
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Joined: 07 Jun 2014
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Helen paid $252 for a conference ticket. If she had purchas [#permalink] New post 02 Jun 2018, 04:02
Expert's post
00:00

Question Stats:

70% (01:46) correct 30% (03:46) wrong based on 10 sessions
Conference Ticket Advance Discounts


5-29 days in advance15%
30-59 days in advance30%
60-89 days in advance40%

Helen paid $252 for a conference ticket. If she had purchased the ticket one day later, she would have paid $306. How many days in advance did she purchase the ticket?

(A) 5
(B) 30
(C) 59
(D) 60
(E) 89
[Reveal] Spoiler: OA

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Re: Helen paid $252 for a conference ticket. If she had purchas [#permalink] New post 02 Jun 2018, 05:48
Helen could have purchase the ticket in one of the three time frame allowing for discounts.

Let us check if she had purchased the ticket on 5th day prior to the conference.
she gets 15% discount from 5th to 29th day hence,
0.85x = 252; x is the original price of the conference and 252 is the amount paid by helen.
x = \(\frac{252}{0.85}\)
or, x = 296..(a non-integer value)
original price cannot have a non-integer value.

Therefore she must have bought the tickets either on 30th day or 60th day
Let us see if she had bought the ticket on 30th day.
for 30-59 days she gets 30% discount hence she pays 0.7x
or, 0.7x = 252
or, x = \(\frac{252}{0.7}\) = 360 which is a tentative original price
\(0.85*360 = 306\). If she had been late by 1 day she would have to pay 85% of the original instead of 70%.
Hence this confirms that she had bought the ticket on 30th day availing of 30% discount.
option B
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GMAT Club Legend
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Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 1659 [0], given: 396

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Re: Helen paid $252 for a conference ticket. If she had purchas [#permalink] New post 14 Jul 2018, 04:58
Expert's post
Explanation

Helen bought a ticket for $252; if she had bought it one day later, she would have paid $54 more. There are three possibilities that represent the dividing lines between the given discount levels:

Possibility 1: She bought the ticket 60 days in advance for a 40% discount (if she’d bought it one day later, or 59 days in advance, she would have received a 30% discount instead).

Possibility 2: She bought the ticket 30 days in advance for a 30% discount (if she’d bought it one day later, or 29 days in advance, she would have received a 15% discount instead).

Possibility 3: She bought the ticket 5 days in advance for a 15% discount (if she’d bought it one day later, or 4 days in advance, she would not have received any kind of discount).

This question is harder than it looks, do not calculate a percent change between $252 and $306. The discounts are percents of the full-price ticket, which is an unknown value. Call it x.

Note that the only three possible answers are 5, 30, and 60 (answers (A), (B), and (D), respectively); 59 days ahead and 89 days ahead do not represent days for which the next day (58 and 88 days ahead, respectively) results in a change in the discount.

Possibility 1 (60 days in advance): $252 would represent a 40% discount from the original price, so the original price would be $252 = 0.6x, and x would be $420.
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Re: Helen paid $252 for a conference ticket. If she had purchas   [#permalink] 14 Jul 2018, 04:58
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